%\documentclass[12pt]{article} \documentclass[12pt,dvipdfmx]{article} %this version: workaround, wegen dvi problems. %make dvi (viewer crashed aber), trotzdem dann pdf mit bildern ok, %aber keine hyperrefs in pdf. % vermutlich geloest: dvipdfm --> dvipdfmx \oddsidemargin 0. true cm \topmargin -2.5 true cm \textheight 24 true cm \textwidth 16 true cm \usepackage{color} \pagecolor{white} \setcounter{secnumdepth}{3} \usepackage{times} \usepackage{longtable} \usepackage{epsf} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsmath} \usepackage{graphicx} \usepackage{epstopdf} \usepackage[unicode=true, % hypertex, % use for activating links in DVI file dvipdfmx, % use for bookmarks in final (pdf) version bookmarks=true,bookmarksnumbered=true,bookmarksopen=true, breaklinks=false,pdfborder={0 0 0},backref=false,colorlinks=true] {hyperref} \hypersetup{pdftitle={AMJUEL Documentation},linkcolor=blue, citecolor=blue, urlcolor=blue, filecolor=blue} \usepackage{bookmark} % use only together with dvipdfm option of hyperref package! \begin{document} \parindent 0pt %titelpage {\LARGE \bf \center \vspace*{3truecm} The data file AMJUEL: \\ Additional Atomic and Molecular Data for EIRENE \vspace*{3truecm} D. Reiter \\ FZJ, Forschungszentrum J\"ulich GmbH \\ 52425 J\"ulich \\ %Post-box 1917 \\ Germany \vspace{3truecm} Version: \today \vspace{1truecm} Available via E-mail from d.reiter@fz-juelich.de, or as part of the EIRENE code git-repository hosted at FZ J\"ulich } \pagenumbering{Roman} \newpage \renewcommand\thesection{\Roman{section}} \newpage \addcontentsline{toc}{section}{Table of contents} \tableofcontents %ende titelpage \newpage %\renewcommand{\thesubsection}{\thesection.\Roman{subsection}} %\renewcommand{\thesubsubsection}{\thesection.\thesubsection.\Roman{subsubsection}} \section{Introduction}\label{sec-intro} %\addcontentsline{toc}{section}{Introduction} Additional atomic data fits, read by EIRENE \subsection{Record:}\label{record} %\addcontentsline{toc}{subsection}{Record:} \begin{itemize} \item update 6.12/94 \\ Bor ionization raten H.2, 2.5B0, 2.5B1 \\ Bor rec. rates H.4, 2.3.5B0, 2.3.5B1 \\ \item update 6.4/95 \\ elast. data revised, from: elrep.dat \\ \item update 25.4/95 \\ H.9, 3.1.8 improved \\ \item update 12. 1/96 \\ Arg ionization rates H.2, 2.18B0, 2.18B1 \\ Arg rec. rates H.4, 2.3.18B0, 2.3.18B1 \\ Arg el.cool H.8, 2.18B0, 2.18B1, H.11,2.18B0\\ Be el.cool H.8, 2.4B0, 2.4B1, H.11,2.4B0\\ B el.cool H.8, 2.5B0, 2.5B1, H.11,2.5B0\\ \item update 12. 2/96 \\ N ionization rate H.2, 2.7B0 \\ \item update 7. 3/96 \\ He+ ionization rate H.4, 2.2C \\ He++ recomb. rate H.4, 2.3.2C \\ \item update 17. 8/96 \\ elast.rate H.3, 0.3T revised \item update 3. 9/96 \\ new: negative ions: H$^-$ contributions to Lyman and Balmer series\\ added: ratios H.12 7.2a, 7.2b 2.0b, 2.0c\\ added: ratios H.11 7.0 2.0a\\ Note regarding the role of vibrationally excited molecules: if H2(v) is present, then in addition to the existing processes one may have: H2(v) + e $\rightarrow$ H + H$^-$, and the H$^-$ may provide a photon (e.g., H-alpha) after mutual neutralisation with protons, or H2(v) + p $\rightarrow$ H$_2^+$ + H , and the H$_2^+$ may provide a photon (e.g., H-alpha) after dissociative recombination Hence a suggested extended procedure in the EIRENE hydrogen line emission routines (e.g. Ba\_alpha): There have been already 4 channels contributing to H-light emissions: \begin{itemize} \item 1.) proportional to H - density PDENA(..) \item 2.) proportional to H$^+$ - density DIIN(..) \item 3.) propportional to H$_2$ - density PDENM(..) \item 4.) proportional to H$_2^+$ - density PDENI(..) \end{itemize} .....................................................\\ now: we add one further channel:\\ .....................................................\\ \begin{itemize} \item 5.) proportional to H$^-$ - density PDENI(..) \end{itemize} For example the CR population coefficient H(n=3)/H$^-$ is stored in AMJUEL, H.12, 7.2a This ratio must be multiplied by the H$^-$ density and by the Einstein coefficient 4.41e7 (as in the other channels) to obtain an emissivity. Since we may not always have computed the H$^-$ density, we multiply instead by the H$_2$ density (PDENM) and by the CR-equilibrium ratio H$^-$/H$_2$ . This latter ratio is stored in AMJUEL H.11, 7.0 To account for the additional new channel producing H$_2^+$ (ion conversion) it is suggested to only replace the H$_2^+$ density (PDENI) in the line emission routines now by H$_2$ (PDENM) and by the CR equilibrium ratio: H$_2^+$/H$_2$. That CR equilibrium ratio is stored in H.12, 2.0c. This equilibrium ratio includes the above mentioned additional process leading to H$_2^+$ production. If instead the H$_2^+$ density PDENI IN EIRENE is computed only from electron impact collisions, not yet including additionally ion impact (ion conversion) collisions, then the CR equilibrium density ratio H.12, 2.0b must be retained in the line emission routines as multiplicative factor for the H$_2$ density, for consistency. \item update 6. 9/96 \\ H- cx multistep recombination, low proton energy, H.4 7.2.3a\\ H- cx multistep ionization, low proton energy, H.4 7.2.3b \item update 26.2/97 \\ Corona H-ionization rate from SOLXY: out, because: wrong, and never used anyway (i.e. H.8 2.1.5G out). \item update 18.3/97 \\ H.4 2.1.5FU, H.4 2.1.8FU (fujimoto rates) (0.1-1e3 eV) \\ H.2 3.2.3 (only slow molecules) \\ H.2 2.2.17 \item update 28.7/97 \\ H.3 3.2.3 = HYDHEL H.3 3.2.3 (vs. Ebeam and Ti) + plus slow vibr. ex. molecules\\ must be modified to account for Ebeam of vibr. excited molecules (scale cross-section). DONE: see below: 11.05.04\\ H.4 2.2.5g, as 2.2.5 but vibr. distribution of H2 molecules \item update 8.8/97 \\ H.2 2.10B0, 2.10B1 \\ H.8 2.10B0, 2.10B1 \\ H.11 2.10B0 \item update 18.8/97 \\ H.3 0.1D 0.2D, 0.3D 0.4D \\ \item update 8.9/97 \\ H.1 3.1.8R (Riviere) revised (better extrapolation to low energy) \\ H.1 3.1.8ST new (Schultz total cx cross-section) \\ H.1 3.1.8SD new (Schultz momentum transfer cross-section) \\ H.1 3.1.8 (Janev total cx cross-section, also: 3.1.8J)\\ H.1 3.1.8J2 new (Janev total cx cross-section *2 = mom trans. x-section)\\ H.1 3.1.8ST2 new (Schultz total cx cross-section *2 = mom trans. x-section)\\ note: 3.1.8SD $\approx$ 2 * 3.1.8ST within line thickness \item update 23.9/97 \\ H.2 2.6B0 strahl carbon data ionization\\ H.4 2.3.6B0 strahl carbon data recombination \\ H.4 2.6A0 ADAS carbon ionization \\ H.4 2.3.6A0 ADAS carbon recombination \\ H.10 2.6A0 ADAS carbon line radiation plus 11.3 per ionization\\ (=electron cooling rate)\\ H.10 2.3.6A0 ADAS carbon line radiation due to recombination\\ (=electron cooling rate)\\ H.12 2.6A0 ADAS carbon line radiation per ionization\\ H.12 2.3.6A0 ADAS carbon line radiation per recombination \item update 22.4/98 \\ H.2 3.1.6FJ Freeman and Jones ion impact ionization, Ebeam=0. \item update 10.10/98 \\ red. pop. coeff revised (n=2, n=3) and new ones (n=4, n=5) now all based on Sawada/Fujimoto's modifications to Johnson/Hinnov\\ H.12 2.1.5 a,b,c,d reduced pop. coeff, coupling to H ground state\\ H.12 2.1.8 a,b,c,d reduced pop. coeff, coupling to H+\\ H.12 2.2.5 a,b,c,d reduced pop. coeff, coupling to H2\\ H.12 2.2.14 a,b,c,d reduced pop. coeff, coupling to H2+\\ H.12 7.2 a,b,c,d reduced pop. coeff, coupling to H-\\ \item update 20.1/99 \\ H.12 2.2.5e Fulcher emissivity ($cm^3/s)$, coupling to H2, relative d state population amongst N=3 triplet: 2/9\\ \item update 17.2/99 \\ H.12 2.2.5g revised (because of low Te extrapolation)\\ new format for plots for H.4, h2, h2fuji, h2fuji-vibr \\ done for 2.2.5, 2.2.5g, 2.2.9, 2.2.11 \item update 10.4/99 \\ Fujimoto He-col.rad model revised.\\ Form.II ionization rate H.4 2.3.9a, done \\ elec. cooling rate H.10 2.3.9a, done \\ $\delta_E/ionis$ H.12 2.3.9a, done \\ Form.I ionization rates revised. \\ K1$\rightarrow$ K10=K1-K12-K13 \\ K2$\rightarrow$ K20=K2-K21-K23 \\ K3$\rightarrow$ K30=K3-K31-K32 \\ H.4 2.3.9b, 2.3.9c 2.3.9d redone \\ (only 2.3.9b,K10, differs from earlier version)\\ H.4 2.3.9e, 2.3.9f 2.3.9g redone \\ (only 2.3.9f,K20, differs from earlier version)\\ H.4 2.3.9h, 2.3.9i 2.3.9j redone \\ (only 2.3.9j,K30, differs from earlier version)\\ \item update 2.7/99 \\ Johnson Hinnov ionization and recombination revised.\\ all rates are now available for Ly-transparent (as in older versions) and (new) for Ly-opaque conditions. The labels for the opaque data have an additional ``o". E.g.: H.4 2.1.5 (for transparent data for effective ionization) and (new): H.4 2.1.5o (same process, but Lyman-opaque conditions). Same for: H.4 2.1.8 and (new) H.4 2.1.8o \item update 2.7/99 \\ During this update, an error in the Johnson Hinnov code was detected. It affects the rate H.10 2.1.8, at $T_e > 10 eV$. The slope of the effective electron cooling rate above this $T_e$ was too steep. H.10 2.1.8 (and, correspondingly: H.12 2.1.8) have been corrected. \item update 23.11/99 \\ H.1, 3.1.6, Freeman and Jones ion impact ionization cross-section, for beam penetration runs.\\ Figure H.12 2.2.5b corrected (was wrong figure). \item update 3.2/00 \\ new: ratio of population coeff. p(6)/p(1)\\ H.12 7.2e added \\ H.12 2.2.14e added \\ H.12 2.2.5e added. Former 2.2.5e (Fulcher emissivity) is now: 2.2.5fl\\ H.12 2.1.5e added. Former 2.1.5e (del-e) is now: 2.1.5de \\ H.12 2.1.8e added. Former 2.1.8e (del-e) is now: 2.1.8de \item update 23.5/00 \\ H.12 2.2.5fl revised: labeling of n=2 triplet levels in Sawada's code corrected. \item update 06.8/00 \\ H.2 2.26B0 and H.2 2.26B1 added (ionization rates for Iron). \item update 26.12/00 \\ H.1 (elastics: p + noble gases). \item update 21.01/01 \\ error detected in H.1, 0.3D, 0.3V and 0.4D, 0.4V, fit coefficients\\ for extrapolation wrong (different expression). Corrected.\\ H.3 (elastics: p + noble gases).\\ Figures included/redone for all elastics H.1 0.1 -- 0.8, \\ and same for H.3, $I_{0,0}$ and $I_{1,0}$ \item update 16.03/01 \\ H.10 and H.12 added for 2.3.13a (He.rec.elec.cooling rates)\\ Figures added, helraecr and helraecc \item update 1.10/01 \\ H.12 2.2.5fu added (to replace 2.2.5fl) \item update 1.11/01 \\ H.12 2.2a, 2.2b, 2.2c 2.3.2a, 2.3.2b, 2.3.2c added \\ Helium population coefficients, for states no. 6,7 and 10 \item update 8.11/01 \\ H.12 2.2c $\rightarrow$ 2.2d ,2.3.2c $\rightarrow$ 2.3.2d \\ newly included: 2.2c, 2.2e, 2.3.2c, 2.3.2e Helium population coefficients, for states no. 8 and 16 \item update 23.01/02 \\ H.0 Potentials for elastic collision processes included\\ fit-flag 01 (repulsive) and fit-flag 02 (Morse) introduced. \item update 13.03/04 \\ 3.1.8L: Langevin approximation for cx , for testing of internal consistency\\ H.1: 3.1.8L done \\ H.2: 3.1.8L done (in July 2015) \\ H.3: 3.1.8L done \\ H.8: 3.1.8L done (in Sept.2016 \\ H.9: 3.1.8L done \\ H.3: 3.1.8org: original fit from Janev's springer 1987 book\\ (only for reference purpose. don't use!) \item update 11.05/04 \\ H.11 2.0a, 2.0b redone, correct $E_{H2}=0.1$ eV\\ H.11 7.0c renamed to H.11 7.0a\\ H.12 2.0a, 2.0b and 2.0c fits and plots new, $E_{H2}=0.1$ eV\\ H.4 2.2.5r, 2.2.5d, 2.2.5i fits and plots, MAR, MAD and MAI rate coeff.\\ H.3 3.2.3 new, $E_{H2}$ consistent for all H2(v) \\ H.2 3.2.3 and 2.2.17 redone, $E_{H2}= 0.1$ \item update 18.04/05 \\ H.12 2.1.5 added: H$^+$ in Col-Rad. equil. with H$_{ground}$ atoms\\ H.12 2.1.8 added: H$_{ground}$ in Col-Rad. equil. with H$^+$ ions\\ \item update 14.02/06 \\ Strahl (ADAS89) data completed for Iron \\ H.8 2.26B0, 2.26B1, H.11 2.26B0 \item update 14.07/06 \\ H.4 7.2.3a 7.2.3b redone\\ Col rad $p + H- \rightarrow H+H$ and $\rightarrow H + p$, for $E_{H^-}=0.1$ eV\\ MAR,MAD,MAI rates via H2+, for condensed H2+, renamed from 2.2.5r,d,i to 3.2.3r,d,i \item update 14.01/07 H.10, 2.1.8-t: for comparison with ADAS PRB \\ remove $d(ln\langle sigv\rangle)/d(ln T)$ corrections in free-bound transition\\ then: good agreement with ADAS PRB found (tested for JET divertor case)\\ hence: this correction seemed to be missing in ADAS\\ Also added: H.12 2.1.8de-t, (DE per event) and figures \\ Old H.12 2.1.5t and 2.1.8t renamed into 2.1.5tot and 2.1.8tot, resp. Sept. 18: The intermediate "test fits" H.10 2.1.8-t, H.12 2-1-8de-t from 2007 removed now. \item update 07.08/07 2.1.5 H.4 and H.10 Johnson-Hinnov renamed to 2.1.5JH\\ new ``default'' is Sawada-Fujimoto: old H.4 2.1.5FU now: H.4 2.1.5\\ and H.10 2.1.5 (FU) is newly added.\\ to be done: H.12 2.1.5de (JH to be replaced by FU: H.12 2.1.5de)\\ H.4 2.1.8 already renamed to H.4 2.1.8JH, and new default is FU: H.4 2.1.8\\ to be done: H.10 2.1.8 H.12 2.1.8de (JH to be replaced by FU) \item update 17.08/07 H.0 0.100 to H.0 0.103: defaults for \\ Fokker-Planck collisions between charged particles,\\ $ee, ei, ie$, and $ii$ collisions. Fit-Flag: 03 \item update Nov. 07: introduce subsections for H.1, to order reactions according to electron impact, proton impact, He+ impact, etc.. \item update oct. 09: fit H.3: 2.1.5, for electron impact of H beam (Eb $>$ 700 eV, across cold edge (Te $<$ 1000 eV) \item update oct. 09: fit H.3: 2.3.9, for electron impact of He beam across cold edge \item update jan. 2010: \\ some text added regarding ADAS CR rates ...A0, in H.4, H.10 and H.12 \item update Mar. 2011: \\ fit H.3: 3.2.3 corrected. Was completely off. Figure was ok, i.e. bug in fit program. Newly fitted using odrpack95. \item remove blanks from parenthesis (e.g. H2(a bc) $\rightarrow$ H2(abc), for online plots under www.eirene.de) \item update Dec. 08 2011: \\ O ionisation, O+ recombination: ADAS 96, H.4 and H.10 fits added 2.8A0 and 2.3.8A0, resp. \item update Dec. 09 2011: \\ N ionisation, N+ recombination: ADAS 96, H.4 and H.10 fits added 2.7A0 and 2.3.7A0, resp. \item update July 12: \\ H.2: 3.2.3o re-introduced, for backward compatibility, i.e. $E_{H_2}=0.37$ eV, (as around year 2000) whereas now (since 2004) in H.2: 3.2.3 this energy is 0.1 eV. \item update August 12: new figures for H4: 2.2.12 and 2.2.14 (the red HYDHEL curves had been missing. Both these fits have problems below 0.1 eV. to be done.\\ reaction H.2 2.2.5 renamed to 2.2.5o (this is the old, incorrect fit from the 87 Springer book), not to be used anyway. \item update Aug. 12: \\ added H.12: 2.2.15a,..2.2.15e red. pop. coeff H(2)...,H(6) with respect to H3+, based on production of H*(n=2) via Janev, HYDHEL H.2: 2.2.15 \item update Sept.13: N,N2,N2+ corona model. \\ 1.) added H.8 and H.11 for N+e ionisation, constant electron energy loss = ionisation potential\\ 2.) revised H.8 and H.11 for Ar and C ionisation, (constant electron energy loss=ionisation potential, to derive electron cooling fits H.8 and H.11 from those for rate coefficients H.2\\ 3.) new H.2 rate coeff. added for N2 and N2+: \\ H.2 2.7.5, 2.7.9, 2.7.10, 2.7.11, 2.7.12, 2.7.15 (and 2.7.14 added Jan 2016) \\ checked: e+N ionisation. cross-section Bell and Brooks are identical. Checked: rate coefficients H.2 2.7, 2.7B0 are identical too. (hence: rate coeffs. should also be identical to open ADAS). further checks: H.4 e + N vs. H.2 e + N?? Is the ADAS corona limit correct?, see plot for H.4 rate coeff., label of red curve incorrect on this plot \item Jan 14:\\ some reaction headers edited, in H.12 (for automatic online processing) \item Jan 15:\\ electron energy loss rates for H$_2$ added: H.10 2.2.H2c (total electron cooling) and H.10 2.2.H2r (radiation energy loss rate only). Both in eV cm$^3$/s. Currently these two rates are related to processes 2.2.5 (DE) plus 2.2.9 (I), but not yet including dissociative ionization channels 2.2.10 \item April 15:\\ HYDHEL cross-section for 3.1.8 (cx) added here too (same as in hydhel.tex file)\\ This can be used for low and high E0 limit extrapolation. to be done: make H.2 rate to be used for low E0 limit extrapolation...Nov. 17 done now ! \item April 15:\\ Some header texts changed, e.g \emph{ratio} $\rightarrow$ \emph{Ratio} in H.12 headers \item June 15:\\ state notations changed for H, H2, He, to remove further blanks from parenthesis, and now also to distinguish meta-stable-resolved effective rates from single meta-stable-QSS rates. The former have an additional ``;r" in their state notation. Also paragraph headers for Trubnikov potentials (H.0) changed. \item July 15:\\ started to add H.2 rates from fits of H.3 rates for Ebeam $\rightarrow 0$ Done for 0.1, 0.2 and 0.3 elastic reactions. The low Ebeam value was found by comparing H.3 rate fits with independent integration of H.1 cross-sections at low E. Strictly: the H.3 fits should automatically become identical to the H.2 fits for low Ebeam, or EIRENE should automatically use these H.2 fits below a critical Ebeam. Similarly: H.4, such that H.2 is the correct corona limit at low densities. And also similarly: low T limit (for H.2, H.3 and H.4) should automatically turn into H.1 cross-section(E) times sqrt(E)...., or at least: threshold behaviour $1/T^2\times \exp(-\Delta E/T)$ ?? \item Oct 15:\\ Further H.2 rates added for heavy particle collisions. These H.2 rates should be scalable to the corresponding Omega integrals for continuum descriptions consistent with the kinetic formulations based on H.3 rates. done: 0.4, 0.5, 0.6, 0.7, 0.8, both: T (total) and D (diffusion) rates. \item Oct 15:\\ started to add T1MIN, T1MAX, N2MIN, N2MAX, E2MIN, E2MAX parameters for extrapolation beyond fit range. Currently all H.4 rates should have N2MIN=1.e8, and be extrapolated with these values taken also for all lower electron densities (Corona limit). In this case $ln^i(\tilde{ne})=0.0, \ i=1,2,\dots,8$, fit must reduce to H.2 format. I.e., these 9 H.2 coefficients can directly be obtained as subset of the 81 H.4 coefficients. \item Jan.16: \\ N2+ diss.rec added: rate: 2.7.14, linear on log-log scale, and hence corresponding H.1 and H.8 data follow analytically. \item May 16: \\ H.2 2.2.17s, H.4 2.2.17r and H.4 2.2.17d: effective, H- condensed, DIS, MAR, MAD rate coefficients for H2, via H2-. \item June 16: \\ H.4 2.1.5 and H.10 2.1.5 CR electron impact ionisation: fit range extended from 1e3 to 2e4 eV, new fits and figures \item Jan. 17: \\ H.11 4.0a added. Ratio of production rate constant for H3+ to destruction rate coefficient (vs.(Te)). From this ratio, by multiplying it with nH2+/ne, one finds the nH3+/nH2 ratio, when H2+ and H3+ are in equilibrium with H2. \item Jun. 17: \\ H.4 2.1.8, H.10 2.1.8 and H.12 2.1.8de redone, fit range extended from 0.1 --1e3, to 0.1..2e4, to avoid spurious recombination rates in hot core plasmas. \item Aug. 17: \\ H.1 3.1.8 and 3.1.8J2 left asympt. (al0) corrected. Slope was correct, but a small jump at E=0.1 eV. H.1 3.1.8ST and 3.1.8ST2 left asympt. added. Was missing. \item Nov. 17: \\ H.1 3.1.8 right asympt. added (taken from hydhel). Also H.2 3.1.8 added, (taken from hydhel) \item Mar. 18: \\ H.12 2.2.5fu, redone. Also: 2.2.5we and 2.2.5ly added (upper werner and lyman band states pop. coef.) \item May 18: \\ 0.13 p,d,t and 0.14 p,d.t added. H.1 and H.3 Elastic cross-sections and rate coeff. (Krstic, Schultz), taken here for vel. dep. relaxation approximation (scattering angle=pi) \item May 18: \\ H.2 3.1 added: ionisation of W, used a few years ago in a PET paper (Mekkaoui et al.) on study of plasma fluctuations on impurity penetration and cx sputtering. \end{itemize} \subsection{to be done:} %\addcontentsline{toc}{subsection}{to be done:} \begin{itemize} \item Check text in H.12, 2.2.5fl: is Aik already multiplied into this ratio fit, i.e. is this fit a ``Fulcher emission rate" (1/s), or is this factor still to be multiplied? \item Further H.2 rate fits available for heavy particle reactions, e.g. 0.5,..., 3.1.6,....still to be implemented \item Check Behringer (Strahl) database for Li ionisation and recomb... \item 2.2.14: H.2 fit made strictly linear on log-log scale, for H.1, H.2 and H.8. Then use H.2 coefficients to derive, exactly, the corresponding H.1 and H.8 coefficients. Done for H.8, 2.2.14, To be done for H.1 for this process, and also for other (probably mostly recombination) processes, e.g. 2.1.8, 2.2.15, 2.3.13, 2.7.14.... \item Aug. 17: 3.1.8 H.2, H.3 and H.9 rate coefs. must be redone, due to Aug. 17 correction of left asmpt. in cross-section. Will perhaps further improve the tracklength estim. energy balance. So far we have no 3.1.8S (Schultz) rate coeff. of any kind. \end{itemize} \newpage Additional atomic data fits, read by EIRENE Format as HYDHEL DATEN \cite{kn:Janev} or METHANE DATEN \cite{kn:Ehrhardt}. See description in HYDHEL.pdf \newpage \section{Numerical Fits to $\sigma$ and $\langle\sigma v\rangle$}\label{sec1} (See again: \cite{kn:Janev}, only slightly generalized version here:) \\ We derived numerical fits for $\sigma$ and $\langle\sigma v\rangle$ so that these processes can be evaluated easily in numerical codes and in other instances that demand simple and/or repeated evaluations. Since $\sigma$ and $\langle\sigma v\rangle$ vary over many orders of magnitude, we made polynomial fits for $\ln \sigma$ in terms of $\ln E$ and for $\ln \langle\sigma v\rangle$ in terms of $\ln T$:\\ $$\ln \sigma = \sum_{n=0}^N a_n (\ln E)^n, $$\\ $$\ln \langle\sigma v\rangle = \sum_{n=0}^N b_n (\ln T)^n, $$\\ For the electron reactions, or any process in which the projectile particle is assumed to be almost at rest relative to the Maxwellian background, $\langle\sigma v\rangle$ is essentially independent of $E$ within the range of energies considered here. A more useful fit for the heavy-particle reactions is a double polynomial fit in both E and T:\\ $$\ln \langle\sigma v\rangle = \sum_{n=0}^N\sum_{m=0}^M \alpha_{n,m}(\ln E)^m(\ln T)^n.$$ Such a fit requires a large number of coefficients in order to be accurate, but can be used for arbitrary $E$ and $T$. Analogously, a fit for the density and temperature dependent reaction rate coefficients is a double polynomial fit in both $n$ and $T$:\\ $$\ln \langle\sigma v\rangle = \sum_{n=0}^N\sum_{m=0}^M \alpha_{n,m}(\ln \tilde{n})^m(\ln T)^n.$$ Most fits in the present database with density and temperature dependence have been set up for density range $1e8 - 1e16$ cm$^{-3}$, but with the density parameter $\tilde n$ being a scaled density: $\tilde n = n/10^8$, $n$ in cm$^{-3}$. As a result, at $n = 10^8, \ln(\tilde{n}) = 0$ the 2-parametric fit collapses to a one parametric fit vs. temperature only: $$\ln \langle\sigma v\rangle(T, n\leq 10^8) = \sum_{n=0}^N \alpha_{n,0}(\ln T)^n$$ which can be taken as Corona (density independent) limit, for proper low density parameter asymptotic behaviour. Further asymptotically correct forms of these fits (at other boundaries of the parameters $E, n, T$, are described below in subsections \ref{sec1.3.1}, \ref{sec1.3.2}, etc.. for the various types of data. \subsection{Example of Use of Fits}\label{sec1.1} As an example (taken from \cite{kn:Janev}) of the use of the tables of fits for cross-sections and reaction rate coefficients consider the calculation of $\langle\sigma v\rangle$ for reaction 2.1.5, $e + H(ls) \rightarrow e + H^+ + e$. We compute\\ $$\ln \langle\sigma v\rangle = \sum_{n=0}^8 b_n(\ln T)^n$$ below for T = 10 eV using the coefficients for reaction 2.1.5 in Sect. 8.2 in \cite{kn:Janev}. In the calculation below, only six digits need to be kept for these to be nearly perfect fits (see Sect. 8.2) and the coefficients have been truncated at six digits.\\ \begin{eqnarray*} \ln \langle\sigma v\rangle & = & -3.27139e+01 \quad\quad\quad\quad \ \ + 1.35365e+01 (2.30259)\\ & & -5.73932e+00 (2.30259)^2 + 1.56315e+00 (2.30259)^3\\ & & -2.87705e-01 (2.30259)^4 + 3.48255e-02 (2.30259)^5\\ & & -2.63197e-03 (2.30259)^6 + 1.11954e-04 (2.30259)^7\\ & & -2.03914e-06 (2.30259)^8\\ \\ \ln \langle\sigma v\rangle & = & -19.07995. \end{eqnarray*} Thus,\\ $$\langle\sigma v\rangle = 5.17228e-09 \ cm^3/s.$$ \subsection{SLREAC.f: Fortran module for reading Data from AMJUEL}\label{sec1.2} %\addcontentsline{toc}{subsection}{SLREAC.f: Fortran module for reading Data from AMJUEL} Single parameter fits are identified by the character string \begin{small}\begin{verbatim} 'p0' in case of H.0 (interaction potential, or differential cross-section) 'a0' in case of H.1 (cross-section) 'b0' in case of H.2 (rate coefficient vs. T-target, E0=0.) 'e0' in case of H.5 (momentum-weighted rate coeff. vs. T-target, E0=0.) 'h0' in case of H.8 (energy-weighted rate coefficient vs. T-target, E0=0.) 'k0' in case of H.11 \end{verbatim}\end{small} Format: E20.12 Double parameter fits are identified by the character string 'Index' Data are transferred from a data file into the EIRENE code by calls to subroutine SLREAC, listed below. \begin{small}\begin{verbatim} C SUBROUTINE SLREAC (IR,FILNAM,H123,REAC,CRC) c C input C FILNAM: read a&m data from file filnam, e.g. AMJUEL, HYDHEL, METHAN, CONST c IR : store data on EIRENE array CREAC(...,...,IR) c H123 : identifyer for data type in filnam, e.g. H.1, H.2, H.3, ... c REAC : number of reaction in filnam, e.g. 2.2.5 c CRC : type of process, e.g. EI, CX, OT, etc C internal C ISW <-- H123 C IO derived from ISW, initial value of 2nd index in CREAC C output c ISWR : EIRENE flag for type of process (1,2,...7) c CREAC : EIRENE storage array for a&m data CREAC(9,0:9,IR) c MODCLF: see below c DELPOT: ionization potential (for H.10 data), c currently handled in input.f. not nice! c IFTFLG: EIRENE flag for type of fitting expression ("fit-flag=...") C DEFAULTS: =2 FOR POTENTIAL (GEN. MORSE) C =0 FOR ALL OTHERS (POLYNOMIAL, DOUBLE POLYNOMIAL) c C READ A&M DATA FROM THE FILES INTO EIRENE ARRAY CREAC C C C OUTPUT (IN COMMON COMXS): C READ DATA FROM "FILNAM" INTO ARRAY "CREAC" C DEFINE PARAMETER MODCLF(IR) (5 DIGITS NMLKJ) C FIRST DECIMAL J =1 POTENTIAL AVAILABLE C (ON CREAC(..,-1,IR)) C J =0 ELSE C SECOND DECIMAL K =1 CROSS-SECTION AVAILABLE C (ON CREAC(..,0,IR)) C K =0 ELSE C THIRD DECIMAL L =1 FOR ONE C PARAMETER E (E.G. C PROJECTILE ENERGY OR ELECTRON C DENSITY) AVAILABLE C (ON CREAC(..,1,IR)) C =2 FOR C 9 PROJECTILE ENERGIES AVAILABLE C (ON CREAC(..,J,IR),J=1,9) C =3 FOR C 9 ELECTRON DENSITIES AVAILABLE C (ON CREAC(..,J,IR),J=1,9) C L =0 ELSE C FOURTH DECIMAL M DATA FOR MOMENTUM EXCHANGE C TO BE WRITTEN C FIFTH DECIMAL N =1 DELTA E FOR ONE PARAMETER E (E.G. C PROJECTILE ENERGY OR ELECTRON C DENSITY) AVAILABLE C (ON CREAC(..,1,IR)) C =2 DELTA E FOR C 9 PROJECTILE ENERGIES AVAILABLE C (ON CREAC(..,J,IR),J=1,9) C =3 DELTA E FOR C 9 ELECTRON DENSITIES AVAILABLE C (ON CREAC(..,J,IR),J=1,9) C N =0 ELSE C USE PRECISION USE PARMMOD USE COMPRT USE COMXS USE PHOTON C current version: see EIRENE on FZJ GIT repository, under: C Eirene/file-handling/slreac.f END \end{verbatim}\end{small} \newpage \subsection{Types of data, general prescriptions}\label{sec1.3} %\addcontentsline{toc}{subsection}{Types of Data, general prescriptions} The present compilation contains data fits for atomic/molecular processes which can utilized in EIRENE runs. Fits are stored here for interaction potentials (H.0), total cross-sections (H.1), rate coefficients (H.2, H.3 and H.4) and momentum- (H.5, H.6 and H.7) and energy-weighted (H.8, H.9, H.10) rate coefficients, respectively, as well as some supplementary data fits (H.11 and H.12), often reduced population coefficients, and meant mainly for post-processing and other purposes. \setcounter{subsubsection}{-1} \subsubsection{H.0: interaction potentials}\label{sec1.3.0} %\addcontentsline{toc}{subsubsection}{H.0: interaction potentials} The classical elastic collision kinetics is determined by the interaction potential $V(r)$. In EIRENE for given (random sampling) impact parameter $b$ and relative collision energy $E_r$ (in eV) the deflection angle $\chi$ in the center of mass system is computed and the test particle velocity is then changed accordingly in the laboratory system. There are various options for potential functions $V(r)$. The potential is always in eV, and the distance $r$ (and also $b$ in EIRENE) are in (atomic) units of the Bohr radius $a_0=0.529 \times 10^{-8}$ cm. The parameter FIT-FLAG determines which particular fit expression is used for the potential. The potential $V(r)$ can be specified then by up to 9 fit coefficients $p_0,\dots,p_8$, see Section \ref{secpot}.\\ FIT-FLAG= \begin{itemize} \item [=1] purely repulsive potential: to be written \item [=2] Morse like potential:\\ \begin{equation}\nonumber V(r) = \epsilon \left[e^{2g(1-\rho)}-2 e^{g(1-\rho)}\right] \end{equation} with \begin{equation} \rho:= r/r_m \quad; \quad g:=\left\{ {g_1 \ \ \ \ \mbox{for} \ \rho < 1 \atop g_1g_2 \ \mbox{for} \ \rho \geq 1} \right. \end{equation} with the parameters:\\ $p_0=\epsilon$ (eV)\\ $p_1=g_1$\\ $p_2=g_2 $\\ $p_3=r_m $ (in units of $a_0$), the minimum of $V(r): V(r_m)=-\epsilon$\\ Derived Parameters are: \\ $p_4=r_0=r_m\left(1-\frac{\ln 2}{g_1}\right)$, the root of $V(r): V(r_0)=0$\\ $p_5=r_w=r_m\left(1+\frac{\ln 2}{g_1g_2}\right)$, the point of inflection of $V(r)$\\ $p_6$ not in use\\ $p_7 = V(r_w)=-\frac{3\epsilon}{4}$ \\ $p_8$ not in use \end{itemize} \subsubsection{H.1: cross-section vs. energy}\label{sec1.3.1} %\addcontentsline{toc}{subsubsection}{H.1: cross-section vs. energy} Fits for $\sigma (E_{lab,1}) \ [cm^2]$ Collision cross are functions of relative velocity, but, due to historic reasons in the EIRENE databases, which initially had been built on data of ref. \cite{kn:Janev}, the laboratory energy of one of the colliding particles (usually the charged particle) is used, with the second collision partner (usually the neutral particle) being at rest. I.e., $\sigma= \sigma(E_{lab,1})$. To convert to center of mass energies, or to other isotopes of the same atom, one uses $E_{lab,1} =m_1/2 \ v_1^2$ and $E_{CM} = \mu/2 \ v_{rel}^2$ with $\mu = m_1m_2/(m_1+m_2)$ being the reduced mass and $v_{rel}=|v_1-v_2|$ the relative collision velocity. Cross-sections for elastic collision processes (classical orbits) are given in this paragraph. We distinguish between total, diffusion and viscosity cross-sections, by capital letters T, D and V attached to a cross-section label. These are defined as (written here as function of relative collision velocity $v_{rel}$): A): the \textbf{``total scattering cross-section"} \begin{equation} \sigma^t(v_{rel}) = \int_0^{\pi} d\theta \frac{\partial\sigma(\theta,v_{rel})}{\partial\theta} \sin(\theta) \end{equation} where $\theta$ is the scattering angle in the center of mass frame and $d\sigma/d\theta$ is the differential scattering cross-section, which, in an EIRENE application is internally derived classically from the interaction potentials specified under H.0, with proper cut-offs at small scattering angles. B): the \textbf{``diffusion cross-section"} \begin{equation} \sigma^d(v_{rel}) = \int_0^{\pi} d\theta \frac{\partial\sigma(\theta,v_{rel})}{\partial\theta} (1-\cos(\theta)) \sin(\theta) \end{equation} in which scattering events are weighted with their momentum transfer efficiency $(1-\cos(\theta))$ C) the \textbf{``viscosity cross-section"} \begin{equation} \sigma^v(v_{rel}) = \int_0^{\pi} d\theta \frac{\partial\sigma(\theta,v_{rel})}{\partial\theta} (1-\cos^2(\theta)) \sin(\theta) \end{equation} arising in continuum descriptions of gas and plasma transport, e.g. the Chapman-Enskog expansion. \paragraph*{\textbf{Special cases, Langevin cross-section}} In some special cases the cross-section fits in polynomial form become exact, both for cross-sections and for their associated (weighted) rate coefficients. This is the case for cross-sections of the form \begin{equation} \sigma(v) = c_r v^r \ [cm^2] \end{equation} with $c_r$ a positive constant and parameter $r>-4$. An important special case is $r=-1$, the Langevin cross-section. The corresponding Maxwellian rate coefficient is \begin{equation} \langle\sigma(v) \cdot v \rangle (T) = \sqrt{\frac {2T}{m}}^{(r+1)} c_r \frac{2}{\sqrt{\pi}} \Gamma(\frac{r}{2}+2) \ [cm^3/s] \end{equation} For the Langevin cross-section, $r=-1$, this reduces simply to a constant rate coefficient: \begin{equation} \langle\sigma(v) \cdot v \rangle (T_p) = c_r \ [cm^3/s] \end{equation} Cross-sections in this present database are fitted vs. ``laboratory" collision energy $E$, rather than vs. collision velocity $v$, with $v=\mbox{cvela} \sqrt{E(eV)/m(amu)}$, the reference velocity in the EIRENE code is $\mbox{cvela} = 1.38912 e6 \ [cm/s]$ and $m$ is the mass of the charged particle, assuming the neutral particle to be at rest (not to be confused with the reduced mass $m_r$). A resulting linear fit (on log-log scale) for $\ln(\sigma(E)) = a_0 + a_1 \ln(E) $ then is: \subsubsection{H.2: rate coefficients vs. temperature (zero beam energy)}\label{sec1.3.2} %\addcontentsline{toc}{subsubsection}{H.2: rate coefficient vs. temperature (zero beam energy)} Fits for $\langle\sigma(v) \cdot v \rangle (T_p) \ [cm^3/s]$ Maxwellian rate coefficients are taken for neutral particle energy $E_0 = 0.0$ eV and for background (plasma) drift velocity ${\bf V}_p ={\bf 0}$ vs. temperature $T_p$ (electron or ion temp., resp.) of the Maxwellian $f_{maxw}(v_p,T_p)$. I.e. : $\langle\sigma v \rangle(T_p) = \int d^3v_p \ \sigma(v_{p}) \cdot v_{p} \cdot f_{maxw}({\bf v}_{p},T_p)$ The rate coefficients can be scaled to different isotopes and to finite neutral particle temperatures $T_0$ by evaluating the fits at an effective temperature $T_{eff}$ given by \begin{equation}\label{rescale} T_{eff} = \frac {m_p}{m_1} T_1 + \frac{m_p}{m_2} T_2 \end{equation} Here $m_p$ is the mass of the background particle (typically ions or electrons)) as used in calculating the rate coefficients, $m_1$ and $m_2$ are the masses of the two isotopes in the particular collision process considered, and $T_1$ and $T_2$ are their two temperatures. For electron impact collisions on heavy (neutral) particles (mass $m_1=m_0$), i.e. with $m_2 =m_p = m_e$ we have: $m_e \ll m_1$, and hence typically $T_{eff} \approx T_e = T_2$, so the re-scaling to an effective temperature is only required for heavy particle (here: ion impact) collisions. \subsubsection{H.3: rate coefficient vs. temperature and energy}\label{sec1.3.3} %\addcontentsline{toc}{subsubsection}{H.3: rate coefficient vs. temperature and energy} Beam-Maxwellian rate coefficients. These coefficients are generalisations of the H.2 (isotropic) Maxwellian rate coefficients and account for either a finite velocity (energy $E_0$) of the test particle (or beam) or a fluid drift ${\bf V_p}$ in the Maxwellian background, or both. Beam-Maxwellian rate coefficients with drifting Maxwellians $f_{maxw}(T_p,V_p)$ of the background particles $``p"$, with temperature $T_p$ of the Maxwellian and with $|{\bf V_p}|= V_p$ can be evaluated in the rest frame of the background $``p"$, i.e. with the beam energy parameter re-defined as \begin{equation}\label{E0rest} \widetilde{E}_0=m_0/2|{\bf V_0}-{\bf V_p}|^2 \end{equation} These rate coefficients are therefore fits with two independent parameters, and averaging is over an isotropic (stationary) Maxwellian: Fits are for $\langle\sigma \cdot v_{rel} \rangle (E_0,T_p) \ [cm^3/s]$ The fit expression is a double polynomial of order 8 in each of the independent variables $E_0$ and $T_p$. The fitted expression is $\ln\langle\sigma \cdot v_{rel} \rangle (\ln{E_0},\ln{T_p})$. Note that the role of the beam particle is now reversed as compared to that of cross-section data, the energy parameter is now the energy of the mono-energetic (neutral) particle beam (with mass $m_0$), which is traveling in a host medium of (charged) particles $``p"$, mass $m_p$, with stationary Maxwellian distribution and temperature $T_p$. \subsubsection{H.4: rate coefficient vs. temperature and density}\label{sec1.3.4} %\addcontentsline{toc}{subsubsection}{H.4: rate coefficient vs. temperature and density} Fits for $\langle\sigma \cdot v_{rel} \rangle (n_p,T_p) \ [cm^3/s]$ Same expression of fit as for Beam-Maxwellian rate coefficients, but with beam energy $E_0$ (eV) replaced by density $n_p$. I.e. these rates are given for a fixed energy of the ``beam-particle'', typically $E_0=0.0$ eV, but a density dependence arises due to multiple (ladder-like) processes involved in one ``effective step". For historic reasons and to preserve backward compatibility, the density $n_p$ in this fit must be given in units of $10^8 \ cm^{-3}$, i.e., with density given in $cm^{-3}$ and the numerical value then divided by $10^8$, or density given in $m^{-3}$ and then divided by $100^3 \times 10^8 = 10^{14}$. \paragraph{Asymptotical behaviour, density parameter} Unless otherwise stated the valid range of the scaled density $\ln(\tilde n) = \ln (n/10^8)$ ranges from $\ln(\tilde n) = \ln(1.0) = 0.0$ (at $n=10^8 \, cm^{-3}$) to $\ln(\tilde n) = \ln(10^8) = 8 \ln(10) \approx 18.421$ (at $n=10^{16} \, cm^{-3}$). Rescaling the fit expression to a density parameter $\hat n = 1/b \ln(n/10^8)$ with $b = 8 \ln(10)$ brings the validity range $[10^8 ,10^{16}]$ of the density parameter $n$ $\, [cm^{-3}]$ to the interval $[0, 1]$ for the scaled density parameter $\hat n$. At these boundaries for the scaled density parameter the collisional radiative rate coefficients become density independent (Corona and LTE conditions, respectively). The fit expression (see \ref{sec1}) $$\ln \langle\sigma v\rangle = \sum_{n=0}^N\sum_{m=0}^M \alpha_{n,m}(\ln \tilde{n})^m(\ln T)^n $$ then becomes $$\ln \langle\sigma v\rangle = \sum_{n=0}^N\sum_{m=0}^M \hat\alpha_{n,m}(\hat{n})^m(\ln T)^n $$ with $ \hat\alpha_{n,m} = b^n \alpha_{n,m}$. At the validity boundaries $\hat n =0$ and $\hat n =1$ this expression collapses to the correct limiting single parameter fits for the temperature dependence: $$\ln \langle\sigma v\rangle = \sum_{n=0}^N\hat\alpha_{n,0}(\ln T)^n $$ at $ n\leq 10^8 \, cm^{-3}$) and $$\ln \langle\sigma v\rangle = \sum_{n=0}^N\hat\beta_{n}(\ln T)^n $$ at $ n \geq 10^{16} \, cm^{-3}$) with $\hat\beta_{n} = \sum_{m=0}^M \hat\alpha_{n,m}$ The range between the density independent Corona and LTE limits, taken here to be $[10^8 ,10^{16}]$, is representative for most relvant applications of EIRENE, but stricktly is also temperature dependent. The range should be made wider (on both boundaries) at lower temperatures (below a few eV) and shrinks (at both boundaries) at higher temperatures. Therefore the density parameter $\hat n$ in the fit might better be made temperature dependent, e.g. as $\hat n = b \ln(a n)/ln(T)$, analogous as for the energy parameter in H.3 fits, see \ref{sec1.3.3}. \paragraph{Asymptotical behaviour, temperature parameter} to be written \subsubsection{H.5: momentum-weighted rates vs. temperature}\label{sec1.3.5} %\addcontentsline{toc}{subsubsection}{H.5: momentum-weighted rates vs. temperature} currently not in use. Probably for electron-neutral friction vs. $T_e$, Omega integrals, etc.. \subsubsection{H.6: momentum-weighted rates vs. temperature and energy}\label{sec1.3.6} %\addcontentsline{toc}{subsubsection}{H.6: momentum-weighted rates vs. temperature and energy} This section contains reaction rates for track-length estimators for momentum sources (EIRENE, options {\tt IESTM=2}). The momentum exchange in a collision of a test particle, subscript $0$ and another (e.g. plasma) particle, subscript $p$, is: \begin{equation} \Delta {\bf P}_0 = m_0 \cdot \left({\bf v}_0-{\bf v}'_0\right) = \mu (1-\cos(\theta)) \left({\bf v}_0-{\bf v}_p\right) \end{equation} with ${\bf v}_0', \mu, \theta$ being the post collision test particle velocity, the reduced mass and the scattering angle in the center of mass frame, respectively. The second equality follows from momentum conservation and the additional assumption that no internal energy is transferred during the collision (i.e., elastic, or resonant ($v_0'=v_p , v_p'=v_0$) charge exchange). Also here: $m_0 = m_0'$ and $m_p = m_p'$. Generalizations to un-symmetric resonant charge exchange are discussed below. \paragraph{Stationary Maxwellian background} \addcontentsline{toc}{paragraph}{Maxwellian background} The rate coefficient of momentum transfer from a single test particle, with velocity ${\bf v_0}$ and energy $E_0$ to the thermal (stationary) plasma background (temperature $T_p$) is \begin{eqnarray}\label{mom-tally} {\bf sm}_0=\langle\sigma\cdot v_{rel}\cdot \Delta {\bf P}_0\rangle(E_0,T_p)&=& \langle\sigma\cdot v_{rel} \cdot \left({\bf v}_0-{\bf v}'_0\right)\cdot m_0\rangle(E_0,T_p)\\\nonumber &=& {\bf e}_0 \ \mu\sqrt{\frac{2T_p}{m_p}}\cdot\left[I^{(1)}_{1)}(E_0,T_p)- \frac{1}{2}\sqrt{\frac{m_0\cdot T_p}{m_p\cdot E_0}}I^{(1)}_{0)}(E_0,T_p)\right] \end{eqnarray} where $\langle \cdots \rangle$ denotes averaging over the stationary Maxwellian distribution for ion velocities (plasma background) $f_{maxw}(v_p,T_p)$;\\ ${\bf e}_0 = {\bf v}_0/v_0$ the speed unit vector in the direction of the test particle flight. Due to symmetry (isotropy) of the background velocity distribution and averaging over this distribution, momentum can be transferred to/from test particles (and hence also to/from bulk (plasma) particles) only in the direction of test particle flight.\\ $\sigma(v_{rel})$ and $v_{rel}$ are the collision cross-section and the relative velocity of colliding particles $v_{rel}=|{\bf v}_0 - {\bf v}_p|$, respectively;\\ $T_p$ and $E_0$ is the plasma temperature and the test particle (beam) energy, respectively;\\ $m_p$ and $m_0$ is the mass of the plasma particle and the test particle, respectively;\\ $\mu=(m_p\cdot m_0)/(m_p+m_0)$ is the reduced mass;\\ ${\bf v}_0$ and ${\bf v}'_0$ is the velocity of the test particle before and after collision, respectively;\\ $I^{(l,n)}(E_0,T_p)$ is the generalized Beam-Maxwellian collision integral introduced in \cite{kn:Reiter-Janev}. $l=0$ stands for using the total collision cross-section $\sigma^t(v_{rel}) = \int d\theta \sin(\theta) \ d\sigma(v_{rel},\theta)/d\theta$, here $d\sigma/d\theta$ denotes the differential scattering cross-section and $\theta$ is the scattering angle. The superscript $l=1,2...$ stands for momentum transfer, viscosity, ... cross-sections, respectively, \begin{equation} \sigma^l(v_{rel}) = \int d\theta \sin(\theta) \ d\sigma(v_{rel},\theta)/d\theta \cdot [1-cos^l(\theta)], l=1,2,.... \end{equation} After averaging the momentum exchange rate coefficient once again, this time over the test particle velocity distribution $f_0({\bf v}_0)$, the resulting momentum transfer rate becomes a vector in the direction of ${\bf V}_0 = \int d^3v_0 {\bf v}_0f_0({\bf v}_0)$, i.e. in the direction of the mean test particle (flow) speed: \begin{equation} {\bf Sm}_0(f_0,T_p) =\langle\langle \sigma\cdot v_{rel}\cdot \Delta {\bf P}_0\rangle\rangle(f_0,T_p) \end{equation} and we see that this rate vanishes for isotropic distributions $f_0$, simply already because of ${\bf V_0} = 0$. \\ \paragraph{drifting Maxwellian background} \addcontentsline{toc}{paragraph}{drifting Maxwellian background} We now turn to momentum exchange rates between the test particle community, subscript $0$ and a background (plasma), subscript $p$. As discussed already for general Beam-Maxwellian rate coefficients, paragraph H.3, in a first step we transform to the rest frame of the plasma: \begin{equation} {\bf V}_p=\int d^3v_p {\bf v}_p f({\bf v}_p) ; \quad \widetilde{{\bf v}}_0= {\bf v}_0 - {\bf V}_p ; \quad \widetilde{E}_0=\frac{m_0}{2} \widetilde{v}_0^2 ; \quad \widetilde{{\bf V}}_0= {\bf V}_0 - {\bf V}_p \end{equation} where $\widetilde{{\bf v}}_0$ is the test particle velocity in the rest frame of the plasma and $\widetilde{E}_0$ is the corresponding energy, Eq. (\ref{E0rest}). Momentum transfer from a single test particle to a drifting Maxwellian plasma background is then in the direction $\widetilde{{\bf e}}_0=\widetilde{{\bf v}}_0/\widetilde{v_0}$ The vector $\widetilde{{\bf V}}_0$ is the average (macroscopic) test particle flow velocity in the rest frame of the plasma; The total rate of momentum transfer from the entire test particle community $``0"$ to the (drifting Maxwellian) background community $``p"$ is a vector in this direction $\widetilde{{\bf E}}_0 = \widetilde{{\bf V}}_0/\widetilde{V}_0$.\\ \textcolor[rgb]{1.00,0.00,0.00}{\textbf{From here on: to be re-written, below: old text from Vlad....}} Parallel momentum transfer rate (momentum {\em loss} for the background (plasma)): $$ {\bf Sm}^i_{mu_\parallel}= {\bf b} \left(\widetilde{{\bf e}}_{mom}{\bf\cdot}{\bf b}\right) \left<\sigma\cdot v_r\cdot p\right> \left(\widetilde{E}_0 ,T_p\right) $$ Where\\ ${\bf V}^L_t$ and ${\bf V}_{dr}$ is the test particle velocity in laboratory frame and the plasma drift velocity;\\ ${\bf b}$ is the magnetic field unit vector.\\ The final rate is in laboratory frame.\\ The programming realization can be found in EIRENE in {\tt volume-processes/fpatha.f, fpathm.f} and {\tt couple\_Tria\_new/uptcop.f} The rates in the present database have been calculated for hydrogen atoms ($m_0=1$ amu) in a hydrogen ion background ($m_p=1$ amu). The mass rescaling is the following. If $\sigma=\sigma(V_r)$ then $I^{(l,n)}=F\left(\frac{E}{m_t}\right),\frac{T}{m_p})$ and $$\left<\sigma\cdot v_r\cdot p\right>(E,T)=\frac{m^n_r}{m^o_r} \left<\sigma\cdot v_r\cdot p\right>(\frac{m^o_t}{m^n_t}E,\frac{m^o_p}{m^n_p}T)$$ This kind of rescaling is applied for charge exchange, see {\tt volume-processes/xstcx.f}. If $\sigma=\sigma(E_r)$ then $I^{l,n}=\frac{1}{\sqrt{m_r}}F\left(\frac{m_r}{m_p}T, \frac{m_r}{m_t}E\right)$ and $$\left<\sigma\cdot v_r\cdot p\right>=\left<\sigma\cdot v_r\cdot p\right>\left(\frac{m^n_r\cdot m^o_p}{m^o_r\cdot m^n_p}T,\frac{m^n_r\cdot m^o_t}{m^o_r\cdot m^n_t}E\right)$$ This rescaling is used for elastic collisions according to~\cite{kn:OakRidge}, see {\tt volume-processes/xstel.f}. Here superscript "o" means the masses for those the fitting was calculated, and "n" means real masses. The rate 0.3 (elastic $p+H_2$ collisions) from this set was successfully compared with the same sources, calculated by collisional estimator. The same test for the resonant CX rates 3.1.8 {\em was not yet successful} \subsubsection{H.7: momentum-weighted rates vs. temperature and density}\label{sec1.3.7} %\addcontentsline{toc}{subsubsection}{H.7: momentum-weighted rates vs. temperature and density} \subsubsection{H.8: energy-weighted rates vs. temperature}\label{sec1.3.8} %\addcontentsline{toc}{subsubsection}{H.8: energy-weighted rates vs. temperature} Under label H.8 energy-weighted rate coefficients are stored, vs. temperature (eV) of the Maxwellian electron or heavy particle distributions. (E.g., unless otherwise stated, these rates are taken for test particles at rest: $E_0 \approx 0.0 eV$). The general relation between the energy-weighted rate coefficients H.8 and the ``ordinary" rate coefficients H.2 is (integration by parts): \begin{equation} H.8 [eV cm^3/s]= kT \times H.2 \times \left[3/2+\frac{d \ln(H.2)}{d \ln T}\right] \end{equation} with rate coefficient H.2 in $cm^3/s$. If the H.2 rate coefficients are fitted as: \begin{equation} \ln(H.2) = \sum_{i=0}^8 b_i \ln^i(T) \end{equation} then \begin{equation} \frac{d \ln(H.2)}{d \ln T}= \sum_{i=0}^7 b_{i+1} (i+1) \ln^i(T) = b_1 + 2b_2 \ln(T) + 3b_3 \ln^2(T) + .... \end{equation} and hence, for the H.8 coefficient, in the same fit format as for the H.2 coefficient: \begin{equation} \ln(H.8) = \ln(kT) + \ln(H.2) + \ln(3/2 + b_1 + 2b_2 \ln(T) - ....) \end{equation} If a H.2 rate coefficient is linear on a log-log scale, as e.g. often the case for recombination processes, then $b_2 =b_3 =....=b_8 = 0$, and hence, for the fit coefficients of the corresponding H.8 rate coefficient: $h_0=b_0 + \ln [3/2 + b_1], h_1=b_1+1, h_2 = h_3 = ....=h_8 = 0$ An explicit numerical example is detailed under H.8 2.2.14 (dissociative combination of $H_2^+(v)$ molecular ions). \subsubsection{H.9: energy-weighted rates vs. temperature and energy}\label{sec1.3.9} %\addcontentsline{toc}{subsubsection}{H.9: energy-weighted rates vs. temperature and energy} \subsubsection{H.10: energy-weighted rates vs. temperature and density}\label{sec1.3.10} %\addcontentsline{toc}{subsubsection}{H.10: energy-weighted rates vs. temperature and density} Fits for $\langle\sigma \cdot v \cdot E \rangle (n_e,T) \ [cm^3/s \cdot eV]$ The units of $T$ and $n$ in the fits are the same as for H.4 and H.7 rates. $E$ is the total energy loss for the electron or ion gas per collision event, in eV. These rates, therefore, if multiplied by the electron charge 1.6022 10$^{-19}$, are electron- or ion energy loss rates in Watt/cm$^3$. Unless otherwise noted these are total energy loss rate coefficients associated with the particular process or set of processes. If such a process is an ``effective process", implicitly including fast transitions between excited states of particles which are considered to be in a certain (collisional radiative) equilibrium, then these total effective rates include also line- (bound-bound) and continuum (free-bound) radiation losses, kinetic energy of products (e.g. in case of dissociation processes) and internal (potential) energy differences between pre- and post-collision particles, but {\bf not} bremsstrahlung (free-free) losses. If the potential energy difference in a particular collision process is negative, as, e.g., in recombination processes or in electron impact de-excitation of meta-stables to a lower level, then this total energy loss rate may become negative, for some values of the parameters, and remain positive for others. I.e., the coefficients may change sign within the parameter range covered by the fit. The fits in this database are, however, often given for the logarithm of the rate coefficient. In such cases we have subtracted the (negative) potential energy contribution from these coefficients before fitting. More generally, the fitted coefficients, therefore, read: $\langle\sigma \cdot v \cdot E \rangle_{fit} = \langle\sigma \cdot v \cdot E \rangle - \Delta E_{subtr.} \langle\sigma \cdot v \rangle$ with $\Delta E_{subtr.} $ specified for each particular rate coefficient below, together with the fitting coefficients. By default we have chosen $\Delta E_{subtr.} = 0.$ in this expression for all processes in which the potential energy is enhanced (``sub-elastic" processes, such as ionization, excitation). For the opposite case (recombination, collisional de-excitation, i.e., ``super-elastic" processes, we have chosen $\Delta E_{subtr.} = \Delta E_{pot}$ One can show with some boring algebra on the matrices which arise in collisional radiative models that with this particular choice of the subtracted energy loss rate for collisional radiative electron cooling rates the remaining fitted expression $\langle\sigma \cdot v \cdot E \rangle_{fit}$ turns out to be exactly the radiation energy loss rate associated with a particular process or set of processes. In other words: the total effective electron cooling rate is the sum of the effective radiation energy loss rate plus the effective potential energy loss rate, however, with the latter rate being simply given as $\langle\sigma \cdot v \cdot \Delta E_{pot} \rangle_{effective} = \Delta E_{pot} \cdot \langle\sigma \cdot v \rangle_{effective}$ In this expression $\langle\sigma \cdot v \rangle_{effective}$ is just the effective rate coefficient for the process under consideration, i.e. the coefficient for the same process as given in section H.4. \\ \textbf{Note:} Electron cooling rate coefficients (as well as radiation rate coefficients) are physically related to a particular species, not necessarily to a particular process. E.g. electron cooling and radiation rates for $H_2$ molecules correspond to electron collisions on $H_2$ and are therefore not related to either dissociative excitation, dissociative ionization or ionization of that molecule individually, but only to the (weighted) sum of these three channels. Similarly, electron cooling rates associated with a Helium atom, if meta-stables He atoms are retained explicitly in the transport equations, are related to a weighted sum of excitation, de-excitation and ionization processes from a particular meta-stable state, but not to these individual processes. \newpage \subsubsection{H.11: other data, e.g. reduced population coefficients}\label{sec1.3.11} %\addcontentsline{toc}{subsubsection}{H.11: other data, e.g. reduced population coefficients} single parameter fit for any other data, e.g. to be used in special user supplied programs, i.e. not generally understood by EIRENE, but can be used in problem specific ``..USR" routines of EIRENE, e.g. for post processing. The data fitted in H.11 are, therefore, typically not rate-coefficients, but often (not always) ratios between two single parameter rate coefficients. This comprises data derived from CR models, such as reduced population coefficients, or QSS equilibrium density ratios. Typically the density ratios $A/B$ are distinguished by the formation process of species $B$, from species $A$: \begin{equation}\label{eq.20} n_A \langle \sigma v; A \rightarrow B\rangle(T) = n_B \langle \sigma v; B_{loss}\rangle(T) \rightarrow n_B/n_A = \frac{\langle \sigma v; A \rightarrow B\rangle(T)}{\langle \sigma v; B_{loss}\rangle(T)} \end{equation} Also reduced population coefficients are such density ratios, however the production of upper level $B$ may result from various multi-step processes, all starting from (``coupled to") $A$. \subsubsection{H.12: other data, e.g. reduced population coefficients}\label{sec1.3.12} %\addcontentsline{toc}{subsubsection}{H.12: other data, e.g. reduced population coefficients} double parameter fit for any other data, e.g. to be used in special user supplied programs, i.e. not generally understood by EIRENE, but can be used in problem specific ``..USR" routines of EIRENE, e.g. for post processing. The data fitted in H.12 are, therefore, typically not rate-coefficients, but often (not always) ratios between two rate coefficients, see (\ref{eq.20}). The double parameter fit data in the present paragraph result if at least one of the two involved rate coefficients have a density dependence in addition to the temperature dependence. Exceptions exist, where a hard-wired reading of data from this section is coded into EIRENE: these are the reduced population coefficients for hydrogenic plasmas, i.e. 2.1.5a,....2.1.5e, 2.2.5a, 2.2.5e, etc... are currently automatically read in EIRENE post processing routines in code section ``output", routines: Ba$\_$alpha, Ly$\_$alpha, Ba$\_$beta, Ba$\_$gamma, Ba$\_$gamma,.. \subsection{End of preface} %\addcontentsline{toc}{subsection}{End of preface. EIRENE starts to read here} This next string is searched by EIRENE in subroutine SLREAC to initialize search for a particular set of fit coefficients. From here on, a character string \textbf{`H.n'} , n an integer, must only appear in the section title, but not in the text. Likewise: identifiers p0, a0, b0, ....,h0, k0 are used in SLREAC and must not appear in the text elsewhere, from here on. \bigskip \begin{small}\begin{verbatim} ........................................... . . . ##BEGIN DATA HERE## . . . ........................................... \end{verbatim}\end{small} \newpage % to make sure that bookmarks stay correct in pdf: % due to roman and arabic section numbering otherwise section1 would be there twice. % and pdf viewer gets confused. \renewcommand{\theHsection}{arabicsection.\thesection} \renewcommand\thesection{\arabic{section}} %\renewcommand{\thesection}{\arabic{section}} %\renewcommand{\thesubsection}{\thesection.\arabic{subsection}} %\renewcommand{\thesubsubsection}{\thesection.\thesubsection.\arabic{subsubsection}} \pagenumbering{arabic} \setcounter{section}{-1} \section{H.0 : Fits for Potentials}\label{secpot} \subsection{ Reaction 0.1T $ p + H(1s) \rightarrow p + H(1s) $ potential, binary elastic } This potential is not yet implemented here. It is still explicitly programmed in EIRENE, elastics.f. It is the first repulsive $H_2^+$ potential. \begin{small}\begin{verbatim} fit-flag 01 p0 0.000000000000D+00 p1 0.000000000000D+00 p2 0.000000000000D+00 p3 0.000000000000D+00 p4 0.000000000000D+00 p5 0.000000000000D+00 p6 0.000000000000D+00 p7 0.000000000000D+00 p8 0.000000000000D+00 \end{verbatim}\end{small} \newpage \subsection{ Reaction 0.2T $ p + He(1s^21S) \rightarrow p + He(1s^21S) $ potential, binary elastic} Morse potential, see \cite{kn:Bachmann} \begin{small}\begin{verbatim} fit-flag 02 p0 2.000000000000D+00 p1 2.200000000000D+00 p2 0.850000000000D+00 p3 1.455600000000D+00 p4 0.996990000000D+00 p5 1.995150000000D+00 p6 0.000000000000D+00 p7 -1.500000000000D+00 p8 0.000000000000D+00 \end{verbatim}\end{small} \newpage \subsection{ Reaction 0.3T $p + H_2 \rightarrow p + H_2 $ potential, binary elastic } Morse potential, see \cite{kn:Bachmann} \begin{small}\begin{verbatim} fit-flag 02 p0 2.700000000000D+00 p1 3.000000000000D+00 p2 1.000000000000D+00 p3 2.835500000000D+00 p4 2.180380000000D+00 p5 3.490687000000D+00 p6 0.000000000000D+00 p7 -2.025000000000D+00 p8 0.000000000000D+00 \end{verbatim}\end{small} \newpage \subsection{ Reaction 0.4T $ He^+ + He \rightarrow He^+ + He $ potential, binary elastic } Morse potential, see \cite{kn:Bachmann} \begin{small}\begin{verbatim} fit-flag 02 p0 2.550000000000D+00 p1 2.350000000000D+00 p2 0.900000000000D+00 p3 1.984200000000D+00 p4 1.399080000000D+00 p5 2.634500000000D+00 p6 0.000000000000D+00 p7 -1.912500000000D+00 p8 0.000000000000D+00 \end{verbatim}\end{small} \newpage \subsection{ Reaction 0.5T $ p + Ne \rightarrow p + Ne $ potential, binary elastic } \begin{small}\begin{verbatim} fit-flag 02 p0 2.280000000000D+00 p1 2.680000000000D+00 p2 0.850000000000D+00 p3 1.870900000000D+00 p4 1.387000000000D+00 p5 2.440200000000D+00 p6 0.000000000000D+00 p7 -1.710000000000D+00 p8 0.000000000000D+00 \end{verbatim}\end{small} \newpage \subsection{ Reaction 0.6T $ p + Ar \rightarrow p + Ar $ potential, binary elastic } \begin{small}\begin{verbatim} fit-flag 02 p0 4.040000000000D+00 p1 2.500000000000D+00 p2 0.860000000000D+00 p3 2.475600000000D+00 p4 1.789200000000D+00 p5 3.273700000000D+00 p6 0.000000000000D+00 p7 -3.030000000000D+00 p8 0.000000000000D+00 \end{verbatim}\end{small} \newpage \subsection{ Reaction 0.7T $ p + Kr \rightarrow p + Kr $ potential, binary elastic } \begin{small}\begin{verbatim} fit-flag 02 p0 4.450000000000D+00 p1 2.500000000000D+00 p2 0.800000000000D+00 p3 2.777900000000D+00 p4 2.007700000000D+00 p5 3.740600000000D+00 p6 0.000000000000D+00 p7 -3.337500000000D+00 p8 0.000000000000D+00 \end{verbatim}\end{small} \newpage \subsection{ Reaction 0.8T $ p + Xe \rightarrow p + Xe $ potential, binary elastic } \begin{small}\begin{verbatim} fit-flag 02 p0 6.750000000000D+00 p1 3.800000000000D+00 p2 1.080000000000D+00 p3 3.288200000000D+00 p4 2.688400000000D+00 p5 3.843600000000D+00 p6 0.000000000000D+00 p7 -5.062500000000D+00 p8 0.000000000000D+00 \end{verbatim}\end{small} \newpage \subsection{Reaction 0.13p $ p + Be \rightarrow p + Be $ potential } Default: scattering by angle PI in CM system (strong collision) \begin{small}\begin{verbatim} fit-flag 1 p0 -1.000000000000D+00 p1 -1.000000000000D+00 p2 -1.000000000000D+00 p3 -1.000000000000D+00 p4 -1.000000000000D+00 p5 -1.000000000000D+00 p6 -1.000000000000D+00 p7 -1.000000000000D+00 p8 -1.000000000000D+00 \end{verbatim}\end{small} \subsection{Reaction 0.14p $ p + C \rightarrow p + C $ potential } Default: scattering by angle PI in CM system (strong collision) \begin{small}\begin{verbatim} fit-flag 1 p0 -1.000000000000D+00 p1 -1.000000000000D+00 p2 -1.000000000000D+00 p3 -1.000000000000D+00 p4 -1.000000000000D+00 p5 -1.000000000000D+00 p6 -1.000000000000D+00 p7 -1.000000000000D+00 p8 -1.000000000000D+00 \end{verbatim}\end{small} \newpage \subsection{Coulomb collisions (not ready)} \subsubsection{ Reaction 0.100 $ e + e_b \rightarrow e + e_b$ Trubnikov potential} bulk-electrons on test-electron, Fokker-Planck elastic \\ Data for Trubnikov Potentials for Fokker-Planck collision operator, bulk-electrons on test-electrons. currently: none \begin{small}\begin{verbatim} fit-flag 03 p0 0.000000000000D+00 p1 0.000000000000D+00 p2 0.000000000000D+00 p3 0.000000000000D+00 p4 0.000000000000D+00 p5 0.000000000000D+00 p6 0.000000000000D+00 p7 0.000000000000D+00 p8 0.000000000000D+00 \end{verbatim}\end{small} \subsection{ Reaction 0.101 $ i + e_b \rightarrow i + e_b$ Trubnikov potential} bulk-electrons + test-ions, Fokker-Planck elastic \\ Data for Trubnikov Potentials for Fokker-Planck collision operator, bulk-electrons on test-ions. currently: none \begin{small}\begin{verbatim} fit-flag 03 p0 0.000000000000D+00 p1 0.000000000000D+00 p2 0.000000000000D+00 p3 0.000000000000D+00 p4 0.000000000000D+00 p5 0.000000000000D+00 p6 0.000000000000D+00 p7 0.000000000000D+00 p8 0.000000000000D+00 \end{verbatim}\end{small} \subsection{ Reaction 0.102 $ e + i_b \rightarrow e + i_b$ Trubnikov potential} bulk-ions on test-electron, Fokker-Planck elastic \\ Data for Trubnikov Potentials for Fokker-Planck collision operator, bulk-ions on test-electrons. currently: none \begin{small}\begin{verbatim} fit-flag 03 p0 0.000000000000D+00 p1 0.000000000000D+00 p2 0.000000000000D+00 p3 0.000000000000D+00 p4 0.000000000000D+00 p5 0.000000000000D+00 p6 0.000000000000D+00 p7 0.000000000000D+00 p8 0.000000000000D+00 \end{verbatim}\end{small} \subsection{ Reaction 0.103 $ i + i_b \rightarrow i + i_b$ Trubnikov potential} bulk-ions + test-ions, Fokker-Planck elastic \\ Data for Trubnikov Potentials for Fokker-Planck collision operator, bulk-ions on test-ions. currently: none \begin{small}\begin{verbatim} fit-flag 03 p0 0.000000000000D+00 p1 0.000000000000D+00 p2 0.000000000000D+00 p3 0.000000000000D+00 p4 0.000000000000D+00 p5 0.000000000000D+00 p6 0.000000000000D+00 p7 0.000000000000D+00 p8 0.000000000000D+00 \end{verbatim}\end{small} \newpage \section{H.1 : Fits for \ $\sigma(E_{lab})$}\label{sect1} \subsection{electron impact processes} \subsubsection{ Reaction 2.2.5org $ e + H_2(X_g^+S) \rightarrow . . . \rightarrow e + H(1s) + H(1s) $ } Fit as given in monograph \cite{kn:Janev}, repeated here only for reference purposes. EIRENE uses in its default database the corresponding fit as given in the unpublished preprint for \cite{kn:Janev}. This latter fit seems to be more plausible and has been put into the file HYDHEL. It is therefore recommended to read these fit coefficients from the database HYDHEL, and not from here (AMJUEL). \begin{displaymath} e + H_2(X_g^+ S) \rightarrow e + H(b^3\Sigma^+_u , a^3\Sigma^+_g, c^3\Pi_u) \rightarrow e + H(1s) + H(1s) \end{displaymath} \begin{small}\begin{verbatim} a0 -2.297914361380e+05 a1 5.303988579693e+05 a2 -5.316636672593e+05 a3 3.022690779470e+05 a4 -1.066224144320e+05 a5 2.389841369114e+04 a6 -3.324526406357e+03 a7 2.624761592546e+02 a8 -9.006246604428e+00 Eth 8.5 Emin 1.08e+01 s(Emin) 1.00e-19 smax 2.92e-17 Error 5.62e-01 \end{verbatim}\end{small} \newpage This page is intentionally left blank \newpage \subsubsection{ Reaction 2.2.14 $ e + H_2^+(v) \rightarrow H(1s) + H(n), (v=0\ldots 9, n\geq 2)$} EIRENE uses in its default database the corresponding fit from \cite{kn:Janev}, but with all fit coefficients except the first two being set to zero, i.e. a linear fit on a log-log scale. This latter fit seems to be more plausible. It is therefore recommended to read these fit coefficients from the present database AMJUEL, and not from HYDHEL. \begin{small}\begin{verbatim} a0 -3.479249259777e+01 a1 -1.103564847459e+00 a2 0.000000000000e+00 a3 0.000000000000e+00 a4 0.000000000000e+00 a5 0.000000000000e+00 a6 0.000000000000e+00 a7 0.000000000000e+00 a8 0.000000000000e+00 Emin 1.00e-01 s(Emin) 9.85e-15 smax 9.85e-15 Error 1.74e-25 Eth 0.0 Mcross 9.1093826E-31 \end{verbatim}\end{small} \newpage \subsection{proton impact collisions}\label{sect1.1} \bigskip Elastic collisions between neutral and charged particles, Bachmann/Reiter (\cite{kn:Bachmann}) cross-sections as function of $E_{lab}$, $E_{lab} = (m_{lab}/2) \cdot v^2$ $m_{lab}$ is the ion mass throughout. ``T" stands for ``total" cross-section (obtained with cut off at impact parameter such that diffusion and viscosity cross-sections remain accurate. ``D" stands for ``diffusion" cross-section, and ``V" for ``viscosity" cross-section. \subsubsection{ Reaction 0.1T $p + H(1s) \rightarrow p + H(1s) $ total cross section} \begin{small}\begin{verbatim} a0 0.000000000000D+00 a1 0.000000000000D+00 a2 0.000000000000D+00 a3 0.000000000000D+00 a4 0.000000000000D+00 a5 0.000000000000D+00 a6 0.000000000000D+00 a7 0.000000000000D+00 a8 0.000000000000D+00 al0 -3.253031352541D+01 al1 -2.559032645641D-01 al2 -1.449996483552D-02 ar0 -3.262937357400D+01 ar1 -8.719626183599D-02 ar2 -7.346647926269D-02 ELABMIN= 1.82060E 00 eV ELABMAX= 1.82060E 00 eV Eth 0.0 \end{verbatim}\end{small} \subsubsection{ Reaction 0.1D $ p + H(1s) \rightarrow p + H(1s)$ diff. cross section} \begin{small}\begin{verbatim} a0 -3.349115100108D+01 a1 -4.047040620920D-01 a2 -4.340959073105D-02 a3 -5.224890973622D-03 a4 -1.019115858754D-04 a5 -3.314157761518D-06 a6 -4.336259011986D-05 a7 -1.781020734395D-06 a8 1.220393550627D-06 al0 -3.320677627738D+01 al1 -2.205942040112D-01 al2 0.000000000000D+00 ar0 -2.753878563969D+01 ar1 -2.000000000000D+00 ar2 0.000000000000D+00 ELABMIN= 0.02000E 00 eV ELABMAX= 2.00000E 02 eV Eth 0.0 \end{verbatim}\end{small} \subsubsection{ Reaction 0.1V $p + H(1s) \rightarrow p + H(1s)$ visc. cross-section } \begin{small}\begin{verbatim} a0 -3.353420922048D+01 a1 -3.522409780724D-01 a2 -3.587214262651D-02 a3 -4.282561006823D-03 a4 -3.230618998917D-04 a5 -4.343173698940D-05 a6 -1.753965583282D-05 a7 -4.580920664987D-07 a8 3.738689325195D-07 al0 -3.330015157525D+01 al1 -1.992625366488D-01 al2 0.000000000000D+00 ar0 -2.709329427260D+01 ar1 -2.000000000000D+00 ar2 0.000000000000D+00 ELABMIN= 0.02000E 00 eV ELABMAX= 2.00000E 02 eV Eth 0.0 \end{verbatim}\end{small} Note: This elastic reaction should only be used, if the resonant charge exchange differential cross-section (and hence: diffusion cross-section) is reduced accordingly. The sum: elastic plus charge exchange transport (``diffusion"-) cross-section should be twice the charge exchange total cross-section. The assumption of an exchange of identity (scattering angle $\pi$ in the center of mass system) at charge exchange produces that factor 2. Hence the need for a revised (smaller) charge exchange scattering angle, if the elastic collision contribution is explicitly added in. \begin{figure} \label{0.1} \epsfxsize=16truecm \epsffile{Amjuel_PS/elast01.ps} \end{figure} \newpage \subsubsection{ Reaction 0.2T $ p + He(1s^21S) \rightarrow p + He (1s^21S)$ total cross-section } \begin{small}\begin{verbatim} a0 -3.357907136508D+01 a1 -9.811659406594D-02 a2 3.798308269292D-01 a3 -1.259671949006D+00 a4 -4.473947519984D-02 a5 1.565182597363D+00 a6 -1.203733922915D+00 a7 3.525830383820D-01 a8 -3.668922671043D-02 al0 -3.355838377904D+01 al1 -2.845473342853D-01 al2 -1.351427675077D-02 ar0 -3.706830076698D+01 ar1 4.204258692619D-01 ar2 -9.648359210100D-02 ELABMIN= 0.50810E 00 eV ELABMAX= 2.94431E 01 eV Eth 0.0 \end{verbatim}\end{small} \subsubsection{ Reaction 0.2D $p + He(1s^21S) \rightarrow p + He (1s^21S) $ diff. cross section } \begin{small}\begin{verbatim} a0 -3.425585328953D+01 a1 -8.999762959781D-01 a2 -3.434858124811D-01 a3 1.549750110754D-02 a4 3.963555202866D-02 a5 3.343570605088D-04 a6 -2.207534449376D-03 a7 -3.378852519380D-05 a8 4.224511209820D-05 al0 -3.390101844960D+01 al1 -2.111706771112D-01 al2 0.000000000000D+00 ar0 -3.034765152080D+01 ar1 -2.000000000000D+00 ar2 0.000000000000D+00 ELABMIN= 0.01250E 00 eV ELABMAX= 1.25000E 02 eV Eth 0.0 \end{verbatim}\end{small} \subsubsection{ Reaction 0.2V $ p + He(1s^21S) \rightarrow p + He (1s^21S) $ visc. cross section } \begin{small}\begin{verbatim} a0 -3.443725345071D+01 a1 -4.337427858507D-01 a2 -2.896488696126D-01 a3 -6.451669335555D-02 a4 2.950009865269D-02 a5 5.752283385868D-03 a6 -1.589840628629D-03 a7 -1.502468439244D-04 a8 3.151161681447D-05 al0 -3.432276031579D+01 al1 -2.111706771112D-01 al2 0.000000000000D+00 ar0 -2.978907423990D+01 ar1 -2.000000000000D+00 ar2 0.000000000000D+00 ELABMIN= 0.01250e 00 eV ELABMAX= 1.25000e 02 eV Eth 0.0 \end{verbatim}\end{small} \begin{figure} \label{0.2} \epsfxsize=16truecm \epsffile{Amjuel_PS/elast02.ps} \end{figure} \newpage \subsubsection{ Reaction 0.3T $p + H_2 \rightarrow p + H_2 $ total cross-section } \begin{small}\begin{verbatim} a0 -3.452141819446D+01 a1 1.092015526305D+01 a2 -2.732690257819D+01 a3 3.466297654768D+01 a4 -2.524607958646D+01 a5 1.092376446349D+01 a6 -2.770065796605D+00 a7 3.796353200921D-01 a8 -2.168988142310D-02 al0 -3.275286840950D+01 al1 -2.351764912137D-01 al2 -1.045602118569D-02 ar0 -3.537275807146D+01 ar1 2.144573517210D-01 ar2 -4.643079956637D-02 ELABMIN= 1.55980E 00 eV ELABMAX= 6.18164E 01 eV Eth 0.0 \end{verbatim}\end{small} \subsubsection{ Reaction 0.3D $ p + H_2 \rightarrow p + H_2 $ diff. cross-section } \begin{small}\begin{verbatim} a0 -3.318680874597D+01 a1 -3.580417289312D-01 a2 -2.274382376951D-01 a3 -5.005702120342D-02 a4 2.369248748869D-02 a5 5.013459267775D-03 a6 -1.357018742589D-03 a7 -1.393776090855D-04 a8 3.029808591929D-05 al0 -3.319348529474D+01 al1 -1.726918000000D-01 al2 0.000000000000D+00 ar0 -2.668769803274D+01 ar1 -2.000000000000D+00 ar2 0.000000000000D+00 ELABMIN= 0.01500E 00 eV ELABMAX= 1.50000E 02 eV Eth 0.0 \end{verbatim}\end{small} \subsubsection{ Reaction 0.3V $ p + H_2 \rightarrow p + H_2 $ visc. cross-section } \begin{small}\begin{verbatim} a0 -3.362402037774D+01 a1 -2.337285826242D-01 a2 -5.404526201247D-02 a3 -4.473235272373D-02 a4 -4.691524784882D-03 a5 3.121568334037D-03 a6 4.229065229431D-04 a7 -6.739555319843D-05 a8 -7.756198335533D-06 al0 -3.342235494450D+01 al1 -1.726917299089D-01 al2 0.000000000000D+00 ar0 -2.658939177532D+01 ar1 -2.000000000000D+00 ar2 0.000000000000D+00 ELABMIN= 0.01500E 00 eV ELABMAX= 1.50000E 02 eV Eth 0.0 \end{verbatim}\end{small} \begin{figure}[hb] \label{0.3a} \epsfxsize=10truecm \epsffile{Amjuel_PS/krstic.eps} \end{figure} Comparison of the classical cross-sections given here with quantal calculations by Krstic et al., J. Phys. B, \textbf{32}, 2415 (1999), the latter converted from center of mass energy to (proton) laboratory energy. \clearpage \newpage \begin{figure} \label{0.3} \epsfxsize=16truecm \epsffile{Amjuel_PS/elast03.ps} \end{figure} \newpage \subsubsection{ Reaction 0.5T $ p + Ne \rightarrow p + Ne $ total cross section } \begin{small}\begin{verbatim} a0 -3.333282545037D+01 a1 -2.591757686627D-01 a2 5.905962318567D-02 a3 -2.001826855775D-01 a4 -5.669049674832D-02 a5 3.137174515541D-01 a6 -2.299821550060D-01 a7 6.688038706682D-02 a8 -6.994996779393D-03 al0 -3.334100609281D+01 al1 -2.660471531811D-01 al2 -1.171591760471D-02 ar0 -3.771378768853D+01 ar1 9.099449063061D-01 ar2 -1.337354731926D-01 ELABMIN= 0.62790E 00 eV ELABMAX= 3.19973E 01 eV Eth 0.0 \end{verbatim}\end{small} \subsubsection{ Reaction 0.5D $p + Ne \rightarrow p + Ne $ diff. cross section } \begin{small}\begin{verbatim} a0 -3.397612223333D+01 a1 -7.944741087630D-01 a2 -3.200443973964D-01 a3 2.143674395544D-02 a4 4.021546316704D-02 a5 -4.263678799110D-04 a6 -2.276386458638D-03 a7 -3.001154820480D-06 a8 4.436110664443D-05 al0 -3.344006570082D+01 al1 -1.264736732177D-01 al2 0.000000000000D+00 ar0 -2.871071324009D+01 ar1 -2.000000000000D+00 ar2 0.000000000000D+00 ELABMIN= 0.01050E 00 eV ELABMAX= 1.05000E 02 eV Eth 0.0 \end{verbatim}\end{small} \subsubsection{ Reaction 0.5V $ p + Ne \rightarrow p + Ne $ visc. cross section } \begin{small}\begin{verbatim} a0 -3.425296680643D+01 a1 -4.079254123231D-01 a2 -2.051623201200D-01 a3 -4.669640022898D-02 a4 1.746802660208D-02 a5 4.241270429401D-03 a6 -7.397954249705D-04 a7 -1.059957777533D-04 a8 1.168831982170D-05 al0 -3.373988599214D+01 al1 -1.264736732177D-01 al2 0.000000000000D+00 ar0 -2.849668424775D+01 ar1 -2.000000000000D+00 ar2 0.000000000000D+00 ELABMIN= 0.01050e 00 eV ELABMAX= 1.05000e 02 eV Eth 0.0 \end{verbatim}\end{small} \begin{figure} \label{0.5} \epsfxsize=16truecm \epsffile{Amjuel_PS/elast05.ps} \end{figure} \newpage \subsubsection{ Reaction 0.6T $ p + Ar \rightarrow p + Ar $ total cross section } \begin{small}\begin{verbatim} a0 -3.252771558768D+01 a1 -2.994313973955D-01 a2 -3.235294539387D-01 a3 1.292660022245D+00 a4 -1.875728041457D+00 a5 1.314385161305D+00 a6 -4.834707764434D-01 a7 8.976263360824D-02 a8 -6.639912411263D-03 al0 -3.255656992304D+01 al1 -2.557987010452D-01 al2 -1.142012674223D-02 ar0 -3.733310020910D+01 ar1 9.621654379319D-01 ar2 -1.332505124850D-01 ELABMIN= 1.00563E 00 eV ELABMAX= 5.43280E 01 eV Eth 0.0 \end{verbatim}\end{small} \subsubsection{ Reaction 0.6D $p + Ar \rightarrow p + Ar $ diff. cross section } \begin{small}\begin{verbatim} a0 -3.300046179597D+01 a1 -5.241652502840D-01 a2 -2.862188345952D-01 a3 -3.808042387800D-02 a4 2.731692136471D-02 a5 3.732186449899D-03 a6 -1.323867831716D-03 a7 -9.428149507977D-05 a8 2.340068227020D-05 al0 -3.200195937779D+01 al1 3.219272946637D-02 al2 0.000000000000D+00 ar0 -2.798873683611D+01 ar1 -2.000000000000D+00 ar2 0.000000000000D+00 ELABMIN= 0.01025E 00 eV ELABMAX= 1.02500E 02 eV Eth 0.0 \end{verbatim}\end{small} \subsubsection{ Reaction 0.6V $ p + Ar \rightarrow p + Ar $ visc. cross section } \begin{small}\begin{verbatim} a0 -3.344659528005D+01 a1 -2.316327281065D-01 a2 -7.902810934692D-02 a3 -7.081702521173D-02 a4 -8.163451484200D-03 a5 5.173767719011D-03 a6 8.930487483240D-04 a7 -1.149225205768D-04 a8 -2.179416064042D-05 al0 -3.222949872234D+01 al1 3.219272946637D-02 al2 0.000000000000D+00 ar0 -2.777200494194D+01 ar1 -2.000000000000D+00 ar2 0.000000000000D+00 ELABMIN= 0.01025e 00 eV ELABMAX= 1.02500e 02 eV Eth 0.0 \end{verbatim}\end{small} \begin{figure} \label{0.6} \epsfxsize=16truecm \epsffile{Amjuel_PS/elast06.ps} \end{figure} \newpage \subsubsection{ Reaction 0.7T $ p + Kr \rightarrow p + Kr $ total cross section } \begin{small}\begin{verbatim} a0 -3.217099198301D+01 a1 -2.966377676688D-01 a2 -2.616163755904D-01 a3 1.046180820426D+00 a4 -1.532374878331D+00 a5 1.080443653930D+00 a6 -3.994323904320D-01 a7 7.448807486523D-02 a8 -5.532560545765D-03 al0 -3.219832641289D+01 al1 -2.577194242716D-01 al2 -1.156457632593D-02 ar0 -3.656299611480D+01 ar1 7.386503642992D-01 ar2 -1.095842303625D-01 ELABMIN= 0.99496E 00 eV ELABMAX= 5.69606E 01 eV Eth 0.0 \end{verbatim}\end{small} \subsubsection{ Reaction 0.7D $p + Kr \rightarrow p + Kr $ diff. cross section } \begin{small}\begin{verbatim} a0 -3.262831875045D+01 a1 -5.132763454362D-01 a2 -2.834710685102D-01 a3 -4.303577717283D-02 a4 2.549874332091D-02 a5 4.067614437201D-03 a6 -1.176633809631D-03 a7 -1.008012190920D-04 a8 1.995735768760D-05 al0 -3.206995069647D+01 al1 -5.998480905376D-02 al2 0.000000000000D+00 ar0 -2.770706826427D+01 ar1 -2.000000000000D+00 ar2 0.000000000000D+00 ELABMIN= 0.01011E 00 eV ELABMAX= 1.01114E 02 eV Eth 0.0 \end{verbatim}\end{small} \subsubsection{ Reaction 0.7V $ p + Kr \rightarrow p + Kr $ visc. cross section } \begin{small}\begin{verbatim} a0 -3.308937458718D+01 a1 -2.158553767021D-01 a2 -6.932630020130D-02 a3 -7.534625980338D-02 a4 -1.066481934150D-02 a5 5.423170191562D-03 a6 1.055574923129D-03 a7 -1.193974259452D-04 a8 -2.508108481903D-05 al0 -3.227537561040D+01 al1 -5.998480905376D-02 al2 0.000000000000D+00 ar0 -2.750803302740D+01 ar1 -2.000000000000D+00 ar2 0.000000000000D+00 ELABMIN= 0.01011e 00 eV ELABMAX= 1.01114e 02 eV Eth 0.0 \end{verbatim}\end{small} \begin{figure} \label{0.7} \epsfxsize=16truecm \epsffile{Amjuel_PS/elast07.ps} \end{figure} \newpage \subsubsection{ Reaction 0.8T $ p + Xe \rightarrow p + Xe $ total cross section } \begin{small}\begin{verbatim} a0 -8.022745305889D+01 a1 1.563497534909D+02 a2 -2.198787103607D+02 a3 1.720041600893D+02 a4 -8.202458014402D+01 a5 2.443504314279D+01 a6 -4.445085155020D+00 a7 4.519723658716D-01 a8 -1.969077046350D-02 al0 -3.273372765185D+01 al1 -1.978370734932D-01 al2 -7.780729379878D-03 ar0 -3.529762555521D+01 ar1 2.820997908369D-01 ar2 -4.141441372472D-02 ELABMIN= 4.11282E 00 eV ELABMAX= 1.22993E 02 eV Eth 0.0 \end{verbatim}\end{small} \subsubsection{ Reaction 0.8D $p + Xe \rightarrow p + Xe $ diff. cross section } \begin{small}\begin{verbatim} a0 -3.318665017785D+01 a1 -1.652711162673D-01 a2 -8.820446797035D-02 a3 -4.031476436668D-02 a4 4.816376369566D-03 a5 2.865304171410D-03 a6 -2.624353623005D-04 a7 -6.271242694944D-05 a8 6.709771809639D-06 al0 -3.367397269144D+01 al1 -2.502739321615D-01 al2 0.000000000000D+00 ar0 -2.275819247054D+01 ar1 -2.000000000000D+00 ar2 0.000000000000D+00 ELABMIN= 0.01008E 00 eV ELABMAX= 1.00760E 03 eV Eth 0.0 \end{verbatim}\end{small} \subsubsection{ Reaction 0.8V $ p + Xe \rightarrow p + Xe $ visc. cross section } \begin{small}\begin{verbatim} a0 -3.353160943338D+01 a1 -1.556474053592D-01 a2 -3.165283483361D-02 a3 -2.954761000116D-02 a4 -1.020213798216D-04 a5 1.787583845145D-03 a6 -4.672186377936D-05 a7 -3.577368889534D-05 a8 2.586881672353D-06 al0 -3.326401521314D+01 al1 -1.220855990887D-01 al2 0.000000000000D+00 ar0 -2.266117187300D+01 ar1 -2.000000000000D+00 ar2 0.000000000000D+00 ELABMIN= 0.01008e 00 eV ELABMAX= 1.00760e 03 eV Eth 0.0 \end{verbatim}\end{small} \begin{figure} \label{0.8} \epsfxsize=16truecm \epsffile{Amjuel_PS/elast08.ps} \end{figure} \newpage \subsection{ Reaction 0.13p $ p + Be \rightarrow p + Be $ } Relaxation model, take: half of the momentum transfer cross-section section [P. Krstic, D. Schultz, PP, vol. 16 (2009), p. 053503] \begin{small}\begin{verbatim} a0 -3.432911046254e+01 a1 -2.981766563063e-01 a2 -2.747140212160e-03 a3 -9.888209801767e-02 a4 1.277819275721e-02 a5 5.604365199896e-03 a6 -1.798975676281e-03 a7 1.873165090959e-04 a8 -6.739311119307e-06 ELABMIN=1.000000e-01 eV ELABMAX=1.000000e+04 eV MAXERR=9.420281e+00 \% MIDERR=3.699055e+00 \% \end{verbatim}\end{small} \subsection{ Reaction 0.13d $ d + Be \rightarrow d + Be $ } Relaxation model, take: half of the momentum transfer cross-section section [P. Krstic, D. Schultz, PP, vol. 16 (2009), p. 053503] \begin{small}\begin{verbatim} a0 -3.429847239061e+01 a1 -2.970572100641e-01 a2 2.225098488848e-02 a3 -1.038644613722e-01 a4 1.090206315848e-02 a5 6.452930419639e-03 a6 -1.922155122744e-03 a7 1.949450215711e-04 a8 -6.904617523867e-06 ELABMIN=1.000000e-01 eV ELABMAX=1.000000e+04 eV MAXERR=9.480029e+00 \% MIDERR=3.721394e+00 \% \end{verbatim}\end{small} \subsection{ Reaction 0.13t $ t + Be \rightarrow t + Be $ } Relaxation model, take: half of the momentum transfer cross-section section [P. Krstic, D. Schultz, PP, vol. 16 (2009), p. 053503] \begin{small}\begin{verbatim} a0 -3.496365351820e+01 a1 -3.001445356961e-01 a2 4.591434817499e-02 a3 -1.076154031752e-01 a4 8.896989671817e-03 a5 7.236320863176e-03 a6 -2.026608049532e-03 a7 2.007699253304e-04 a8 -7.009352516893e-06 ELABMIN=1.000000e-01 eV ELABMAX=1.000000e+04 eV MAXERR=9.649480e+00 \% MIDERR=3.664496e+00 \% \end{verbatim}\end{small} \newpage \subsection{ Reaction 0.14p $ p + C \rightarrow p + C $ } Relaxation model, take: half of the momentum transfer cross-section section [P. Krstic, D. Schultz, PP, vol. 13 (2006), p. 053501] \begin{small}\begin{verbatim} a0 -3.469669448083e+01 a1 -6.465336127803e-01 a2 -2.507493283133e-01 a3 5.150725759535e-02 a4 2.606050422216e-02 a5 -1.200069052688e-02 a6 1.870487465021e-03 a7 -1.320377335268e-04 a8 3.583861884216e-06 ELABMIN=1.000000e-01 eV ELABMAX=1.000000e+04 eV MAXERR=1.359190e+01 \% MIDERR=3.567110e+00 \% \end{verbatim}\end{small} \subsection{ Reaction 0.14d $ d + C \rightarrow d + C $ } Relaxation model, take: half of the momentum transfer cross-section section [P. Krstic, D. Schultz, PP, vol. 13 (2006), p. 053501] \begin{small}\begin{verbatim} a0 -3.467431708479e+01 a1 -6.039120001583e-01 a2 -2.291079734779e-01 a3 3.028388597223e-02 a4 2.684378189799e-02 a5 -9.913519764240e-03 a6 1.329864451784e-03 a7 -7.980666826518e-05 a8 1.784639219274e-06 ELABMIN=1.000000e-01 eV ELABMAX=1.000000e+04 eV MAXERR=1.766724e+01 \% MIDERR=4.238927e+00 \% \end{verbatim}\end{small} \subsection{ Reaction 0.14t $ t + C \rightarrow t + C $ } Relaxation model, take: half of the momentum transfer cross-section section [P. Krstic, D. Schultz, PP, vol. 13 (2006), p. 053501] \begin{small}\begin{verbatim} a0 -3.534658901399e+01 a1 -5.578781967387e-01 a2 -2.132235368452e-01 a3 1.089144735337e-02 a4 2.797214775907e-02 a5 -8.126362752782e-03 a6 8.523433043919e-04 a7 -3.327701820563e-05 a8 1.778193853599e-07 ELABMIN=1.000000e-01 eV ELABMAX=1.000000e+04 eV MAXERR=2.049295e+01 \% MIDERR=4.869674e+00 \% \end{verbatim}\end{small} \newpage \subsubsection{ Reaction 3.1.6FJ $ p + H \rightarrow . . . \rightarrow p + e + p $ } Freeman and Jones coefficients, transformed from the keV to eV energy scale, E is the proton energy, \cite{kn:Freeman}. \begin{small}\begin{verbatim} a0 -5.607099441961D+02 a1 2.905103863403D+02 a2 -6.871403140568D+01 a3 8.714435377189D+00 a4 -6.169007495812D-01 a5 2.294651604603D-02 a6 -3.495444000000D-04 a7 0.000000000000D+00 a8 0.000000000000D+00 Eth 0.0 \end{verbatim}\end{small} \newpage This page is intentionally left blank \newpage \subsubsection{ Reaction 3.1.8org $ p + H(1s) \rightarrow H(1s) + p $ } original Janev-Langer fit as in 1987 Springer book, i.e. without asympt. energy correction. \begin{small}\begin{verbatim} a0 -3.274123792568e+01 a1 -8.916456579806e-02 a2 -3.016990732025e-02 a3 9.205482406462e-03 a4 2.400266568315e-03 a5 -1.927122311323e-03 a6 3.654750340106e-04 a7 -2.788866460622e-05 a8 7.422296363524e-07 Emin 1.00e-01 s(Emin) 7.00e-15 smax 7.00e-15 Error 2.25e-03 Eth 0.0 Mcross 1.0E+00 \end{verbatim}\end{small} \subsubsection{ Reaction 3.1.8 $ p + H(1s) \rightarrow H(1s) + p $ } same as HYDHEL cx total cross-section. Improved from original Janev-Langer fit at low energies by asymptotic fit.: al0 + al1* ln(E) al0 changed in Aug.17., ar0,.... added in Nov. 17 \begin{small}\begin{verbatim} a0 -3.274123792568e+01 a1 -8.916456579806e-02 a2 -3.016990732025e-02 a3 9.205482406462e-03 a4 2.400266568315e-03 a5 -1.927122311323e-03 a6 3.654750340106e-04 a7 -2.788866460622e-05 a8 7.422296363524e-07 al0 -3.294589355000e+01 al1 -1.713112000000e-01 al2 0.000000000000e+00 ar0 -5.787734011000E+01 ar1 7.671416829000E+00 ar2 -5.208376804000E-01 ELABMIN= 0.10000E 00 eV ELABMAX= 5.00000E 05 eV Emin 1.00e-01 s(Emin) 7.00e-15 smax 7.00e-15 Error 2.25e-03 Eth 0.0 Mcross 1.0E+00 \end{verbatim}\end{small} \subsubsection{ Reaction 3.1.8J2 $ p + H(1s) \rightarrow H(1s) + p $ } Janev cross-section for momentum exchange ( = cx total cross-sections times 2), obtained by increasing absolute coefficients $a_0$ and $al_0$ by adding $\ln(2)$ \begin{small}\begin{verbatim} a0 -3.204809074000e+01 a1 -8.916456579806e-02 a2 -3.016990732025e-02 a3 9.205482406462e-03 a4 2.400266568315e-03 a5 -1.927122311323e-03 a6 3.654750340106e-04 a7 -2.788866460622e-05 a8 7.422296363524e-07 al0 -3.225274637000e+01 al1 -1.713112000000e-01 al2 0.000000000000e+00 ELABMIN= 0.10000E 00 eV Eth 0.0 \end{verbatim}\end{small} \subsubsection{ Reaction 3.1.8R $ p + H(1s) \rightarrow H(1s) + p $ } Riviere cross-section formula for charge exchange (\cite{kn:Riviere}), fitted into ``Janev-Langer (polynomial) format" \cite{kn:Janev} \begin{small}\begin{verbatim} a0 -3.260293402651D+01 a1 -1.302091929244D-01 a2 -3.264584699247D-03 a3 -2.837612246121D-03 a4 2.259716141071D-04 a5 3.105542152111D-04 a6 -9.613308889191D-05 a7 1.043010252591D-05 a8 -3.944350620003D-07 Max. rel. Error: .7501 % Mean rel. Error: .2304 % Eth 0.0 \end{verbatim}\end{small} \subsubsection{ Reaction 3.1.8ST $ p + H(1s) \rightarrow H(1s) + p $ } D.Schultz total cross-section for charge exchange fitted into ``Janev format", left asympt. added. \begin{small}\begin{verbatim} a0 -3.296040048723D+01 a1 -9.877533792693D-02 a2 2.622855374688D-03 a3 -3.210858385884D-03 a4 -2.175078820057D-04 a5 2.394562232339D-05 a6 1.665865000000D-05 a7 0.000000000000D+00 a8 0.000000000000D+00 al0 -3.307949733000D+01 al1 -1.713112000000D-01 al2 0.000000000000e+00 ar0 -3.291743242047D+01 ar1 -1.358551000000D-01 ar2 0.000000000000D+00 ELABMIN= 0.10000E 00 eV ELABMAX= 2.00000E 01 eV Eth 0.0 \end{verbatim}\end{small} \subsubsection{ Reaction 3.1.8ST2 $ p + H(1s) \rightarrow H(1s) + p $ } D.Schultz total cross-section for charge exchange *2 increase absolute coefficients $a_0$ and $ar_0$ by adding ln(2) \begin{small}\begin{verbatim} a0 -3.226725330000D+01 a1 -9.877533792693D-02 a2 2.622855374688D-03 a3 -3.210858385884D-03 a4 -2.175078820057D-04 a5 2.394562232339D-05 a6 1.665865000000D-05 a7 0.000000000000D+00 a8 0.000000000000D+00 al0 -3.238635015000D+01 al1 -1.713112000000D-01 al2 0.000000000000e+00 ar0 -3.222428522000D+01 ar1 -1.358551000000D-01 ar2 0.000000000000D+00 ELABMAX= 2.00000E 01 eV Eth 0.0 \end{verbatim}\end{small} \subsubsection{ Reaction 3.1.8SD $ p + H(1s) \rightarrow H(1s) + p $ } D.Schultz ``diffusion" cross-section for momentum exchange (elastic plus cx) fitted into ``Janev format". Should be close to ST2, total cx cross-section times 2. \begin{small}\begin{verbatim} a0 -3.225844350904D+01 a1 -1.220948860470D-01 a2 7.214005848073D-03 a3 5.997760021277D-04 a4 -1.060316696581D-03 a5 -7.487092727391D-05 a6 3.824773000000D-05 a7 0.000000000000D+00 a8 0.000000000000D+00 ar0 -3.221533966214D+01 ar1 -1.386002000000D-01 ar2 0.000000000000D+00 ELABMAX= 2.00000E 01 eV Eth 0.0 \end{verbatim}\end{small} \begin{figure} \label{318RS} \epsfxsize=16truecm \epsffile{Amjuel_PS/sigmacx.ps} \end{figure} \newpage \subsubsection{ Reaction 3.1.8L $ p + H(1s) \rightarrow H(1s) + p $ } For testing purposes: Langevin cross-section: $\sigma(v)=A0 \times v^{-1}$, or, for hydrogen mass: $\sigma(E)=A \times E^{-1/2}$ such that the rate coefficient, $\langle\sigma \times v_{rel} \rangle= const = A0 = 2.0~ 10^{-8}$ cm$^3$/s\\ (Note: $\pi a_0^2 v_0 = 1.923 10^{-8}$, the reference rate coefficient with $a_0$: Bohr radius and $v_0 =e^2/\hbar$: unit velocity in atomic units) Here: $A = A0/1.3891e 06$, when $v$ is in cm/s and $E$ in eV, a hydrogen energy. \begin{small}\begin{verbatim} a0 -3.187171457000e+01 a1 -0.500000000000e-00 a2 0.000000000000e-00 a3 0.000000000000e+00 a4 0.000000000000e+00 a5 0.000000000000e+00 a6 0.000000000000e+00 a7 0.000000000000e+00 a8 0.000000000000e+00 Eth 0.0 \end{verbatim}\end{small} \newpage \subsection{He$^+$ impact processes} \subsubsection{ Reaction 0.4T $ He^+(1s) + He(1s^21S) \rightarrow He^+(1s) + He(1s^21S) $ total cross-section } \begin{small}\begin{verbatim} a0 -3.336949020454D+01 a1 4.374909804779D+00 a2 -1.517973301721D+01 a3 2.345459194687D+01 a4 -1.969436659467D+01 a5 9.472303986781D+00 a6 -2.604153028956D+00 a7 3.801132783280D-01 a8 -2.282922057203D-02 al0 -3.291071330248D+01 al1 -2.416669402887D-01 al2 -9.821377921757D-03 ar0 -3.664691925424D+01 ar1 4.752719886448D-01 ar2 -8.280792916138D-02 ELABMIN= 1.21220E 00 eV ELABMAX= 6.46090E 01 eV Eth 0.0 \end{verbatim}\end{small} \subsubsection{ Reaction 0.4D $He^+(1s) + He(1s^21S) \rightarrow He^+(1s) + He(1s^21S)$ diff. cross-section } \begin{small}\begin{verbatim} a0 -3.332091557452D+01 a1 -3.823354679977D-01 a2 -2.666453887008D-01 a3 -8.177418933677D-02 a4 2.593188019755D-02 a5 8.320863897668D-03 a6 -1.649825718076D-03 a7 -2.491587647454D-04 a8 4.351897658362D-05 al0 -3.302935901459D+01 al1 -1.115060000000D-01 al2 0.000000000000D+00 ar0 -2.789589583796D+01 ar1 -2.000000000000D+00 ar2 0.000000000000D+00 ELABMIN= 0.02000E 00 eV ELABMAX= 2.00000E 02 eV Eth 0.0 \end{verbatim}\end{small} \subsubsection{ Reaction 0.4V $ He^+(1s) + He(1s^21S) \rightarrow He^+(1s) + He(1s^21S) $ visc. cross-section } \begin{small}\begin{verbatim} a0 -3.379346231200D+01 a1 -1.740525006979D-01 a2 -8.091712353563D-02 a3 -8.223847315134D-02 a4 -1.443276051210D-03 a5 6.530393601967D-03 a6 -5.593294441844D-05 a7 -1.742244159818D-04 a8 1.068285383642D-05 al0 -3.335648222384D+01 al1 -1.115060177785D-01 al2 0.000000000000D+00 ar0 -2.751718958486D+01 ar1 -2.000000000000D+00 ar2 0.000000000000D+00 ELABMIN= 0.02000E 00 eV ELABMAX= 2.00000E 02 eV Eth 0.0 \end{verbatim}\end{small} \begin{figure} \label{0.4} \epsfxsize=16truecm \epsffile{Amjuel_PS/elast04.ps} \end{figure} \newpage \section{H.2 : Fits for $\langle\sigma v \rangle (T)$} \label{sect2} Some (single parameter) Maxwellian rate coefficients, obtained algebraically from corresponding Beam-Maxwellian fits, at the limit of low ($\approx$ zero) beam energies. The suitable low beam energy limit of these 2-parameter fits was identified by independent integration of cross-sections which have proper low energy extrapolation. \subsection{ Reaction 0.1T $p + H(1s) \rightarrow p + H(1s)$ total rate coef. } Maxwellian rate coefficient vs. $T_p$, with $H(1s)$ at rest, obtained by taking the corresponding Beam-Maxw. rate coefficient at Eb=0.08 eV and verification by independent integration of cross-section \begin{small}\begin{verbatim} b0 -1.833882000000E+01 b1 2.368705000000E-01 b2 -1.469575000000E-02 b3 -1.139850000000E-02 b4 6.379644000000E-04 b5 3.162724000000E-04 b6 -6.681994000000E-05 b7 3.812123000000E-06 b8 8.652321000000E-09 \end{verbatim}\end{small} \subsection{ Reaction 0.1D $p + H(1s) \rightarrow p + H(1s)$ diff. rate coef. } Maxwellian rate coefficient vs. $T_p$, with $H(1s)$ at rest, obtained by taking the corresponding Beam-Maxw. rate coefficient at Eb=0.08 eV and verification by independent integration of cross-section \begin{small}\begin{verbatim} b0 -1.937499000000E+01 b1 1.064443000000E-01 b2 -5.831768000000E-02 b3 -2.768932000000E-02 b4 1.018222000000E-02 b5 1.253253000000E-03 b6 -1.245254000000E-03 b7 2.110022000000E-04 b8 -1.121733000000E-05 \end{verbatim}\end{small} \subsection{ Reaction 0.2T $p + He(1s^21S) \rightarrow p + He(1s^21S)$ total rate coef. } Maxwellian rate coefficient vs. $T_p$, with $He(1s^21S)$ at rest, obtained by taking the corresponding Beam-Maxw. rate coefficient at Eb=0.2 eV and verification by independent integration of cross-section \begin{small}\begin{verbatim} b0 -1.940685000000E+01 b1 1.706015000000E-01 b2 5.518956000000E-03 b3 -1.073297000000E-02 b4 -1.744782000000E-02 b5 1.271241000000E-03 b6 1.541255000000E-03 b7 -3.211063000000E-04 b8 1.805115000000E-05 \end{verbatim}\end{small} \subsection{ Reaction 0.2D $p + He(1s^21S) \rightarrow p + He(1s^21S)$ diff. rate coef. } Maxwellian rate coefficient vs. $T_p$, with $He(1s^21S)$ at rest, obtained by taking the corresponding Beam-Maxw. rate coefficient at Eb=0.2 eV and verification by independent integration of cross-section \begin{small}\begin{verbatim} b0 -2.030007000000E+01 b1 -3.092379000000E-01 b2 -1.701258000000E-01 b3 1.495117000000E-02 b4 1.340661000000E-02 b5 -1.869797000000E-03 b6 -6.819520000000E-04 b7 1.622554000000E-04 b8 -9.363090000000E-06 \end{verbatim}\end{small} \subsection{ Reaction 0.3T $p + H_2 \rightarrow p + H_2$ total rate coef. } Maxwellian rate coefficient vs. $T_p$, with $H_2$ at rest, obtained by taking the corresponding Beam-Maxw. rate coefficient at Eb=0.06 eV and verification by independent integration of cross-section \begin{small}\begin{verbatim} b0 -1.857812000000E+01 b1 2.411708000000E-01 b2 1.046088000000E-02 b3 -1.203649000000E-02 b4 -3.679626000000E-03 b5 2.895358000000E-04 b6 1.354441000000E-04 b7 -2.712317000000E-06 b8 -1.356528000000E-06 \end{verbatim}\end{small} \subsection{ Reaction 0.3D $p + H_2 \rightarrow p + H_2$ diff. rate coef. } Maxwellian rate coefficient vs. $T_p$, with $H_2$ at rest, obtained by taking the corresponding Beam-Maxw. rate coefficient at Eb=0.1 eV and verification by independent integration of cross-section \begin{small}\begin{verbatim} b0 -1.914667000000E+01 b1 7.511853000000E-03 b2 -1.408236000000E-01 b3 -7.208816000000E-03 b4 1.464363000000E-02 b5 5.237593000000E-05 b6 -9.787576000000E-04 b7 1.491343000000E-04 b8 -6.478446000000E-06 \end{verbatim}\end{small} \subsection{ Reaction 0.4T $He^+(1s) + He(1s^21S) \rightarrow He^+(1s) + He(1s^21S)$ total rate coef. } Maxwellian rate coefficient vs. $T_{He^+}$, with $He$ at rest, obtained by taking the corresponding Beam-Maxw. rate coefficient at Eb=0.2 eV and verification by independent integration of cross-section \begin{small}\begin{verbatim} b0 -1.938952000000E+01 b1 1.284344000000E-01 b2 2.749434000000E-02 b3 1.321028000000E-02 b4 -1.215805000000E-02 b5 -1.771858000000E-03 b6 1.250552000000E-03 b7 -1.586374000000E-04 b8 6.000872000000E-06 \end{verbatim}\end{small} \subsection{ Reaction 0.4D $He^+(1s) + He(1s^21S) \rightarrow He^+(1s) + He(1s^21S)$ diff. rate coef. } Maxwellian rate coefficient vs. $T_{He^+}$, with $He$ at rest, obtained by taking the corresponding Beam-Maxw. rate coefficient at Eb=0.2 eV and verification by independent integration of cross-section \begin{small}\begin{verbatim} b0 -2.002066000000E+01 b1 -8.176109000000E-02 b2 -1.436536000000E-01 b3 -1.526248000000E-02 b4 1.239665000000E-02 b5 3.669366000000E-04 b6 -7.044353000000E-04 b7 9.121888000000E-05 b8 -3.350873000000E-06 \end{verbatim}\end{small} \subsection{ Reaction 0.5T $p + Ne \rightarrow p + Ne$ total rate coef. } Maxwellian rate coefficient vs. $T_{p}$, with $Ne$ at rest, obtained by taking the corresponding Beam-Maxw. rate coefficient at Eb=0.2 eV and verification by independent integration of cross-section \begin{small}\begin{verbatim} b0 -1.919918000000E+01 b1 2.302126000000E-01 b2 -6.513570000000E-03 b3 -2.016719000000E-02 b4 -1.221527000000E-02 b5 2.242603000000E-03 b6 9.298891000000E-04 b7 -2.398546000000E-04 b8 1.462516000000E-05 \end{verbatim}\end{small} \subsection{ Reaction 0.5D $p + Ne \rightarrow p + Ne$ diff. rate coef. } Maxwellian rate coefficient vs. $T_{p}$, with $Ne$ at rest, obtained by taking the corresponding Beam-Maxw. rate coefficient at Eb=0.1 eV and verification by independent integration of cross-section \begin{small}\begin{verbatim} b0 -2.002715000000E+01 b1 -2.621343000000E-01 b2 -1.469315000000E-01 b3 2.687596000000E-02 b4 1.266229000000E-02 b5 -2.448273000000E-03 b6 -6.258496000000E-04 b7 1.654175000000E-04 b8 -9.716880000000E-06 \end{verbatim}\end{small} \subsection{ Reaction 0.6T $p + Ar \rightarrow p + Ar$ total rate coef. } Maxwellian rate coefficient vs. $T_{p}$, with $Ar$ at rest, obtained by taking the corresponding Beam-Maxw. rate coefficient at Eb=0.05 eV and verification by independent integration of cross-section \begin{small}\begin{verbatim} b0 -1.840169000000E+01 b1 2.394376000000E-01 b2 -2.360132000000E-02 b3 6.595325000000E-03 b4 -8.347203000000E-03 b5 -1.735906000000E-03 b6 1.204285000000E-03 b7 -1.658480000000E-04 b8 6.963785000000E-06 \end{verbatim}\end{small} \subsection{ Reaction 0.6D $p + Ar \rightarrow p + Ar$ diff. rate coef. } Maxwellian rate coefficient vs. $T_{p}$, with $Ar$ at rest, obtained by taking the corresponding Beam-Maxw. rate coefficient at Eb=0.07 eV and verification by independent integration of cross-section \begin{small}\begin{verbatim} b0 -1.906021000000E+01 b1 -4.674038000000E-02 b2 -1.962414000000E-01 b3 -7.174255000000E-03 b4 2.020135000000E-02 b5 -8.507943000000E-04 b6 -1.210751000000E-03 b7 2.196434000000E-04 b8 -1.117489000000E-05 \end{verbatim}\end{small} \subsection{ Reaction 0.7T $p + Kr \rightarrow p + Kr$ total rate coef. } Maxwellian rate coefficient vs. $T_{p}$, with $Ar$ at rest, obtained by taking the corresponding Beam-Maxw. rate coefficient at Eb=0.05 eV and verification by independent integration of cross-section \begin{small}\begin{verbatim} b0 -1.803236000000E+01 b1 1.992221000000E-01 b2 -3.227483000000E-03 b3 1.395545000000E-02 b4 -1.344849000000E-02 b5 -1.615546000000E-03 b6 1.484410000000E-03 b7 -2.152296000000E-04 b8 9.514869000000E-06 \end{verbatim}\end{small} \subsection{ Reaction 0.7D $p + Kr \rightarrow p + Kr$ diff. rate coef. } Maxwellian rate coefficient vs. $T_{p}$, with $Kr$ at rest, obtained by taking the corresponding Beam-Maxw. rate coefficient at Eb=0.1 eV and verification by independent integration of cross-section \begin{small}\begin{verbatim} b0 -1.865129000000E+01 b1 -1.062916000000E-01 b2 -1.827846000000E-01 b3 -2.368024000000E-03 b4 1.711988000000E-02 b5 -6.251324000000E-04 b6 -1.097944000000E-03 b7 1.970191000000E-04 b8 -9.968727000000E-06 \end{verbatim}\end{small} \subsection{ Reaction 0.8T $p + Xe \rightarrow p + Xe$ total rate coef. } Maxwellian rate coefficient vs. $T_{p}$, with $Xe$ at rest, obtained by taking the corresponding Beam-Maxw. rate coefficient at Eb=0.2 eV and verification by independent integration of cross-section \begin{small}\begin{verbatim} b0 -1.850781000000E+01 b1 2.709525000000E-01 b2 4.983184000000E-03 b3 -5.736578000000E-03 b4 1.424879000000E-03 b5 -6.005354000000E-04 b6 -2.027911000000E-04 b7 8.186987000000E-05 b8 -6.300191000000E-06 \end{verbatim}\end{small} \subsection{ Reaction 0.8D $p + Xe \rightarrow p + Xe$ diff. rate coef. } Maxwellian rate coefficient vs. $T_{p}$, with $Xe$ at rest, obtained by taking the corresponding Beam-Maxw. rate coefficient at Eb=0.1 eV and verification by independent integration of cross-section \begin{small}\begin{verbatim} b0 -1.903991000000E+01 b1 2.089862000000E-01 b2 -7.784350000000E-02 b3 -1.756400000000E-02 b4 5.522983000000E-03 b5 9.448506000000E-04 b6 -2.428668000000E-04 b7 -5.632953000000E-08 b8 1.296757000000E-06 \end{verbatim}\end{small} \newpage This page is intentionally left blank \newpage Data from Freeman and Jones \cite{kn:Freeman}, for comparison with old cases. Note: Maxwellian rate coefficients are taken at neutral particle energy = 0.0 eV vs. temperature (electron or ion temp., resp.) of the Maxwellian $f_{maxw}$. I.e. : $\langle\sigma v \rangle = \int d^3v_p \ \sigma(v_{p}) \cdot v_{p} \cdot f_{maxw}(v_{p})$ The ion impact rates can be scaled to different isotopes and to finite neutral particle temperatures $T_n$ by evaluating the fits at an effective temperature $T_{eff}$ given by $T_{eff} = \frac {M}{M_1} T_1 + \frac{M}{M_2} T_2 $ Here $M$ is the mass of the ion as used in the Freeman/Jones rate coefficients, $M_1$ and $M_2$ are the masses of the two isotopes in the particular collision process considered, and $T_1$ and $T_2$ are the two temperatures. \bigskip \subsection{ Reaction 2.1.5FJ $e + H(1s) \rightarrow e + H^+ + e$ } \begin{small}\begin{verbatim} b0 -0.317385000000e+02 b1 0.114381800000e+02 b2 -0.383399800000e+01 b3 0.704669200000e+00 b4 -0.743148620000e-01 b5 0.415374900000e-02 b6 -0.948696700000e-04 b7 0.000000000000e-00 b8 0.000000000000e+00 \end{verbatim}\end{small} \subsection{ Reaction 3.1.6FJ $p + H(1s) \rightarrow p + p + e $ } This fit seems to be completely corrupted. Probably misprints in original F.J. CLM-R-137 report. Checked also with old AURORA code (PPPL, ca. 1979) implementation. Identical fit used there. Recommendation: Use cross-section and HYDKIN online integration to rate coefficients. \begin{small}\begin{verbatim} b0 -0.149086100000e+03 b1 0.759257500000e+02 b2 -0.220928100000e+02 b3 0.390970900000e+01 b4 -0.440216800000e+00 b5 0.320904700000e-01 b6 -0.149340900000e-02 b7 0.409415100000e-04 b8 -0.506977700000e-06 \end{verbatim}\end{small} \subsection{ Reaction 3.1.8 $ p + H(1s) \rightarrow H(1s) + p$} added by DR: single parameter Maxwellian rate coeff., vs. $T_p$, for neutral target at rest, obtained from corresponding fit for Beam-Maxwellian rate coeff. evaluated at $E_b =0.1$ eV and then verified by independent integration of cross-section with proper low energy asymptotics. \begin{small}\begin{verbatim} b0 -1.850280000000E+01 b1 3.708409000000E-01 b2 7.949876000000E-03 b3 -6.143769000000E-04 b4 -4.698969000000E-04 b5 -4.096807000000E-04 b6 1.440382000000E-04 b7 -1.514243000000E-05 b8 5.122435000000E-07 \end{verbatim}\end{small} \subsection{ Reaction 3.1.8FJ $p + H(1s) \rightarrow H(1s) + p $ } \begin{small}\begin{verbatim} b0 -0.184175600000e+02 b1 0.528295000000e+00 b2 -0.220047700000e+00 b3 0.975019200000e-01 b4 -0.174918300000e-01 b5 0.495429800000e-03 b6 0.217491000000e-03 b7 -0.253020600000e-04 b8 0.823075100000e-06 \end{verbatim}\end{small} \newpage This page is intentionally left blank \newpage \subsection{ Reaction 2.2.5org $e + H_2(X_g\!^+ S ) \rightarrow . . .\rightarrow e + H(1s) + H(1s)$} Old fit as given in \cite{kn:Janev}, probably based on incorrect cross-section data.\\ EIRENE uses, as default, the fit as given in preprint for \cite{kn:Janev}, unless otherwise specified, for this dissociation process. This latter fit seems to be more plausible. Therefore, the (presumably more correct) preprint data are stored in file HYDHEL, whereas the original data from ref.\cite{kn:Janev} are given here in AMJUEL, for reference purposes only. \begin{displaymath} e + H_2(X_g^+ S) \rightarrow e + H(b^3\Sigma^+_u , a^3\Sigma^+_g, c^3\Pi_u) \rightarrow e + H(1s) + H(1s) \end{displaymath} \begin{small}\begin{verbatim} b0 -2.858072836568e+01 b1 1.038543976082e+01 b2 -5.383825026583e+00 b3 1.950636494405e+00 b4 -5.393666392407e-01 b5 1.006916814453e-01 b6 -1.160758573972e-02 b7 7.411623859122e-04 b8 -2.001369618807e-05 Tmin 1.26e+00 (Tmin) 3.25e-12 max 3.82e-09 Error 1.07e-06 \end{verbatim}\end{small} \begin{figure} \label{2.2.5.or} \epsfxsize=16truecm \epsffile{Amjuel_PS/fig225.ps} \end{figure} \newpage \subsection{ Reaction 2.2.14 $ e + H_2^+(v) \rightarrow H(1s) + H(n) (v=0\ldots 9, n \geq 2)$} Fit as given in \cite{kn:Janev} but with all higher coefficients b2,b3,...b8 set to zero, for this dissociative recombination process. This latter fit seems to be more plausible. Therefore, the (presumably more correct) data are stored here, whereas the original data from ref.\cite{kn:Janev} are still given in HYDHEL, for reference purposes only. \begin{small}\begin{verbatim} b0 -1.670435653561e+01 b1 -6.035644995682e-01 b2 0.000000000000e+00 b3 0.000000000000e+00 b4 0.000000000000e+00 b5 0.000000000000e+00 b6 0.000000000000e+00 b7 0.000000000000e+00 b8 0.000000000000e+00 Tmin 1.00e-01 (Tmin) 2.23e-07 max 2.23e-07 Error 3.30e-13 \end{verbatim}\end{small} \newpage \subsection{ Reaction 2.2.17 $e + H_2 \rightarrow e + H_2(v) \rightarrow H + H^-$ } Effective dissociative attachment rate. $ \langle\sigma v \rangle_{eff} = \langle\sigma v \rangle_{H_2(v=0)} + \sum_{v=1}^{14} \langle\sigma v \rangle_{H_2(v)} \cdot pH_2(v) $ Vibrational distribution $pH_2(v,T_e)$ (vs. $T_e$) taken into account. Only coupling to $H_2(v)$ electronic ground state. No population of $H_2(v)$ from electronically excited $H_2^*$, no radiative transitions between vibrational levels. Assume: incident $H_2$ particle with 0.1 eV (for the rate taken to be for $H_2$ at rest) and $T_i = T_e$, hence: density independent vibrational distribution and effective rate, as well as neutral molecule energy independent rate. Competing processes: see ion conversion, below, and contribution to dissociation via vibrational states, i.e., enhanced transition into repulsive triplett $^3b....$ state. \begin{small}\begin{verbatim} b0 -2.278396332892D+01 b1 8.634828071751D-01 b2 -1.686619409809D+00 b3 4.392288378207D-01 b4 -4.393128035945D-01 b5 2.640299048385D-01 b6 -6.748601049114D-02 b7 7.753368735736D-03 b8 -3.328288267126D-04 Max. rel. Error: 11.6159 % Mean rel. Error: 5.8452 % \end{verbatim}\end{small} \subsection{ Reaction 2.2.17s $e + H_2 \rightarrow H + H +e $ (Diss via $H^-$, cold $H_2$) } Effective (intermediate $H^-$ condensed) dissociation rate coefficient, via $H_2^- --> H + H^-$ channel. Vibrational distribution $pH_2(v,T_e)$ (vs. $T_e$) taken into account. Only coupling to $H_2(v)$ electronic ground state. No population of $H_2(v)$ from electronically excited $H_2^*$, no radiative transitions between vibrational levels. Assume: incident $H_2$ particle with 0.1 eV (for the rate taken to be for $H_2$ at rest) and $T_i = T_e$, hence: density independent vibrational distribution and effective rate, as well as neutral molecule energy independent rate. Competing processes: see $H^-$ MAR, $H^-$ MAD, below. \begin{small}\begin{verbatim} b0 -2.412637388641D+01 b1 2.933435541120D+00 b2 -3.070089133892D+00 b3 5.421534021185D-01 b4 -1.096901334427D-01 b5 5.895406094562D-02 b6 -1.454957631310D-02 b7 1.472799599671D-03 b8 -5.199158850052D-05 Max. rel. Error: 0.220E+02 % Mean rel. Error: 0.113E+02 % \end{verbatim}\end{small} \subsection{ Reaction 3.1.8L $p + H(1s) \rightarrow H(1s) + p $ } Langevin rate coefficient, constant at 2e-8 \begin{small}\begin{verbatim} b0 -1.772753356000D+01 b1 0.000000000000D+00 b2 0.000000000000D+00 b3 0.000000000000D+00 b4 0.000000000000D+00 b5 0.000000000000D+00 b6 0.000000000000D+00 b7 0.000000000000D+00 b8 0.000000000000D+00 \end{verbatim}\end{small} \subsection{ Reaction 3.2.3 $p + H_2 \rightarrow H + H_2^+ $ } Effective ion conversion rate (charge exchange on $H_2$) $ \langle\sigma v \rangle_{eff} = \langle\sigma v \rangle_{H_2(v=0)} + \sum_{v=1}^{14} \langle\sigma v \rangle_{H_2(v)} \cdot pH_2(v) $ Same vibrational distribution (as function of $T_e$) as above. Therefore: single parameter fit vs. $T_e$, since vibrational distribution does not depend upon density, $E_0$ is fixed (0.1 eV) and $T_p = T_e = T$. \begin{small}\begin{verbatim} b0 -2.163099643422D+01 b1 3.206843053514D+00 b2 -3.369939911269D+00 b3 1.290238400703D+00 b4 -3.988189754178D-01 b5 1.462287796966D-01 b6 -3.524154596754D-02 b7 4.146324082808D-03 b8 -1.846022446828D-04 Max. rel. Error: 10.2031 % Mean rel. Error: 6.3799 % \end{verbatim}\end{small} Competing process at low T: see above: dissociative electron attachment, process 2-2-17 \begin{figure} \label{3.2.3} \epsfxsize=16truecm \epsffile{Amjuel_PS/ionconv1.ps} \end{figure} \newpage \subsection{ Reaction 3.2.3o $p + H_2 \rightarrow H + H_2^+ $} Effective ion conversion rate (charge exchange on $H_2$ (old version before 2004) $ <\sigma v>_{eff} = <\sigma v>_{H_2(v=0)} + \sum_{v=1}^{14} <\sigma v>_{H_2(v)} \cdot pH_2(v) $ Same vibrational distribution (as function of $T_e$) as above. Therefore: single parameter fit vs. $T_e$, since vibrational distribution does not depend upon density, $E_0$ is fixed (0.37 eV) and $T_p = T_e = T$. \begin{small}\begin{verbatim} b0 -2.141025782776D+01 b1 2.159799627973D+00 b2 -2.275674008102D+00 b3 5.413573872835D-01 b4 -6.391621888218D-03 b5 1.566655266221D-02 b6 -1.068539042185D-02 b7 1.770824218105D-03 b8 -9.267718112477D-05 Max. rel. Error: 10.9657 % Mean rel. Error: 6.2957 % \end{verbatim} \end{small} same as 3-2-3, above, previous reaction, but here evaluated with old default $H_2$ energy: E = 0.37 eV, rather than the current choice of E =0.1 eV. Old data are kept here only for backward compatibility. (The old rate coefficient is mostly used in ITER applications and SOLPS4.x in general). Strictly this rate coefficient should be evaluated for stationary $H_2$ (energy=0.0) to permit correct mass scaling in the Maxwellian averages. \\ Competing process at low T: see above: dissociative electron attachment, process 2-2-17 \begin{figure} \label{3.2.3o} \epsfxsize=16truecm \epsffile{Amjuel_PS/ionconv_2.eps} \end{figure} \newpage Next few reactions: rate coefficients, vs. Te, for a number of $N_2, N_2^+$ corona dissociation and ionisation channels \subsection{ Reaction 2.7.5 $e + N_2 \rightarrow e + N + N$ } Dissociation from ground state $N_2$, cross-section from \cite{kn:Cosby}, $\Delta E_{el} = 9.7527 $ eV, KER: 0.95 eV (spectra with two peaks, at 0.8 and 1.1 eV resp.) \begin{small}\begin{verbatim} b0 -3.093625000000E+01 b1 1.094180000000E+01 b2 -2.878686000000E+00 b3 -2.524814000000E-01 b4 3.966283000000E-01 b5 -1.209670000000E-01 b6 1.849840000000E-02 b7 -1.461561000000E-03 b8 4.746380000000E-05 \end{verbatim}\end{small} \subsection{ Reaction 2.7.9 $e + N_2 \rightarrow e + N_2^+ + e$ } ionisation cross-section: total: \cite{kn:Rapp1}, I, DI separate \cite{kn:Rapp2} (branching ratio R(E)) Here: ionisation to $N_2^+$ \\ $\Delta E_{el} = 15.581 $ eV KER=0. \begin{small}\begin{verbatim} b0 -3.455402000000E+01 b1 1.633449000000E+01 b2 -7.480952000000E+00 b3 2.334744000000E+00 b4 -5.161607000000E-01 b5 7.902320000000E-02 b6 -7.919992000000E-03 b7 4.635395000000E-04 b8 -1.191714000000E-05 \end{verbatim}\end{small} \subsection{ Reaction 2.7.10 $e + N_2 \rightarrow e + N + N^+ +e$ } ionisation cross-section: total: \cite{kn:Rapp1}, I, DI separate \cite{kn:Rapp2} (branching ratio R(E)) Here: dissociative ionisation to $N + N^+$ \\ $\Delta E_{el} = 24.34 $ eV, KER: 8 eV (estimated, not clearly specified in paper) \begin{small}\begin{verbatim} b0 -4.583945000000E+01 b1 2.487449000000E+01 b2 -1.169168000000E+01 b3 4.066783000000E+00 b4 -1.070205000000E+00 b5 1.985772000000E-01 b6 -2.383370000000E-02 b7 1.636738000000E-03 b8 -4.849195000000E-05 \end{verbatim}\end{small} \begin{figure} \label{n2rates} \epsfxsize=16truecm \epsffile{Amjuel_PS/n2-rates.eps} \end{figure} \newpage \subsection{ Reaction 2.7.11 $e + N_2^+ \rightarrow e + 2 N^+ +e$ } Dissociative ionisation, cross-section: \cite{kn:Bahati} $\Delta E_{el} = 31.2 $ eV, KER: max: 11.8 eV \begin{small}\begin{verbatim} b0 -5.137074000000E+01 b1 3.135383000000E+01 b2 -1.560923000000E+01 b3 5.444979000000E+00 b4 -1.354319000000E+00 b5 2.264527000000E-01 b6 -2.359782000000E-02 b7 1.362664000000E-03 b8 -3.285464000000E-05 \end{verbatim}\end{small} \subsection{ Reaction 2.7.12 $e + N_2^+ \rightarrow e + N + N^+ $ } Dissociative excitation, cross-section: \cite{kn:Bahati} $\Delta E_{el} = 8.4 $ eV, KER: max. of 6.4 eV at 120 eV, KER nearly = 0 near threshold (i.e. pre-dissociation via various channels). \begin{small}\begin{verbatim} b0 -2.695366000000E+01 b1 8.978136000000E+00 b2 -4.296075000000E+00 b3 1.392124000000E+00 b4 -3.247302000000E-01 b5 5.222337000000E-02 b6 -5.327033000000E-03 b7 3.023081000000E-04 b8 -7.105405000000E-06 \end{verbatim}\end{small} \subsection{ Reaction 2.7.14 $e + N_2^+ \rightarrow N + N$ } Dissociative recombination, cross-section: \cite{kn:Petersen} $\Delta E_{el}$ can be taken from electron energy weighted rate coefficient. KER: 1.06 - 5.824 eV at zero electron impact energy, depending on vibrational state of $N_2^+$ and electronic state of products. Suggestion: KER = 3.5 eV \begin{small}\begin{verbatim} b0 -1.668240000000E+01 b1 -0.300000000000E+00 b2 0.000000000000E+00 b3 0.000000000000E+00 b4 0.000000000000E+00 b5 0.000000000000E+00 b6 0.000000000000E+00 b7 0.000000000000E+00 b8 0.000000000000E+00 \end{verbatim}\end{small} \subsection{ Reaction 2.7.15 $e + N_2^+ \rightarrow e + N_2^{++} +e$ } Single ionisation of $N_2^+$, cross-section: \cite{kn:Bahati} $\Delta E_{el} = 27.12 $ eV, KER=0. \begin{small}\begin{verbatim} b0 -4.675067000000E+01 b1 2.768681000000E+01 b2 -1.260874000000E+01 b3 3.402022000000E+00 b4 -5.302686000000E-01 b5 3.823736000000E-02 b6 6.310561000000E-04 b7 -2.798009000000E-04 b8 1.272992000000E-05 \end{verbatim}\end{small} \begin{figure} \label{n2+} \epsfxsize=16truecm \epsffile{Amjuel_PS/n2+-rates.eps} \end{figure} \newpage \subsection{ Reaction 2.2FJ $e + He(1s^21S) \rightarrow e + He^+(1s) + e$ } Freeman and Jones rate coefficient for electron impact ionization of helium atoms \cite{kn:Freeman} . \begin{small}\begin{verbatim} b0 -0.445091700000e+02 b1 0.244298800000e+02 b2 -0.102571400000e+02 b3 0.247093100000e+01 b4 -0.342636620000e+00 b5 0.250510000000e-01 b6 -0.743867500000e-03 b7 0.000000000000e-00 b8 0.000000000000e+00 \end{verbatim}\end{small} \newpage this page is intentionally left blank \newpage Data from impurity transport code ``STRAHL" (K. Behringer) \cite{kn:Behringer} All reaction data with label ..aB0 or ..aB1 are taken from that reference. ``a'' is the nuclear charge number. aB0: ionisation of neutral atom. aB1: ionisation of singly charged ion. Ionization Rate for neutral Helium Atoms \subsection{ Reaction 2.2B0 $e + He(1s^21S) \rightarrow e + He^+(1s) + e $ } \begin{small}\begin{verbatim} b0 -4.445750823378D+01 b1 2.505856927901D+01 b2 -1.196552488672D+01 b3 3.715887422949D+00 b4 -7.729722462758D-01 b5 1.055704673374D-01 b6 -9.047513943647D-03 b7 4.403714187787D-04 b8 -9.276447001487D-06 Max. rel. Error: 0.4138 % Mean rel. Error: 0.1636 % \end{verbatim}\end{small} Ionization Rate for single charged Helium Ions \subsection{ Reaction 2.2B1 $e + He^+(1s) \rightarrow e + He^{++} + e$ } \begin{small}\begin{verbatim} b0 -7.559669902889D+01 b1 5.464529470916D+01 b2 -2.644507121426D+01 b3 8.159073714053D+00 b4 -1.694080618046D+00 b5 2.348225872648D-01 b6 -2.073277438991D-02 b7 1.049056816265D-03 b8 -2.305310731172D-05 Max. rel. Error: 0.9472 % Mean rel. Error: 0.5457 % \end{verbatim}\end{small} \begin{figure} \label{2.2B} \epsfxsize=16truecm \epsffile{Amjuel_PS/fig2_2B.ps} \end{figure} \newpage Ionization Rates for neutral Beryllium Atoms \subsection{ Reaction 2.4B0 $e + Be \rightarrow e + Be^+ + e $ } \begin{small}\begin{verbatim} b0 -2.701191641765D+01 b1 9.882275334399D+00 b2 -4.581384174259D+00 b3 1.463446005529D+00 b4 -3.282155444497D-01 b5 4.895458945839D-02 b6 -4.558103660501D-03 b7 2.382205094374D-04 b8 -5.319547065990D-06 Max. rel. Error: .1411 % Mean rel. Error: .0582 % \end{verbatim}\end{small} Ionization Rates for single charged Beryllium Ions \subsection{ Reaction 2.4B1 $e + Be^+ \rightarrow e + Be^{++} + e $ } \begin{small}\begin{verbatim} b0 -3.677989427190D+01 b1 1.855869089956D+01 b2 -8.843053626300D+00 b3 2.708167857179D+00 b4 -5.651333671979D-01 b5 7.947570447499D-02 b6 -7.160867067297D-03 b7 3.705422825861D-04 b8 -8.322700230771D-06 Max. rel. Error: .3962 % Mean rel. Error: .2225 % \end{verbatim}\end{small} \begin{figure} \label{2.4B} \epsfxsize=16truecm \epsffile{Amjuel_PS/beryi.ps} \end{figure} \newpage \subsection{ Reaction 2.5B0 $e + B \rightarrow e + B^+ + e $ } Ionization Rates for neutral Boron Atoms \begin{small}\begin{verbatim} b0 -2.652112807432D+01 b1 8.818502481012D+00 b2 -3.832208851779D+00 b3 1.206778920817D+00 b4 -2.766330884306D-01 b5 4.255759023412D-02 b6 -4.078840883672D-03 b7 2.185455019432D-04 b8 -4.985646766233D-06 \end{verbatim}\end{small} \subsection{ Reaction 2.5B1 $e + B^+ \rightarrow e + B^{++} + e $ } Ionization Rates for single charged Boron Ions \begin{small}\begin{verbatim} b0 -4.420568125967D+01 b1 2.558429301929D+01 b2 -1.226766585830D+01 b3 3.790617724445D+00 b4 -7.898969090461D-01 b5 1.094004163863D-01 b6 -9.602179535698D-03 b7 4.812751663763D-04 b8 -1.045722639512D-05 \end{verbatim}\end{small} \newpage This page is intentionally left blank \newpage \subsection{ Reaction 2.6B0 $e + C \rightarrow e + C^+ + e $ } Ionization rate for neutral Carbon Atoms $ \langle sigma*vrel \rangle(Te) (cm**3/s), C --> C^+$ \begin{small}\begin{verbatim} b0 -2.955122753053D+01 b1 1.180604026361D+01 b2 -5.438799573749D+00 b3 1.750648117869D+00 b4 -3.946542606866D-01 b5 5.887749368990D-02 b6 -5.469027807326D-03 b7 2.850693136991D-04 b8 -6.354758903485D-06 Max. rel. Error: .3712 % Mean rel. Error: .1458 % \end{verbatim}\end{small} \subsection{ Reaction 2.6B1 $e + C^+ \rightarrow e + C^{++} + e $ } Ionization rate for Carbon Ions \begin{small}\begin{verbatim} b0 -4.406752926798D+01 b1 2.464907506907D+01 b2 -1.157330396759D+01 b3 3.619195611010D+00 b4 -7.853469883899D-01 b5 1.149856668829D-01 b6 -1.070995852675D-02 b7 5.681198605329D-04 b8 -1.299242985961D-05 Max. rel. Error: .9478 % Mean rel. Error: .4820 % \end{verbatim}\end{small} \newpage This page is intentionally left blank \newpage \subsection{ Reaction 2.7B0 $e + N \rightarrow e + N^+ + e $ } Ionization rate coefficient for neutral Nitrogen Atoms (Bell et al., CLM-R216) \cite{kn:Bell} $ \langle sigma*vrel \rangle(Te) (cm**3/s), N --> N^+$ \begin{small}\begin{verbatim} b0 -3.267927139870D+01 b1 1.487745850177D+01 b2 -7.393982038208D+00 b3 2.552657836634D+00 b4 -6.031414732283D-01 b5 9.299608313666D-02 b6 -8.862541230616D-03 b7 4.718778196780D-04 b8 -1.071093371002D-05 \end{verbatim}\end{small} \subsection{ Reaction 2.7 $e + N \rightarrow e + N^+ + e $ } cross-section data from Brook, \cite{kn:Brook} for $ e + N -> N^+ + 2e $, same cross-section data source was used for the Bell rate coefficient. (Checked, Oct.2013: original Bell report and Brook cross-sections are identical) $\Delta E_{el} = 14.5$ \begin{small}\begin{verbatim} b0 -3.218851E+01 b1 1.430745E+01 b2 -6.932106E+00 b3 2.271990E+00 b4 -4.951687E-01 b5 6.792600E-02 b6 -5.419575E-03 b7 2.123706E-04 b8 -2.405294E-06 \end{verbatim}\end{small} \begin{figure} \label{2.7B0} \epsfxsize=16truecm \epsffile{Amjuel_PS/nitri.ps} \end{figure} \newpage \subsection{ Reaction 2.8B0 $e + O \rightarrow e + O^+ + e $ } Ionization rate for neutral Oxygen Atoms $ \langle sigma*vrel \rangle(Te) (cm**3/s), O --> O^+$ \begin{small}\begin{verbatim} b0 -3.193820900000D+01 b1 3.246161040000D+01 b2 -3.545538700000D+01 b3 2.559678950000D+01 b4 -1.215735520000D+01 b5 3.673666600000D+00 b6 -6.763574930000D-01 b7 6.905007430000D-02 b8 -2.994628570000D-03 \end{verbatim}\end{small} \subsection{ Reaction 2.8B1 $e + O^+ \rightarrow e + O^{++} + e $ } Ionization rate for singly charged Oxygen Ions \begin{small}\begin{verbatim} b0 -5.489947730000D+01 b1 8.1057031200000D+01 b2 -8.7719154800000D+01 b3 6.043339780000D+01 b4 -2.7530283600000D+01 b5 8.1635002700000D+00 b6 -1.505562720000D+00 b7 1.5615477900000D-01 b8 -6.9385679400000D-03 \end{verbatim}\end{small} Ionization Rate for neutral Neon Atoms \subsection{ Reaction 2.10B0 $e + Ne \rightarrow e + Ne^+ + e $ } \begin{small}\begin{verbatim} b0 -4.164979646286D+01 b1 2.217184105146D+01 b2 -1.042613793789D+01 b3 3.175650981066D+00 b4 -6.293446783142D-01 b5 7.941711930007D-02 b6 -6.140370720421D-03 b7 2.651559926489D-04 b8 -4.900429196295D-06 Max. rel. Error: .0200 % Mean rel. Error: .0103 % \end{verbatim}\end{small} Ionization Rate for single charged Neon Ions \subsection{ Reaction 2.10B1 $ e + Ne^+ \rightarrow e + Ne^{++} + e $ } \begin{small}\begin{verbatim} b0 -6.100121276752D+01 b1 4.015006828838D+01 b2 -1.879440280294D+01 b3 5.630907545903D+00 b4 -1.119573454119D+00 b5 1.458082247661D-01 b6 -1.192136518944D-02 b7 5.544020624369D-04 b8 -1.117943418062D-05 Max. rel. Error: .1916 % Mean rel. Error: .0814 % \end{verbatim}\end{small} \begin{figure} \label{2.10B0} \epsfxsize=16truecm \epsffile{Amjuel_PS/neoni.ps} \end{figure} \newpage \subsection{ Reaction 2.18B0 $e + Ar \rightarrow e + Ar^+ + e$ } Ionization Rate for neutral Argon Atoms \begin{small}\begin{verbatim} b0 -3.330347417325D+01 b1 1.627861918393D+01 b2 -7.765170847889D+00 b3 2.446384994382D+00 b4 -5.186581624286D-01 b5 7.184868450814D-02 b6 -6.200405891186D-03 b7 3.018464732517D-04 b8 -6.325074170944D-06 Max. rel. Error: .1093 % Mean rel. Error: .0503 % \end{verbatim}\end{small} \subsection{ Reaction 2.18B1 $e + Ar^+ \rightarrow e + Ar^{++} + e$ } Ionization Rate for single charged Argon Ions \begin{small}\begin{verbatim} b0 -4.577132769437D+01 b1 2.796761945871D+01 b2 -1.347073209993D+01 b3 4.188634468306D+00 b4 -8.778893409977D-01 b5 1.220883796618D-01 b6 -1.073976899816D-02 b7 5.386460788345D-04 b8 -1.169793339733D-05 Max. rel. Error: .3659 % Mean rel. Error: .2214 % \end{verbatim}\end{small} \begin{figure} \label{2.18B} \epsfxsize=16truecm \epsffile{Amjuel_PS/argi.ps} \end{figure} \newpage \subsection{ Reaction 2.26B0 $e + Fe \rightarrow e + Fe^+ + e$ } Ionization Rate for neutral Iron Atoms \begin{small}\begin{verbatim} b0 -2.457959373433D+01 b1 8.433391049230D+00 b2 -3.846892092374D+00 b3 1.185976759143D+00 b4 -2.459329335625D-01 b5 3.266162856106D-02 b6 -2.642594731066D-03 b7 1.182305727446D-04 b8 -2.237621366618D-06 Max. rel. Error: .0907 % Mean rel. Error: .0450 % \end{verbatim}\end{small} \subsection{ Reaction 2.26B1 $e + Fe^+ \rightarrow e + Fe^{++} + e$ } Ionization Rate for single charged Iron Ions \begin{small}\begin{verbatim} b0 -3.437574762141D+01 b1 1.685181764677D+01 b2 -7.911217139035D+00 b3 2.442620345655D+00 b4 -5.072788444089D-01 b5 6.899131935535D-02 b6 -5.866292819569D-03 b7 2.825378750379D-04 b8 -5.881378739141D-06 Max. rel. Error: .2106 % Mean rel. Error: .1105 % \end{verbatim}\end{small} \begin{figure} \label{2.26B} \epsfxsize=16truecm \epsffile{Amjuel_PS/fei.ps} \end{figure} \subsection{ Reaction 3.1 $W + e \rightarrow W^+ + 2e $ } \begin{small}\begin{verbatim} %tungsten coef. rate b0 -23.79630000000D+00 b1 8.522300000000D+00 b2 -4.027100000000D+00 b3 1.339000000000D+00 b4 -0.339800000000D+00 b5 0.063800000000D+00 b6 -0.008200000000D+00 b7 0.000600000000D+00 b8 0.000000000000D+00 \end{verbatim}\end{small} \newpage \section{H.3 : Fits for $\langle\sigma v \rangle (E,T)$}\label{sect3} \subsection{ Reaction 0.1T $p + H(1s) \rightarrow p + H(1s)$ , elastic, $\ I_{0,0}$ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -1.823472394862D+01 1.043929094352D-01 3.385021298310D-02 1 1.218869427323D-01 -8.071776515805D-02 -6.163024588310D-03 2 2.183144859635D-02 6.947238019788D-03 -1.029753867911D-02 3 -8.144414285471D-03 7.950619428888D-03 1.480212482573D-03 4 -2.414158185489D-03 -1.610515523206D-03 1.147576632073D-03 5 4.042335482230D-04 -3.333068266837D-04 -2.109287055048D-04 6 6.684610364551D-05 1.395481729149D-04 -3.872093410396D-05 7 -1.814826813629D-05 -1.589238118662D-05 1.137141330233D-05 8 1.049993252610D-06 6.124957529757D-07 -6.966443729323D-07 E-Index: 3 4 5 T-Index: 0 -2.048059867515D-03 -4.577324303045D-03 5.174052650323D-05 1 8.404776509987D-03 5.448141329729D-04 -6.017991251450D-04 2 -1.660137737426D-03 1.687354957150D-03 1.123876140912D-05 3 -1.907814505083D-03 2.558232467687D-05 1.587671168547D-04 4 5.801892116713D-04 -2.945348864215D-04 -2.556467005779D-05 5 8.053144974289D-05 2.875034864587D-05 -9.746625582656D-06 6 -5.043290334814D-05 1.493675458929D-05 3.216371174204D-06 7 6.798870422148D-06 -3.269371275613D-06 -3.202325463122D-07 8 -3.006730549005D-07 1.854263211106D-07 1.033863743276D-08 E-Index: 6 7 8 T-Index: 0 2.673201510283D-04 -4.451268371503D-05 2.199498285047D-06 1 3.536937592691D-05 9.054714466075D-06 -8.596768109209D-07 2 -1.224423097417D-04 2.126181472934D-05 -1.100195177512D-06 3 -2.858120151811D-05 1.112919746718D-06 4.374805864224D-08 4 2.747846551451D-05 -4.380086290415D-06 2.202510674285D-07 5 -6.360748557750D-07 3.783870577323D-07 -2.732689440408D-08 6 -1.738436960565D-06 2.363371059212D-07 -1.072861195261D-08 7 3.156490387804D-07 -5.006550452098D-08 2.526895478569D-09 8 -1.655735806555D-08 2.801053970232D-09 -1.467609659450D-10 Max. rel. Error: 0.5284 % Mean rel. Error: 0.0853 % \end{verbatim}\end{small} \begin{figure} \label{0.1T} \epsfxsize=16truecm \epsffile{Amjuel_PS/bachr1.ps} \end{figure} \newpage \subsection{ Reaction 0.1D $p + H(1s) \rightarrow p + H(1s)$ , elastic, $\ I_{1,0}$ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -1.934778779385D+01 2.193162842747D-02 -5.787610534513D-04 1 8.400121290584D-04 -5.025758478606D-02 9.405606314808D-03 2 -1.072570686950D-02 1.258217951174D-02 -7.629292880371D-03 3 -7.329656452946D-03 1.017355462044D-02 -2.212101744320D-03 4 -1.548110966373D-03 -4.141816249813D-03 1.623377903131D-03 5 8.780715214347D-05 -5.483013774324D-04 1.371503461028D-04 6 6.351915617491D-05 4.711920962053D-04 -1.702351291260D-04 7 -1.071915622348D-05 -7.653900655552D-05 2.828377077442D-05 8 5.468789447600D-07 3.989227802803D-06 -1.457895095025D-06 E-Index: 3 4 5 T-Index: 0 -9.555854995025D-03 -3.071069026823D-03 5.668304238739D-04 1 1.213464571187D-02 -3.615417883123D-03 -8.289738887452D-04 2 -3.222678509228D-03 2.181349883244D-03 1.491076548317D-04 3 -4.530314087059D-03 1.707627243838D-03 3.285319171515D-04 4 1.894095127078D-03 -8.173359548467D-04 -1.268607651578D-04 5 2.806873100807D-04 -1.147859100868D-04 -2.036026302326D-05 6 -2.386998803904D-04 9.947217842552D-05 1.676927171418D-05 7 3.936468195914D-05 -1.609704117822D-05 -2.801579443731D-06 8 -2.077060263537D-06 8.298532548793D-07 1.504259503231D-07 E-Index: 6 7 8 T-Index: 0 1.023499873278D-04 -4.375997865613D-05 3.554762032992D-06 1 4.794896057762D-04 -7.011568552117D-05 3.413857855011D-06 2 -2.352460376261D-04 4.210499686989D-05 -2.314387560956D-06 3 -2.365796504952D-04 3.759133611684D-05 -1.934588738006D-06 4 1.083092577128D-04 -1.817871861306D-05 9.758474990215D-07 5 1.584828965214D-05 -2.554030249359D-06 1.314431146313D-07 6 -1.358046593907D-05 2.254690862488D-06 -1.202340694084D-07 7 2.216781743757D-06 -3.678764178035D-07 1.970465840287D-08 8 -1.154459633382D-07 1.906633038081D-08 -1.021379321893D-09 Max. rel. Error: 2.5240 Mean rel. Error: 0.4077 \end{verbatim}\end{small} \newpage This page is intentionally left blank \newpage \subsection{ Reaction 0.2T $ p + He(1s^21S) \rightarrow p + He(1s^21S) ,\ $ elastic, $ \ I_{0,0} $ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -1.934393021918D+01 6.563446707236D-02 -1.132533853318D-01 1 1.301350106064D-01 -4.071555273225D-02 2.016906859537D-02 2 1.828664127573D-02 1.460635793653D-02 6.745665311224D-03 3 -1.572566883649D-02 -3.953675178715D-03 1.747850519967D-03 4 -1.651243630315D-02 -2.847284094044D-04 -1.016420463987D-03 5 1.536731193440D-03 5.204625005620D-04 -1.110404741405D-04 6 1.407936221176D-03 -1.273303544933D-04 7.874267771795D-05 7 -3.024575206489D-04 1.258652128299D-05 -9.943699290077D-06 8 1.717075379788D-05 -4.489657191575D-07 3.942435517534D-07 E-Index: 3 4 5 T-Index: 0 -2.108203840264D-02 5.126981927132D-02 -3.332060792240D-03 1 4.145056754712D-03 -1.207683748654D-02 9.777916409735D-04 2 -2.343836845279D-03 -2.643817205066D-03 4.122233549648D-04 3 1.316616725294D-03 -3.328603688720D-04 -1.025202074732D-04 4 2.115185323595D-04 3.305924890461D-04 -4.422649148500D-05 5 -2.096646478748D-04 4.907753719257D-05 1.750257851569D-05 6 3.694523090258D-05 -3.137559296212D-05 -2.054573401396D-06 7 -2.076330117601D-06 3.934064976552D-06 7.117080375326D-08 8 5.837947019108D-09 -1.543181228289D-07 1.142825149606D-09 E-Index: 6 7 8 T-Index: 0 -5.396242466413D-03 1.236276138019D-03 -7.628885182442D-05 1 1.273531852240D-03 -3.057392495993D-04 1.949879233267D-05 2 2.238463116916D-04 -5.822708605029D-05 3.713522343609D-06 3 3.644852940119D-05 -2.948705115200D-06 2.772902778994D-08 4 -2.296832307757D-05 5.703124977270D-06 -3.560603032570D-07 5 -7.404629231556D-06 8.730873892378D-07 -3.238131969596D-08 6 3.004305767140D-06 -4.823864866020D-07 2.370653749977D-08 7 -3.116821151336D-07 4.985170981511D-08 -2.366645009836D-09 8 9.670471248063D-09 -1.366953072466D-09 5.308492125136D-11 Max. rel. Error: 43.0372 % Mean rel. Error: 3.6615 % \end{verbatim}\end{small} \begin{figure} \label{0.2T} \epsfxsize=16truecm \epsffile{Amjuel_PS/bachr2.ps} \end{figure} \newpage \subsection{ Reaction 0.2D $ p + He(1s^21S) \rightarrow p + He(1s^21S) ,\ $ elastic, $ \ I_{1,0} $ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.038078616420D+01 -4.993496998398D-02 2.460551521383D-02 1 -3.301657139332D-01 -3.084287321372D-02 1.554461839749D-02 2 -1.250516030333D-01 3.495799299565D-02 -1.424614705786D-02 3 6.328424290736D-03 -3.821208294684D-03 -1.623627120526D-03 4 1.127524699096D-02 -2.410962290755D-03 1.757598241612D-03 5 -1.287708708939D-03 4.847023005705D-04 9.455808977270D-05 6 -6.368309748535D-04 4.413818051866D-05 -1.552922023412D-04 7 1.421859797928D-04 -1.659744792044D-05 2.551798508100D-05 8 -8.055939868827D-06 1.038460845033D-06 -1.289836231544D-06 E-Index: 3 4 5 T-Index: 0 -1.517017165274D-02 -2.397648448576D-02 3.029365163804D-03 1 3.040700264374D-02 -2.593835985009D-03 -3.146176415388D-03 2 -9.657174093701D-03 7.433666067399D-03 4.191585645845D-04 3 -2.321909525809D-03 7.614727149051D-04 2.681001889717D-04 4 1.188908537635D-03 -1.115315269461D-03 -4.859218322237D-05 5 3.089582619996D-05 7.699187722499D-06 -8.863762072239D-06 6 -6.629197652130D-05 8.154996921696D-05 1.796356820001D-06 7 9.800954064911D-06 -1.473582389149D-05 6.040382986474D-08 8 -4.465334549154D-07 7.821310450330D-07 -1.548297648690D-08 E-Index: 6 7 8 T-Index: 0 2.120043324652D-03 -5.206063712236D-04 3.229462400161D-05 1 6.652125688558D-04 -2.834612166641D-05 -1.127219264426D-06 2 -8.556829101842D-04 1.582340533265D-04 -8.789744795492D-06 3 -1.226460004470D-04 1.517380199975D-05 -6.070841562603D-07 4 1.341954089088D-04 -2.572769659598D-05 1.459166812937D-06 5 -8.619326544178D-07 6.166331772717D-07 -5.093661426041D-08 6 -9.360612397745D-06 1.830066731050D-06 -1.043424396036D-07 7 1.676084936402D-06 -3.453407619810D-07 2.029350887316D-08 8 -8.843599781403D-08 1.879251002731D-08 -1.123059892608D-09 Max. rel. Error: 4.5211 Mean rel. Error: 1.0118 \end{verbatim}\end{small} \newpage This page is intentionally left blank \newpage \subsection{ Reaction 0.3T $p + H_2 \rightarrow p + H_2 ,\ $ elastic, $\ I_{0,0}$ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -1.850658754996D+01 7.211082264457D-02 2.881570478725D-02 1 2.020169165482D-01 -6.382135800278D-02 -1.628749501583D-02 2 2.598024510290D-02 1.330939790463D-02 -3.589374170071D-03 3 -1.678447543630D-02 1.969680248144D-03 2.420309504140D-03 4 -3.805013471382D-03 -8.538366688716D-04 1.219958125509D-04 5 5.832875302941D-04 1.404105142335D-05 -1.373999872185D-04 6 1.183272287480D-04 1.754003746153D-05 4.575214200943D-06 7 -9.013768167130D-06 -1.593144865711D-06 2.703806954321D-06 8 -7.237839929582D-07 1.856207389335D-08 -2.288152742189D-07 E-Index: 3 4 5 T-Index: 0 2.824670772476D-03 -1.925459417470D-03 -3.785321033027D-04 1 3.609681973946D-03 2.430555593258D-03 -5.689585982541D-04 2 -2.973717962634D-03 -2.983530508154D-05 4.140245564780D-04 3 1.164630658778D-04 -3.334041165620D-04 -1.688850581453D-05 4 2.448727242148D-04 3.615934391216D-06 -2.949112340307D-05 5 -3.662763983152D-05 2.253519645066D-05 4.135548971992D-06 6 -4.332949346678D-06 -1.278290014948D-06 5.039287664347D-07 7 1.185717497396D-06 -5.094274460491D-07 -1.239318519727D-07 8 -6.264732541905D-08 4.920894679796D-08 5.881467421248D-09 E-Index: 6 7 8 T-Index: 0 1.364568368798D-04 1.549425706176D-05 -6.618501118923D-06 1 -1.393818486289D-04 6.326271239195D-05 -6.695217940204D-06 2 -9.885614172244D-06 -3.254217622645D-05 4.703412615895D-06 3 1.899933955654D-05 -1.395858712371D-06 6.819987383210D-08 4 1.515103150938D-06 1.989212957512D-06 -3.032181942708D-07 5 -1.527239138118D-06 -2.816863864732D-08 1.345210099656D-08 6 3.182007050723D-08 -4.398423525407D-08 6.503053760354D-09 7 3.952472363950D-08 8.350979668461D-10 -3.926411713518D-10 8 -3.379572792986D-09 3.141592395102D-10 -2.459493010474D-11 Max. rel. Error: 3.4420 % Mean rel. Error: 1.2045 % Ti: 0.01---1000, EB: 0.1---100 \end{verbatim}\end{small} \begin{figure} \label{0.3T} \epsfxsize=16truecm \epsffile{Amjuel_PS/bachr3.ps} \end{figure} \newpage \subsection{ Reaction 0.3D $p + H_2 \rightarrow p + H_2 ,\ $ elastic, $\ I_{1,0}$ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -1.919275366997D+01 -1.865238346305D-02 4.682617815803D-02 1 -5.947780482087D-02 -5.971382726967D-02 5.854568958623D-03 2 -9.004077564531D-02 3.225709371997D-02 -6.402554946956D-03 3 -1.870459871354D-02 -1.438038218134D-03 2.190778358004D-03 4 1.491376597764D-02 -1.614133948666D-03 -1.009422051586D-03 5 9.563126960467D-04 3.707880488168D-04 -7.731975035804D-05 6 -1.330077285945D-03 -5.353962725785D-05 1.351235395106D-04 7 2.020583687196D-04 6.849923024482D-06 -2.550615695507D-05 8 -9.277851726161D-06 -4.082429350941D-07 1.441579661485D-06 E-Index: 3 4 5 T-Index: 0 -8.932266130300D-03 -2.903882752834D-02 3.477806471368D-03 1 1.637194804434D-02 -3.291459604645D-04 -1.492225099738D-03 2 -1.308998760658D-03 2.367849536658D-03 -2.633913429665D-04 3 -2.828299306442D-04 -4.686890203582D-07 4.818941917867D-05 4 -5.326505552258D-04 1.673303613736D-04 6.564947466483D-05 5 2.493241008729D-05 -2.434562819338D-05 -5.585591947606D-06 6 6.595946297185D-05 -2.509630806820D-05 -5.474903148493D-06 7 -1.420945572125D-05 6.290869308799D-06 1.207885423899D-06 8 8.431661832790D-07 -4.002257378192D-07 -7.135379893415D-08 E-Index: 6 7 8 T-Index: 0 2.790218940150D-03 -6.908438427090D-04 4.338681573230D-05 1 1.443370523034D-04 2.409850106077D-05 -2.849926680503D-06 2 -1.712112384677D-04 4.233619961041D-05 -2.665571098691D-06 3 -1.902274102571D-05 2.446426035585D-06 -9.693955463859D-08 4 -2.847616427622D-05 3.578927723952D-06 -1.517016799547D-07 5 4.669438326556D-06 -7.601170248698D-07 3.823110747713D-08 6 3.257943960303D-06 -4.775908920414D-07 2.342435491722D-08 7 -8.361574596535D-07 1.290522448864D-07 -6.505820743915D-09 8 5.318078186713D-08 -8.385721089159D-09 4.277930018700D-10 Max. rel. Error: 5.2866 Mean rel. Error: 1.2591 \end{verbatim}\end{small} \newpage This page is intentionally left blank \newpage \subsection{ Reaction 0.4T $He^+(1s) + He(1s^21S) \rightarrow He^+(1s) + He(1s^21S) ,\ $ elastic, $\ I_{0,0}$ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -1.932287393135D+01 -6.254173654177D-02 7.946623543420D-02 1 7.420452433663D-02 -1.124812231885D-02 -2.699799758379D-02 2 4.578246117879D-02 5.807748349427D-03 -6.767337797049D-03 3 9.376519610500D-03 3.743869063612D-03 1.935668442071D-03 4 -1.232363387636D-02 -1.100675144650D-03 3.439916049619D-04 5 -1.307054294818D-03 -8.910211076373D-05 -1.851109052007D-04 6 1.118562583548D-03 5.617956521495D-05 4.722943119535D-05 7 -1.434031268233D-04 -6.365356860650D-06 -7.103013883339D-06 8 5.358989072610D-06 2.334269507353D-07 4.090109024266D-07 E-Index: 3 4 5 T-Index: 0 8.838505558116D-02 -2.793201134092D-02 -9.954061526499D-03 1 -1.884565424365D-02 1.123857510199D-02 1.596841699378D-03 2 -2.495042935023D-03 1.439511185350D-04 2.861967025267D-04 3 -2.047050990056D-03 -1.947991019023D-04 2.018359028340D-04 4 7.434976678383D-04 -4.730384293613D-05 -6.250784297096D-05 5 1.117168152610D-04 3.115251093953D-05 -1.325389437604D-05 6 -5.881739628460D-05 -1.308533305864D-05 6.051250040246D-06 7 6.666955388827D-06 2.380955160803D-06 -7.094040977952D-07 8 -2.367498282831D-07 -1.427503775556D-07 2.786934787376D-08 E-Index: 6 7 8 T-Index: 0 3.764403463819D-03 -3.408466490224D-04 6.412518246520D-06 1 -1.389644457539D-03 2.161107270253D-04 -1.049187773127D-05 2 -4.171591875990D-06 -1.196874977368D-05 1.094079145119D-06 3 -1.598805546650D-05 -2.311078550298D-06 2.483893468689D-07 4 1.280702702425D-05 -7.877322455546D-07 9.482501133602D-09 5 -2.131389375108D-07 3.650222503579D-07 -2.688165319879D-08 6 1.603031094261D-07 -1.683294115673D-07 1.140269704662D-08 7 -1.056486811884D-07 3.540020523528D-08 -2.124298972987D-09 8 9.141132772747D-09 -2.324505150923D-09 1.328831955405D-10 Max. rel. Error: 45.6817 Mean rel. Error: 5.1917 \end{verbatim}\end{small} \begin{figure} \label{0.4T} \epsfxsize=16truecm \epsffile{Amjuel_PS/bachr4.ps} \end{figure} \newpage \subsection{ Reaction 0.4D $He^+(1s) + He(1s^21S) \rightarrow He^+(1s) + He(1s^21S) ,\ $ elastic, $\ I_{1,0}$ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.005856706409D+01 -2.416298567134D-02 -1.290643907647D-01 1 -1.723033466633D-01 -2.876974997211D-02 6.358697996829D-02 2 -8.480540790141D-02 2.121102722373D-02 1.060648053441D-03 3 -1.583772608067D-02 2.831738365425D-04 3.604228124024D-04 4 7.141918601934D-03 -2.712847139884D-03 -1.390046088713D-03 5 1.050415524504D-03 3.514199969505D-04 -1.430457735837D-04 6 -5.609743409859D-04 1.114910501595D-04 1.776137463792D-04 7 5.528775780351D-05 -2.849479698839D-05 -2.957402039735D-05 8 -1.298487796038D-06 1.744141312203D-06 1.511018855995D-06 E-Index: 3 4 5 T-Index: 0 -7.609374902789D-02 2.051842775759D-02 6.700343984959D-03 1 1.484173774740D-02 -1.259800535085D-02 -3.314345389346D-04 2 7.437796246116D-03 -1.933320600619D-03 -8.197110013265D-04 3 5.722003993817D-04 1.577284882295D-04 -1.165904265498D-04 4 -7.836120750894D-04 5.279763008829D-04 7.329216329788D-05 5 -8.871424676206D-05 1.610771935311D-06 9.934442032629D-06 6 6.401396318081D-05 -5.184619145829D-05 -4.985193070868D-06 7 -7.539210289621D-06 9.524059409052D-06 4.297672500003D-07 8 2.529392826633D-07 -5.084304524420D-07 -5.932611004947D-09 E-Index: 6 7 8 T-Index: 0 -2.466827019035D-03 2.195450363238D-04 -4.275624910534D-06 1 9.943338501590D-04 -1.676144873446D-04 8.508217370560D-06 2 3.610884437671D-04 -4.659019201525D-05 2.019277552554D-06 3 1.134360853468D-05 9.293505569914D-07 -1.249357290876D-07 4 -6.844730630933D-05 1.119496625366D-05 -5.759041144367D-07 5 -1.298801064099D-06 -4.988842872544D-08 9.924160039487D-09 6 6.074150104979D-06 -1.029965177536D-06 5.399132209393D-08 7 -1.048375199655D-06 1.905679254148D-07 -1.033208843896D-08 8 5.357991449124D-08 -1.021819231976D-08 5.659599344410D-10 Max. rel. Error: 4.6006 Mean rel. Error: 1.4030 \end{verbatim}\end{small} \newpage This page is intentionally left blank \newpage \subsection{ Reaction 0.5T $p + Ne \rightarrow p + Ne ,\ $ elastic, $\ I_{0,0}$ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -1.920759314942D+01 -5.203892840321D-02 6.256738740832D-02 1 2.301174650324D-01 4.598103585536D-02 -4.529061500977D-02 2 -2.844809537536D-03 -2.458775402853D-03 5.193663554519D-03 3 -2.057818892403D-02 -7.174444135106D-03 1.007438682679D-03 4 -1.247725873726D-02 1.478687710859D-03 3.953183188726D-04 5 2.157436023407D-03 3.355091844482D-04 -8.112880498847D-05 6 9.992078785249D-04 -1.437802559650D-04 -5.015798225079D-05 7 -2.519290342081D-04 1.679868230149D-05 1.313639535025D-05 8 1.528819949488D-05 -6.582462835809D-07 -8.420538426381D-07 E-Index: 3 4 5 T-Index: 0 3.570384214557D-02 -2.599370622275D-02 -1.307788828471D-03 1 -3.361904573721D-02 1.857018937894D-02 1.960502872244D-03 2 4.605054021354D-03 -1.471661007966D-03 -3.978819729213D-04 3 3.298168445875D-03 -9.406952560414D-04 -2.831787775281D-04 4 -7.251750861538D-04 -7.779131291367D-05 8.979474917231D-05 5 -1.832873740518D-04 7.101665930610D-05 1.518922775711D-05 6 7.431587797692D-05 4.751928717840D-06 -9.288005671637D-06 7 -8.355288839969D-06 -3.287000259239D-06 1.308988935499D-06 8 3.123866169547D-07 2.487732705021D-07 -6.106353269941D-08 E-Index: 6 7 8 T-Index: 0 3.079721700396D-03 -5.958055457558D-04 3.413526344209D-05 1 -2.294912090837D-03 4.037290717482D-04 -2.198722138819D-05 2 1.769972448752D-04 -2.083969105626D-05 8.333041368586D-07 3 1.507107647921D-04 -2.125246166296D-05 9.847199659415D-07 4 -7.898054427499D-07 -3.134863355412D-06 2.737318021218D-07 5 -1.088302678431D-05 1.723721432651D-06 -8.713592846203D-08 6 7.411456169336D-07 1.836531987751D-07 -2.021065290807D-08 7 2.067606837134D-07 -9.097454398809D-08 6.730401523292D-09 8 -2.086750507882D-08 6.592902645608D-09 -4.544772018004D-10 \end{verbatim}\end{small} \begin{figure} \label{0.5T} \epsfxsize=16truecm \epsffile{Amjuel_PS/bachr5.ps} \end{figure} \newpage \subsection{ Reaction 0.5D $p + Ne \rightarrow p + Ne ,\ $ elastic, $\ I_{1,0}$ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.002574827025D+01 -9.486205506769D-03 -1.916286734818D-02 1 -2.537906409600D-01 1.220589506641D-02 -4.405411696435D-03 2 -1.492855002501D-01 2.319954090051D-04 1.263929021478D-02 3 2.277262949762D-02 -4.830188456031D-03 -2.750452234840D-03 4 1.454565132881D-02 1.634829233387D-03 -7.315594083272D-04 5 -2.459106378105D-03 3.600089747182D-05 2.671541616531D-04 6 -7.404449444601D-04 -9.641735194704D-05 -7.552824895881D-06 7 1.859174611798D-04 1.571912622960D-05 -4.091377459615D-06 8 -1.080632769187D-05 -7.917702265677D-07 3.295235267228D-07 E-Index: 3 4 5 T-Index: 0 3.064150950343D-04 5.770565072378D-03 -1.288012249760D-03 1 -9.350961151995D-03 2.046783521289D-03 1.263699863822D-03 2 5.587555734861D-03 -3.892475694794D-03 -2.567575758703D-04 3 3.929098223217D-04 4.312366386482D-04 -1.038820514086D-04 4 -7.648388450741D-04 3.694752429370D-04 4.454311674256D-05 5 9.309623048752D-05 -7.252696686113D-05 -1.552983373470D-06 6 2.291515177534D-05 -9.054806193408D-06 -1.496738021147D-06 7 -5.643860949550D-06 3.070565006104D-06 2.494317965158D-07 8 3.263260078468D-07 -1.924412405804D-07 -1.206274348614D-08 E-Index: 6 7 8 T-Index: 0 -6.056764332700D-04 1.841533150445D-04 -1.268081106690D-05 1 -3.065943896812D-04 6.450450819580D-06 1.427066945930D-06 2 4.415539725039D-04 -8.037605353389D-05 4.426529308029D-06 3 -2.150818421027D-05 8.166836349571D-06 -6.038520579569D-07 4 -5.066174985198D-05 9.122002151237D-06 -5.057086230537D-07 5 7.660825723624D-06 -1.561716894668D-06 9.411992094619D-08 6 1.670809775312D-06 -3.122277677479D-07 1.755858285560D-08 7 -4.493868279400D-07 8.907923424961D-08 -5.237533360927D-09 8 2.688180498679D-08 -5.445051092452D-09 3.250534258748D-10 \end{verbatim}\end{small} \newpage This page is intentionally left blank \newpage \subsection{ Reaction 0.6T $p + Ar \rightarrow p + Ar ,\ $ elastic, $\ I_{0,0}$ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -1.839897580907D+01 4.030184662143D-03 1.802460470789D-03 1 2.037060320748D-01 -5.396105402336D-03 -7.769954287934D-04 2 1.248391636263D-02 2.603532176725D-03 -3.227588765414D-04 3 7.219811509122D-03 -4.061565358391D-04 -3.750257185540D-04 4 -1.470827813902D-02 2.065674500382D-05 3.333229773836D-04 5 -8.480842849852D-04 -4.796563627170D-05 -5.309221423582D-05 6 1.475843994216D-03 2.151994248608D-05 -7.098388544357D-06 7 -2.369733723824D-04 -3.291364962627D-06 2.359507987294D-06 8 1.134634185229D-05 1.702489707640D-07 -1.506817496256D-07 E-Index: 3 4 5 T-Index: 0 3.294800134968D-04 1.465250143471D-04 8.663294112725D-05 1 -6.037520883955D-05 -7.833105742017D-04 -7.893554189454D-05 2 2.800210419328D-04 7.133616427016D-04 -7.316301877565D-05 3 -3.944497369254D-04 1.428880614656D-07 6.395999790794D-05 4 1.035484083951D-04 -1.259450451777D-04 -6.254483715556D-06 5 2.614410225361D-05 2.546750118822D-05 -5.673820883686D-06 6 -1.539637991363D-05 2.130859838243D-06 1.919659151259D-06 7 2.333187328954D-06 -9.290655798117D-07 -2.320465866922D-07 8 -1.174046627783D-07 6.235484198986D-08 1.001839767228D-08 E-Index: 6 7 8 T-Index: 0 6.685225434320D-07 -4.106232974060D-06 2.723608800669D-07 1 7.183376311050D-05 -7.472067446331D-06 1.322655803936D-07 2 -7.138077909744D-05 1.620936024346D-05 -9.673898950970D-07 3 -1.770621609979D-06 -2.727090501391D-06 2.643852072903D-07 4 1.305037799181D-05 -2.175685933563D-06 1.088658237035D-07 5 -2.138483570591D-06 6.604985427235D-07 -4.569211762479D-08 6 -4.041031701627D-07 -3.355268537350D-09 2.937036162249D-09 7 1.213582669967D-07 -1.417846453379D-08 4.992956309007D-10 8 -7.672622548871D-09 1.110090107209D-09 -5.119220753399D-11 \end{verbatim}\end{small} \begin{figure} \label{0.6T} \epsfxsize=16truecm \epsffile{Amjuel_PS/bachr6.ps} \end{figure} \newpage \subsection{ Reaction 0.6D $p + Ar \rightarrow p + Ar ,\ $ elastic, $\ I_{1,0}$ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -1.902636300376D+01 3.001140234133D-03 -5.268608243610D-03 1 -1.190527528568D-01 -9.553336489669D-03 8.838025019236D-03 2 -1.730087103659D-01 4.587817497859D-03 -1.385574331019D-03 3 -1.555030094420D-04 -6.909759775226D-05 -2.299454149526D-03 4 1.652235885356D-02 -2.381913347984D-04 8.373956786709D-04 5 -8.324171609940D-04 -2.293808078785D-05 5.460206572452D-05 6 -1.029303844386D-03 2.488294466911D-05 -6.512005353386D-05 7 1.906300286920D-04 -3.895517435876D-06 1.038339787073D-05 8 -9.787840807784D-06 1.909716194883D-07 -5.237600871611D-07 E-Index: 3 4 5 T-Index: 0 -3.745428185818D-03 1.799497927500D-03 3.198330217071D-04 1 3.207879804088D-03 -4.594149568994D-03 3.457996925194D-06 2 7.517190218616D-04 1.585823173330D-03 -2.165980750364D-04 3 -1.236341581941D-03 6.255302087543D-04 7.892735992329D-05 4 2.230976227599D-04 -3.347480301314D-04 5.331115058296D-06 5 7.233602681294D-05 -4.639425388458D-06 -6.590740254953D-06 6 -3.100626413849D-05 2.210113950523D-05 1.029508831544D-06 7 3.988838107824D-06 -3.769212293593D-06 -4.076159591930D-08 8 -1.769431052019D-07 1.950084020747D-07 -1.116568059624D-09 E-Index: 6 7 8 T-Index: 0 -2.403744917992D-04 2.279983724758D-05 -1.931788624409D-08 1 4.912047383164D-04 -9.410833593792D-05 5.088836276642D-06 2 -1.484255933008D-04 3.868365832252D-05 -2.534300688720D-06 3 -6.764773601651D-05 1.041550065999D-05 -5.033712296102D-07 4 3.231656107374D-05 -6.733195279376D-06 4.029898146395D-07 5 9.314900214037D-07 5.580215548355D-08 -1.063413052225D-08 6 -2.175492032074D-06 4.036437533899D-07 -2.288971303250D-08 7 3.569143181296D-07 -7.087085127829D-08 4.174797773877D-09 8 -1.803893978156D-08 3.691585310844D-09 -2.208748178924D-10 \end{verbatim}\end{small} \newpage This page is intentionally left blank \newpage \subsection{ Reaction 0.7T $p + Kr \rightarrow p + Kr ,\ $ elastic, $\ I_{0,0}$ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -1.804373557904D+01 1.559321831821D-03 1.404133353439D-03 1 2.031777449493D-01 -2.592160804293D-03 -1.467585847319D-03 2 9.686882765703D-03 1.516696535508D-03 3.516527725030D-05 3 8.643169704852D-03 -2.293872602067D-04 2.022613761542D-04 4 -1.424299843875D-02 -3.467610803097D-05 2.405799623813D-05 5 -1.048137401376D-03 -1.163533423390D-05 -4.664386608096D-05 6 1.430609919337D-03 1.091497123198D-05 1.254896476704D-05 7 -2.194259131788D-04 -1.955482471322D-06 -1.369663518077D-06 8 1.009389168927D-05 1.086879702977D-07 5.472917240108D-08 E-Index: 3 4 5 T-Index: 0 3.120877691343D-04 -1.817512879035D-04 4.117059852657D-05 1 1.242877797139D-04 9.112376503933D-05 -1.233416285351D-04 2 -1.573876413696D-04 2.563895433480D-04 4.138546015912D-05 3 -1.420956386480D-04 -1.528253798614D-04 2.912014736234D-05 4 9.590594342402D-05 5.645092477734D-07 -1.535634290988D-05 5 -6.142656580682D-06 1.596912487433D-05 1.203913423509D-07 6 -5.141525041188D-06 -4.044272726929D-06 9.881486025146D-07 7 1.084914594786D-06 3.915011722907D-07 -1.811507168253D-07 8 -6.255863642133D-08 -1.333876245529D-08 9.821435035614D-09 E-Index: 6 7 8 T-Index: 0 2.839905184310D-05 -6.378458873924D-06 3.184713992614D-07 1 -1.279935281113D-05 8.614723298861D-06 -6.786954072347D-07 2 -2.600699325895D-05 2.200678327510D-06 -2.925585047627D-09 3 1.312098730964D-05 -3.454115928930D-06 2.098391843619D-07 4 9.219516369433D-07 4.847045590986D-07 -4.845129241580D-08 5 -1.422113360703D-06 2.351780708953D-07 -1.060289207166D-08 6 2.602916257409D-07 -8.197279350456D-08 5.265588912826D-09 7 -1.502708544211D-08 9.287156417397D-09 -6.890608304608D-10 8 4.565464331790D-11 -3.636906385821D-10 3.037183480051D-11 \end{verbatim}\end{small} \begin{figure} \label{0.7T} \epsfxsize=16truecm \epsffile{Amjuel_PS/bachr7.ps} \end{figure} \newpage \subsection{ Reaction 0.7D $p + Kr \rightarrow p + Kr ,\ $ elastic, $\ I_{1,0}$ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -1.865545505448D+01 -2.224653891670D-03 3.512510248126D-03 1 -1.067068862517D-01 -2.372607771064D-03 -2.528011293662D-03 2 -1.793062289927D-01 3.411244442908D-03 -5.757528343672D-04 3 -3.949316377716D-03 -9.122323825167D-04 7.332721562736D-04 4 1.720673370392D-02 -8.376797069854D-05 -5.923952768477D-05 5 -5.292205338392D-04 5.171588105599D-05 -6.998516881937D-05 6 -1.123585474018D-03 -1.123489868132D-06 2.209356688942D-05 7 1.995670109878D-04 -1.062124014473D-06 -2.542259189383D-06 8 -1.005942932112D-05 8.744976036870D-08 1.047152545942D-07 E-Index: 3 4 5 T-Index: 0 5.208166935036D-04 -1.718161556721D-03 1.592709184582D-04 1 4.342669746539D-04 6.205372491923D-04 -2.512144246616D-04 2 -6.548561119095D-04 7.557892819154D-04 8.655880993873D-05 3 -1.170727706000D-06 -4.588074844111D-04 3.617188469585D-05 4 1.148785626919D-04 2.681963226773D-05 -2.204300778275D-05 5 -1.734332538201D-05 3.427749154446D-05 3.700519676902D-07 6 -4.518652819335D-06 -9.660892785904D-06 1.410244055501D-06 7 1.243519343884D-06 1.011493440280D-06 -2.646219750940D-07 8 -7.777508674647D-08 -3.800858381217D-08 1.452395343502D-08 E-Index: 6 7 8 T-Index: 0 1.760192998914D-04 -4.823181012443D-05 3.283695269304D-06 1 -5.953843658876D-05 2.746473855990D-05 -2.212169538346D-06 2 -8.109653911492D-05 1.104868697474D-05 -4.181441820322D-07 3 4.537025011410D-05 -1.035893652496D-05 6.333257556842D-07 4 -1.525645889670D-06 1.261725358435D-06 -1.056714078118D-07 5 -3.440639370908D-06 6.338548661992D-07 -3.391092703214D-08 6 8.551857146979D-07 -2.188109556451D-07 1.399325047660D-08 7 -7.894576610417D-08 2.545593595077D-08 -1.763312508912D-09 8 2.520441766028D-09 -1.046876612281D-09 7.719196237445D-11 \end{verbatim}\end{small} \newpage This page is intentionally left blank \newpage \subsection{ Reaction 0.8T $p + Xe \rightarrow p + Xe ,\ $ elastic, $\ I_{0,0}$ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -1.837022175444D+01 1.966234873272D-01 -8.045525227882D-02 1 1.805905055691D-01 -9.802945396045D-02 3.544388629813D-03 2 3.047012359914D-02 6.128643067258D-03 -4.012918398972D-03 3 -6.923416688779D-03 5.221800119943D-03 4.204812055154D-03 4 -3.195025138086D-04 -1.316526854062D-03 6.034285640091D-04 5 -1.935784557781D-04 -7.420136378842D-05 -4.344482793235D-04 6 -1.933096968862D-04 9.094117569189D-05 5.180202859895D-06 7 7.175836632929D-05 -1.543061104752D-05 1.174663734921D-05 8 -5.568595272341D-06 8.358080592792D-07 -9.761323315864D-07 E-Index: 3 4 5 T-Index: 0 -4.848631362553D-02 4.750879899677D-02 5.610953213302D-04 1 1.612499614172D-02 -5.523987597225D-03 -9.460219395869D-04 2 6.794095254509D-04 -9.895305035946D-04 -2.861258121115D-05 3 -1.150110473980D-03 -7.631572145165D-04 1.776787179903D-04 4 3.981780177076D-04 -1.483284811460D-04 -3.107860031349D-05 5 6.891189917320D-06 1.027084520227D-04 -1.030852624977D-05 6 -3.951029440916D-05 7.160419132800D-06 4.694154796307D-06 7 8.033492283600D-06 -4.946108320253D-06 -6.642328462598D-07 8 -4.761690151100D-07 3.755070632999D-07 3.283487948208D-08 E-Index: 6 7 8 T-Index: 0 -5.413232395756D-03 1.094586062581D-03 -6.392041039556D-05 1 7.755701996850D-04 -1.315661918085D-04 7.128051226064D-06 2 1.645431285623D-04 -3.499826315853D-05 2.119997135712D-06 3 3.410974410072D-05 -1.133727004658D-05 7.517805454064D-07 4 1.782649548441D-05 -2.411600549323D-06 1.058674617194D-07 5 -7.065840257206D-06 1.628340574934D-06 -9.783727086764D-08 6 -1.830471247020D-06 2.273687191682D-07 -9.553571528267D-09 7 6.407304183785D-07 -1.061766307764D-07 5.519134501912D-09 8 -4.447805281256D-08 7.735214914952D-09 -4.130970468715D-10 \end{verbatim}\end{small} \begin{figure} \label{0.8T} \epsfxsize=16truecm \epsffile{Amjuel_PS/bachr8.ps} \end{figure} \newpage \subsection{ Reaction 0.8D $p + Xe \rightarrow p + Xe ,\ $ elastic, $\ I_{1,0}$ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -1.897424529930D+01 6.759221376448D-02 2.831656966128D-02 1 7.880568783648D-02 -1.013433977091D-01 -4.803501715713D-04 2 -2.211004195406D-02 2.780616010153D-02 -9.803026089070D-03 3 -1.881720757004D-02 7.288240524563D-03 3.622352023952D-03 4 1.881626843867D-03 -3.506478495212D-03 1.038874766045D-04 5 1.555723381321D-03 -6.488785021639D-05 -3.629668747278D-04 6 -2.155563511636D-04 1.904734853680D-04 9.263791323244D-05 7 -1.309212493163D-05 -2.940905387089D-05 -9.735247959278D-06 8 2.085088015611D-06 1.405276321600D-06 3.784816393936D-07 E-Index: 3 4 5 T-Index: 0 -1.132739367386D-02 -1.136836207882D-02 1.644151842499D-03 1 1.616595589060D-02 -6.630385050040D-04 -1.261647418326D-03 2 -3.466486887128D-03 2.154814681750D-03 6.929992653084D-05 3 -1.469864494259D-03 -3.263588910597D-04 1.619007714736D-04 4 5.655409965690D-04 -6.761053529597D-05 -3.542760579601D-05 5 7.812054156187D-06 5.307617978533D-05 -6.584683292245D-06 6 -2.696200061727D-05 -1.593650897407D-05 3.272732707082D-06 7 4.097153412890D-06 2.165559988365D-06 -4.226732919171D-07 8 -1.941951920917D-07 -1.068579438469D-07 1.856975994299D-08 E-Index: 6 7 8 T-Index: 0 9.347764278165D-04 -2.260015561966D-04 1.349778327834D-05 1 2.184449544252D-04 -4.870473229076D-06 -6.585679719393D-07 2 -1.768547787859D-04 3.062903702294D-05 -1.606726635371D-06 3 -5.383734875328D-06 -3.242779246901D-06 2.887563512048D-07 4 8.898390092703D-06 -5.828977975784D-07 2.514867221936D-09 5 -2.668417682123D-06 6.656669113253D-07 -4.118906229906D-08 6 9.467025678674D-07 -2.778964165257D-07 1.810797219300D-08 7 -1.603923367792D-07 4.412968572947D-08 -2.823552915243D-09 8 9.066091691589D-09 -2.353837415803D-09 1.478176477260D-10 \end{verbatim}\end{small} \newpage This page is intentionally left blank \newpage \subsection{ Reaction 2.1.5 $e + H \rightarrow 2e + H^+ ,\ $ } Valid for $ 700 < E_H < 1.0~ E5$ and $T_e < 1000$ eV. Needed for beam penetration across cold electron (edge) plasma. \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.250886702080D+02 2.690772962219D+02 -9.333762356936D+01 1 -6.667333547390D+01 7.233538183560D+01 -2.570910666822D+01 2 -4.983434468076D+01 2.412479733168D+01 -3.884870450118D+00 3 2.670550884979D+00 -1.723167957478D+00 5.587782905216D-01 4 6.674948903612D-01 -4.124756061678D-01 1.712842277416D-02 5 6.808976023219D-02 2.688754230792D-03 6.611670857544D-03 6 -1.438915473788D-02 -1.901194630463D-04 7.298416521085D-05 7 1.098989211142D-03 2.219783796362D-05 -3.960365474618D-05 8 -6.711866174955D-05 2.280924070357D-05 -4.884031598541D-06 E-Index: 3 4 5 T-Index: 0 1.424150846209D+01 -4.467268971241D-01 -1.584732741666D-01 1 4.380976345270D+00 -3.009427651758D-01 -8.501949526254D-03 2 -3.398932408165D-02 4.907514406262D-02 2.703730871097D-05 3 -3.351001372815D-02 -6.702807790436D-03 7.244114949870D-04 4 5.697717251645D-03 -2.395062750188D-04 -2.620114677424D-06 5 -1.699139379366D-03 5.177635368277D-05 6.870966611037D-06 6 2.324432128978D-05 5.858353012396D-06 -1.366593951118D-06 7 5.355353697737D-06 -6.855890659797D-07 9.381430540897D-08 8 7.838237578617D-07 -9.827043958796D-08 9.095791108734D-09 E-Index: 6 7 8 T-Index: 0 2.361460417677D-02 -1.345770476010D-03 2.864129137742D-05 1 2.358018185463D-03 -1.102091465927D-04 1.382211119292D-06 2 -5.608636378890D-04 3.536474507865D-05 -5.535259754631D-07 3 -8.650970561566D-06 6.995157343181D-08 -5.266956839472D-08 4 -3.717702510307D-06 2.369570100312D-07 5.319224060533D-10 5 1.019488700190D-07 -4.942023555843D-08 1.311808222738D-09 6 8.201753350995D-08 -2.693263792508D-09 8.430296741463D-11 7 -1.145196074924D-08 9.355510173137D-10 -3.109161125504D-11 8 -3.977195669572D-10 -6.688281017183D-12 7.995091233984D-13 Max. rel. Error: 22.9827 % Mean rel. Error: 1.3423 % \end{verbatim}\end{small} \begin{figure} \label{2.1.5H3} \epsfxsize=16truecm \epsffile{Amjuel_PS/H3-2.1.5.ps} \end{figure} \newpage \subsection{ Reaction 2.3.9 $e + He(1s^21S) \rightarrow 2e + He^+(1s) ,\ $ } Valid for $ 700 < E_{He} < 1.0~ E5$ and $T_e < 1000$ eV. Needed for beam penetration across cold electron (edge) plasma. \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 1.310034245752D+03 -8.508771372056D+02 2.066760366749D+02 1 -2.508353150675D+02 1.015419189021D+02 -1.581037633890D+01 2 9.417451507809D+01 -1.778751771269D+01 -2.824530306780D+00 3 -3.009050226462D+01 6.654788597405D+00 2.915588715563D-01 4 4.385660180646D+00 -1.117837142443D+00 -1.511745757585D-02 5 -4.443019677779D-02 4.662788141049D-02 -5.658517658565D-04 6 -5.383557897871D-02 3.946435769665D-03 1.039284516303D-03 7 5.931731041041D-03 -7.716369089119D-04 -2.018331102194D-05 8 -1.677718659922D-04 1.297692472884D-05 1.627194163577D-06 E-Index: 3 4 5 T-Index: 0 -2.021517461823D+01 -6.037177234072D-01 3.448434382624D-01 1 2.160874670018D+00 -3.181962238105D-01 3.285332322121D-02 2 6.741447605303D-01 -3.148060740119D-02 7.078822091135D-04 3 -8.288011998601D-02 -1.758799128561D-03 -1.384555059849D-04 4 1.167648389744D-02 -1.409170634544D-04 9.546658161713D-05 5 -6.515681704203D-04 -4.715250869462D-05 9.071842143868D-06 6 -1.534799377103D-05 -1.066216257020D-05 -4.208681902142D-07 7 -1.528843582156D-05 2.822659922448D-06 1.096321036847D-07 8 1.009911437330D-06 -2.105689698877D-07 4.570730739908D-09 E-Index: 6 7 8 T-Index: 0 -3.436317750271D-02 1.530379719746D-03 -2.666449302822D-05 1 -2.281896275305D-03 1.104943101710D-04 -2.667926304328D-06 2 -1.624346097258D-05 -1.339087397064D-05 8.519546024053D-07 3 5.890695384015D-05 1.457482299662D-06 -2.463663989543D-07 4 -1.459401479449D-05 -8.971022779692D-08 3.962468074256D-08 5 3.123976730622D-08 -1.013694223158D-08 -7.468250327850D-10 6 2.419036579858D-09 1.458105491288D-08 -7.464201861260D-10 7 -2.457770000492D-08 -9.361060954216D-11 5.503065552145D-11 8 8.004030822610D-10 -1.580695841260D-11 -1.314359641034D-12 Max. rel. Error: 7.5847 % Mean rel. Error: 0.8667 % \end{verbatim}\end{small} \begin{figure} \label{2.3.9H3} \epsfxsize=16truecm \epsffile{Amjuel_PS/H3-2.3.9.ps} \end{figure} \newpage \subsection{ Reaction 3.1.8 $ p + H(1s) \rightarrow H(1s) + p $ } Charge exchange between protons and hydrogen atoms. Cross-section: 3.1.8, improved fit. (Identically in: HYDHEL.tex) $ \langle sigma*vrel \rangle$(Ti,Ebeam) (cm**3/s) \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -1.831670498376D+01 1.650239332070D-01 5.025740610454D-02 1 2.143624996483D-01 -1.067658289373D-01 -5.304993033743D-03 2 5.139117192662D-02 9.536923957409D-03 -1.306075129405D-02 3 -9.896180369559D-04 6.315097684976D-03 2.655464630308D-03 4 -2.495327546080D-03 -1.265503371044D-03 7.569269700468D-04 5 -2.417046684097D-05 -6.945512319613D-05 -2.956984088728D-04 6 1.177406072793D-04 3.698501620365D-05 3.424317896619D-05 7 -1.483036457978D-05 -3.348172574417D-06 -1.527018819072D-06 8 5.351909441226D-07 9.728230870242D-08 1.676354786072D-08 E-Index: 3 4 5 T-Index: 0 5.288358515136D-03 -2.437122342843D-03 -4.461891214720D-04 1 8.289383645942D-03 -9.698773663345D-05 -4.470180279338D-04 2 -1.033166370333D-03 1.280464204775D-03 -8.453294908907D-05 3 -1.365781346175D-03 -1.859939123743D-04 1.237942304972D-04 4 2.756946036257D-04 -1.107375149384D-04 -7.217379426085D-06 5 2.318277483195D-05 3.704494397140D-05 -6.066558692480D-06 6 -9.815693511794D-06 -4.285719813022D-06 1.169257650609D-06 7 8.362050692462D-07 2.058392726953D-07 -7.463594884928D-08 8 -2.237567830699D-08 -3.081685803820D-09 1.450862501121D-09 E-Index: 6 7 8 T-Index: 0 1.731631548110D-04 -1.588434781959D-05 4.482291414386D-07 1 7.944326905066D-05 -5.303688417551D-06 1.235167254501D-07 2 -3.040874906105D-05 4.747888095498D-06 -1.923953750574D-07 3 -1.588253432932D-05 6.603560345800D-07 -1.970606344918D-09 4 5.769971321188D-06 -6.717311113584D-07 2.440961351104D-08 5 -4.951573401626D-07 1.437520597154D-07 -6.998724470004D-09 6 -4.968953461875D-10 -1.618948982477D-08 9.440094842562D-10 7 5.924370389093D-10 1.078208689229D-09 -6.619767848464D-11 8 4.434231893204D-11 -3.324377862622D-11 1.935019679501D-12 Max. rel. Error: 1.1026 % Mean rel. Error: 0.3105 % \end{verbatim}\end{small} \newpage This page is intentionally left blank \newpage \subsection{ Reaction 0.13p $p + Be \rightarrow p + Be$, elastic} Integral 0.5*I(1,0) for cross-sections from [P. Krstic, D. Schultz, PP, vol. 16 (2009), p. 053503] \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.014045187283e+01 -2.345625000690e-02 3.305320330967e-03 1 1.633235466137e-02 9.980449030332e-03 -7.067639616596e-03 2 -3.302490936436e-02 -6.598307698802e-03 -1.473079734140e-04 3 -2.690595407156e-02 5.590562085972e-03 1.477424631936e-03 4 2.553977796175e-03 -1.198166632910e-03 -1.524065320318e-04 5 1.172235136758e-03 -1.627408163499e-04 -1.042267671149e-04 6 -3.266982332705e-04 8.416159467290e-05 2.904236972264e-05 7 3.149289760802e-05 -9.814022851618e-06 -2.783408339643e-06 8 -1.076486147594e-06 3.734238744568e-07 9.357156799975e-08 E-Index: 3 4 5 T-Index: 0 1.622640980311e-02 -2.885998551391e-03 -1.852231865164e-03 1 -8.621417251817e-03 1.995454066090e-03 7.882913154204e-04 2 3.438592757542e-04 1.915119499255e-04 3.167930363372e-05 3 -6.421972752548e-04 -1.406068934136e-04 6.824350317931e-05 4 3.247948234786e-04 -4.440977842360e-05 -3.426686939963e-05 5 1.259107326962e-05 1.754218150033e-05 -2.903525712509e-06 6 -2.000702118557e-05 -1.316461187594e-06 2.530910339762e-06 7 2.750657732561e-06 -4.943105315783e-08 -3.306763428407e-07 8 -1.137313391413e-07 6.118327388870e-09 1.336258126385e-08 E-Index: 6 7 8 T-Index: 0 5.421800944799e-04 -5.322004264036e-05 1.832505454673e-06 1 -2.997846142138e-04 3.377208808135e-05 -1.279370584937e-06 2 -2.736718480233e-05 3.730502557681e-06 -1.525714105067e-07 3 -2.323654071260e-06 -1.001562341663e-06 7.501383504538e-08 4 1.110870800408e-05 -1.161197671721e-06 4.065284401394e-08 5 -8.530135081745e-07 2.096419478952e-07 -1.142479721401e-08 6 -4.412259984447e-07 2.047224411741e-08 1.657880705324e-10 7 7.676685086250e-08 -5.969845881133e-09 1.375019627044e-10 8 -3.463828351937e-09 3.040257273837e-10 -8.604737523486e-12 E2MIN=1.000000e-01 eV E2MAX=1.000000e+04 eV T1MIN=1.000000e-01 eV T1MAX=1.000000e+04 eV MAXERR=5.469149e+00 \% MIDERR=7.773394e-01 \% \end{verbatim}\end{small} \newpage \subsection{ Reaction 0.13d $d + Be \rightarrow d + Be$, elastic} Integral 0.5*I(1,0) for the cross-section from [P. Krstic, D. Schultz, PP, vol. 16 (2009), p. 053503] \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.044307298348e+01 -1.435241859928e-03 1.536041365683e-02 1 2.282279489380e-02 -1.083413843840e-02 -1.474843156363e-02 2 -3.170234700651e-02 -8.490883393848e-03 2.079688557536e-03 3 -2.416047263489e-02 9.432119244308e-03 2.845241397793e-04 4 1.612944406737e-03 -1.129269279296e-03 1.052724354051e-04 5 1.205969880650e-03 -5.902894606367e-04 -6.217142758003e-05 6 -3.042059744854e-04 1.796859651710e-04 8.003975381593e-06 7 2.824343373145e-05 -1.807466354009e-05 -3.081218221035e-07 8 -9.440508892226e-07 6.302872079617e-07 -1.339799374312e-09 E-Index: 3 4 5 T-Index: 0 5.278833185608e-03 -4.469538509276e-03 -6.491235580500e-04 1 8.841283319500e-04 1.826216287017e-03 -2.939210322706e-04 2 7.657158765681e-04 -1.946476894373e-05 1.867693028736e-05 3 -2.207552889630e-03 3.239632365588e-04 2.103141514803e-04 4 2.762713059735e-04 -9.265776869906e-05 -2.429517900194e-05 5 2.007011160713e-04 -2.487759075076e-05 -2.147229167781e-05 6 -6.121399958981e-05 1.092764172317e-05 6.327259228592e-06 7 6.243585391457e-06 -1.262789392490e-06 -6.350894325811e-07 8 -2.197691313245e-07 4.791605625816e-08 2.208688569691e-08 E-Index: 6 7 8 T-Index: 0 3.450099986899e-04 -3.955146569842e-05 1.483280922015e-06 1 -2.313493476983e-05 7.116368703341e-06 -3.656772740674e-07 2 -2.058020487807e-05 3.396561608698e-06 -1.601568020599e-07 3 -6.822453223473e-05 7.105361952178e-06 -2.495941974516e-07 4 1.283283500423e-05 -1.653037734175e-06 6.795382247769e-08 5 6.650188435941e-06 -6.799250049849e-07 2.350487416086e-08 6 -2.280587373535e-06 2.549634635361e-07 -9.522348114958e-09 7 2.442175006227e-07 -2.824182688477e-08 1.083669713484e-09 8 -8.866460450561e-09 1.047525061112e-09 -4.087338886486e-11 E2MIN=1.000000e-01 eV E2MAX=1.000000e+04 eV T1MIN=1.000000e-01 eV T1MAX=1.000000e+04 eV MAXERR=6.574404e+00 \% MIDERR=8.464843e-01 \% \end{verbatim}\end{small} \newpage \subsection{ Reaction 0.13t $t + Be \rightarrow t + Be$, elastic} Integral 0.5*I(1,0) for the cross-section from [P. Krstic, D. Schultz, PP, vol. 16 (2009), p. 053503] \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.129504307011e+01 1.773225057252e-02 1.880909643601e-02 1 2.546933381457e-02 -2.324877220081e-02 -1.682441670552e-02 2 -2.981010432291e-02 -9.794461284777e-03 3.725523265517e-03 3 -2.203655582429e-02 9.891081092090e-03 -7.870974350538e-04 4 9.964028273375e-04 -6.435065292429e-04 2.019639487327e-04 5 1.172605871159e-03 -7.189019182284e-04 1.838780642892e-05 6 -2.758762887050e-04 1.835500405043e-04 -1.518921596258e-05 7 2.485043659547e-05 -1.689818645796e-05 2.005438908327e-06 8 -8.151836846467e-07 5.511097601102e-07 -8.189837190188e-08 E-Index: 3 4 5 T-Index: 0 -5.132900735360e-03 -4.421925566607e-03 3.914099368416e-04 1 6.590793034811e-03 1.268075388723e-03 -8.863334795471e-04 2 1.288530049780e-03 -2.754660024957e-04 -3.072806984273e-05 3 -2.235933725670e-03 5.344193391390e-04 2.000597752829e-04 4 3.631519990032e-05 -7.422560675901e-05 2.446011993064e-06 5 2.349882452429e-04 -4.838038543847e-05 -2.356761071496e-05 6 -5.519654333492e-05 1.507441074875e-05 5.230990882083e-06 7 4.849741630919e-06 -1.539910716377e-06 -4.401471679875e-07 8 -1.511215532691e-07 5.397860122684e-08 1.312783790155e-08 E-Index: 6 7 8 T-Index: 0 9.754804763614e-05 -1.653532824608e-05 7.049898523652e-07 1 1.579820086189e-04 -1.220944882003e-05 3.527637498767e-07 2 5.755383129853e-06 2.384782937003e-07 -3.938740456374e-08 3 -8.253882854736e-05 9.685611260827e-06 -3.750354024418e-07 4 5.655895591655e-06 -9.924327352819e-07 4.744625742485e-08 5 9.018349071660e-06 -1.037798443713e-06 3.976147439343e-08 6 -2.385966333490e-06 2.959527372233e-07 -1.195770882126e-08 7 2.250364369523e-07 -2.909177070852e-08 1.208277625427e-09 8 -7.428846811499e-09 9.919713207429e-10 -4.206437314661e-11 E2MIN=1.000000e-01 eV E2MAX=1.000000e+04 eV T1MIN=1.000000e-01 eV T1MAX=1.000000e+04 eV MAXERR=6.852958e+00 \% MIDERR=9.227778e-01 \% \end{verbatim}\end{small} \newpage \subsection{ Reaction 0.14p $p + C \rightarrow p + C$, elastic} Integral 0.5*I(1,0) the cross-section from [P. Krstic, D. Schultz, PP, vol. 13 (2006), p. 053501] \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.070325937875e+01 -1.606842198142e-02 8.714205649382e-03 1 -1.649258379129e-01 -1.370586397944e-02 -8.610928985264e-03 2 -8.228323037947e-02 1.042893658701e-02 2.920352519091e-03 3 1.291744053436e-02 -4.056102000351e-05 -4.279330275042e-04 4 4.972022465187e-03 -1.142479600302e-03 -1.823021533207e-05 5 -1.658137593639e-03 3.005724020801e-04 2.552407020562e-05 6 1.313758641539e-04 -3.251665906188e-05 -5.645220513458e-06 7 5.599391312349e-07 1.536984797877e-06 5.394244202523e-07 8 -2.939698517936e-07 -2.321423842233e-08 -1.912639278713e-08 E-Index: 3 4 5 T-Index: 0 4.463808489764e-03 -5.048490029821e-03 -5.485971584014e-04 1 5.941389343177e-03 1.591030489357e-03 -6.724348380444e-04 2 -2.167804845149e-03 2.090440852555e-04 2.551690026771e-04 3 -7.729931321856e-04 9.617898796550e-06 7.887372433086e-05 4 3.057086385239e-04 -5.118348604852e-05 -3.010408438357e-05 5 8.168255647779e-06 7.542836997958e-06 -2.112912729057e-06 6 -1.289999822011e-05 5.408322650236e-07 1.620261227354e-06 7 1.614389314707e-06 -1.609136480749e-07 -1.933340387247e-07 8 -6.208603824932e-08 7.883780259005e-09 7.301712180137e-09 E-Index: 6 7 8 T-Index: 0 4.753915903398e-04 -6.407354904082e-05 2.631638764433e-06 1 4.244975247061e-05 3.663120971952e-06 -3.285624239340e-07 2 -8.069104998325e-05 8.696126832052e-06 -3.209550762837e-07 3 -1.424206928869e-05 7.815274543195e-07 -7.191976670581e-09 4 1.013975911159e-05 -1.079636710772e-06 3.886976338792e-08 5 -2.792752786643e-07 9.100460959963e-08 -5.111179984264e-09 6 -3.490894641470e-07 2.449855146898e-08 -4.889613885858e-10 7 5.016256863184e-08 -4.331776839658e-09 1.234776996758e-10 8 -2.052868727602e-09 1.896731767020e-10 -5.862153355385e-12 ELABMIN=1.000000e-01 eV ELABMAX=1.000000e+04 eV TMIN=1.000000e-01 eV TMAX=1.000000e+04 eV MAXERR=4.502810e+00 \% MIDERR=6.356092e-01 \% \end{verbatim}\end{small} \newpage \subsection{ Reaction 0.14d $d + C \rightarrow d + C$, elastic} Integral 0.5*I(1,0) the cross-section from [P. Krstic, D. Schultz, PP, vol. 13 (2006), p. 053501] \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.101813469909e+01 6.489171371708e-03 4.901025644886e-03 1 -1.516889520308e-01 -2.470762179054e-02 -1.463167664648e-03 2 -7.453976358810e-02 1.017233018332e-02 1.214375528209e-03 3 7.618704589773e-03 -9.301827218280e-05 -9.984709341439e-04 4 4.787096833727e-03 -7.691694929083e-04 2.180371997435e-04 5 -1.061371660357e-03 1.971538044810e-04 1.333591660518e-05 6 -2.611197691070e-06 -2.228824297723e-05 -9.942256019663e-06 7 1.244816787057e-05 1.224609831860e-06 1.170723630532e-06 8 -6.769910487661e-07 -2.666403772875e-08 -4.404252434081e-08 E-Index: 3 4 5 T-Index: 0 -1.455339394665e-02 -3.081622015142e-03 1.402095087223e-03 1 1.350947310121e-02 -4.798802447621e-04 -1.349325857828e-03 2 -6.950748629568e-04 2.872915794277e-04 4.662582695229e-05 3 -1.214397303373e-03 2.233321486915e-04 1.275394051016e-04 4 7.599744499071e-05 -6.336940059363e-05 -2.985716810841e-06 5 9.546689677128e-05 -9.724010172447e-06 -1.185798104005e-05 6 -2.358526693542e-05 4.777607503632e-06 2.759385297831e-06 7 2.131249678191e-06 -5.428934065172e-07 -2.441680332756e-07 8 -6.877886538867e-08 2.018352694021e-08 7.786080358510e-09 E-Index: 6 7 8 T-Index: 0 -6.630931867974e-05 -1.282323960899e-05 9.612329327013e-07 1 3.203078193087e-04 -2.808404180189e-05 8.728428841695e-07 2 -3.437225083080e-05 4.758395513068e-06 -2.029214764132e-07 3 -4.113910109706e-05 4.190543564938e-06 -1.444698458017e-07 4 4.739036860771e-06 -6.721181446886e-07 2.826795931179e-08 5 3.315817743830e-06 -3.169812151056e-07 1.038065294736e-08 6 -9.498884071161e-07 1.013104127800e-07 -3.620554915035e-09 7 9.310944420933e-08 -1.038636437355e-08 3.832761193363e-10 8 -3.193093520991e-09 3.667768696803e-10 -1.381157363749e-11 E2MIN=1.000000e-01 eV E2MAX=1.000000e+04 eV T1MIN=1.000000e-01 eV T1MAX=1.000000e+04 eV MAXERR=4.812259e+00 % MIDERR=6.856970e-01 % \end{verbatim}\end{small} \newpage \subsection{ Reaction 0.14t $t + C \rightarrow t + C$, elastic} Integral 0.5*I(1,0) the cross-section from [P. Krstic, D. Schultz, PP, vol. 13 (2006), p. 053501] \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.188182287316e+01 1.454179492997e-02 -2.384032349700e-03 1 -1.354699933152e-01 -2.467760316153e-02 4.334653134039e-03 2 -7.060750858774e-02 9.399641668674e-03 8.481034134188e-04 3 2.864022450514e-03 -5.997943672361e-04 -1.380612802836e-03 4 4.981251211249e-03 -5.556527566954e-04 2.241298739717e-04 5 -6.269621444826e-04 1.920636450763e-04 4.700039868950e-05 6 -1.106351233133e-04 -2.866120650169e-05 -1.720762234455e-05 7 2.242128826376e-05 2.112462685008e-06 1.768524963647e-06 8 -1.005706263641e-06 -6.234864792351e-08 -6.175770363502e-08 E-Index: 3 4 5 T-Index: 0 -2.397323674331e-02 -1.240783245409e-03 2.302905154607e-03 1 1.387587499142e-02 -1.507728991767e-03 -1.294765807979e-03 2 4.651760567797e-04 1.680622109107e-04 -9.233250740936e-05 3 -9.635680205527e-04 3.061725227014e-04 9.789384481491e-05 4 -8.260913884022e-05 -4.654027458768e-05 1.346465972623e-05 5 9.503215133225e-05 -2.034050613835e-05 -1.108666689667e-05 6 -1.687203771025e-05 6.428514127795e-06 1.879502286805e-06 7 1.223944073583e-06 -6.489118024901e-07 -1.325772816947e-07 8 -3.237088551006e-08 2.257395302166e-08 3.416404221018e-09 E-Index: 6 7 8 T-Index: 0 -3.707252919630e-04 1.872349911606e-05 -1.381007109570e-07 1 3.668635462607e-04 -3.575440980571e-05 1.214465065926e-06 2 7.098045828556e-06 5.013656731141e-07 -5.200474146650e-08 3 -4.091586513333e-05 4.654803151256e-06 -1.739935848177e-07 4 6.912225143953e-08 -2.203785010051e-07 1.320720305232e-08 5 3.905694982934e-06 -4.228074741734e-07 1.534216866201e-08 6 -8.828000916527e-07 1.061224417073e-07 -4.120856941484e-09 7 7.736267322509e-08 -9.874970633391e-09 3.973883678734e-10 8 -2.453765580729e-09 3.278998627368e-10 -1.354402027084e-11 E2MIN=1.000000e-01 eV E2MAX=1.000000e+04 eV T1MIN=1.000000e-01 eV T1MAX=1.000000e+04 eV MAXERR=4.267937e+00 \% MIDERR=6.880224e-01 \% \end{verbatim}\end{small} \newpage \subsection{ Reaction 3.1.8org $ p + H(1s) \rightarrow H(1s) + p $ } original fit from Janev's springer book 1987 in HYDHEL.tex. Now there is the improved fit (see above), leading to better energy balance with tracklength estimators and the energy weighted rate (below) \begin{small}\begin{verbatim} E Index 0 1 2 T Index 0 -1.829079581680e+01 1.640252721210e-01 3.364564509137e-02 1 2.169137615703e-01 -1.106722014459e-01 -1.382158680424e-03 2 4.307131243894e-02 8.948693624917e-03 -1.209480567154e-02 3 -5.754895093075e-04 6.062141761233e-03 1.075907881928e-03 4 -1.552077120204e-03 -1.210431587568e-03 8.297212635856e-04 5 -1.876800283030e-04 -4.052878751584e-05 -1.907025662962e-04 6 1.125490270962e-04 2.875900435895e-05 1.338839628570e-05 7 -1.238982763007e-05 -2.616998139678e-06 -1.171762874107e-07 8 4.163596197181e-07 7.558092849125e-08 -1.328404104165e-08 E Index 3 4 5 T Index 0 9.530225559189e-03 -8.519413589968e-04 -1.247583860943e-03 1 7.348786286628e-03 -6.343059502294e-04 -1.919569450380e-04 2 -3.675019470470e-04 1.039643390686e-03 -1.553840717902e-04 3 -8.119301728339e-04 8.911036876068e-06 3.175388949811e-05 4 1.361661816974e-04 -1.008928628425e-04 1.080693990468e-05 5 1.141663041636e-05 1.775681984457e-05 -3.149286923815e-06 6 -4.340802793033e-06 -7.003521917385e-07 2.318308730487e-07 7 3.517971869029e-07 -4.928692832866e-08 1.756388998863e-10 8 -9.170850253981e-09 3.208853883734e-09 -3.952740758950e-10 E Index 6 7 8 T Index 0 3.014307545716e-04 -2.499323170044e-05 6.932627237765e-07 1 4.075019351738e-05 -2.850044983009e-06 6.966822400446e-08 2 2.670827249272e-06 7.695300597935e-07 -3.783302281524e-08 3 -4.515123641755e-06 2.187439283954e-07 -2.911233951880e-09 4 5.106059413591e-07 -1.299275586093e-07 5.117133050290e-09 5 3.105491554749e-08 2.274394089017e-08 -1.130988250912e-09 6 -6.030983538280e-09 -1.755944926274e-09 1.005189187279e-10 7 -1.446756795654e-10 7.143183138281e-11 -3.989884105603e-12 8 2.739558475782e-11 -1.693040208927e-12 6.388219930167e-14 Error 8.88e-04 (B) \end{verbatim}\end{small} \newpage This page is intentionally left blank \newpage \subsection{ Reaction 3.1.8L $ p + H(1s) \rightarrow H(1s) + p $ } Langevin approximation: sigma v = const = 2e-8 \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -1.772753356000D+01 0.000000000000D+00 0.000000000000D+00 1 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 2 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 3 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 4 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 5 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 6 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 7 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 8 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 E-Index: 3 4 5 T-Index: 0 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 1 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 2 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 3 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 4 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 5 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 6 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 7 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 8 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 E-Index: 6 7 8 T-Index: 0 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 1 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 2 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 3 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 4 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 5 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 6 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 7 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 8 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 Max. rel. Error: 0.0000 % Mean rel. Error: 0.0000 % \end{verbatim}\end{small} \newpage This page is intentionally left blank \newpage \subsection{ Reaction 3.2.3 $ p + H_2(v) \rightarrow H + H_2^+ $ } Effective ion conversion (Charge exchange on $H_2$) as function of $T_p$ (from Janev,\cite{kn:Janev}). vibrational distribution $H_2(v)$ is density independent, assume: $T_e = T_p = T$ hence: function of $E_{beam} = E_{H2}$ and $T$ \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.133104980000E+01 2.961905900000E-01 -2.876892150000E-02 1 2.308461720000E+00 -1.064800460000E+00 2.310120950000E-01 2 -2.026151710000E+00 1.142806740000E+00 -2.621943460000E-01 3 1.648000330000E-01 -4.675786500000E-01 1.242261910000E-01 4 1.651993580000E-01 5.766584690000E-02 -3.659922760000E-02 5 -2.598458070000E-02 1.349144350000E-02 8.871659800000E-03 6 -4.330453510000E-03 -5.246404340000E-03 -1.636107180000E-03 7 1.187405610000E-03 6.281964210000E-04 1.740000360000E-04 8 -6.897815380000E-05 -2.667160440000E-05 -7.528040300000E-06 E-Index: 3 4 5 T-Index: 0 -3.323271590000E-02 7.234558340000E-03 2.940230100000E-04 1 6.809382980000E-02 -4.241210420000E-02 8.271152020000E-03 2 -6.877694430000E-02 4.012716970000E-02 -6.143307540000E-03 3 1.774294860000E-02 -1.157658350000E-02 1.311061300000E-03 4 7.083346120000E-03 3.403537010000E-04 -2.752152790000E-04 5 -5.231162040000E-03 3.324241650000E-04 1.985585660000E-04 6 1.242023150000E-03 -4.524774630000E-05 -6.369415730000E-05 7 -1.337853740000E-04 6.784609160000E-07 8.284840740000E-06 8 5.516687380000E-06 1.140207820000E-07 -3.837975410000E-07 E-Index: 6 7 8 T-Index: 0 -8.005031610000E-05 0.000000000000E+00 0.000000000000E+00 1 -6.275988100000E-04 0.000000000000E+00 0.000000000000E+00 2 3.233852920000E-04 0.000000000000E+00 0.000000000000E+00 3 -1.125957730000E-05 0.000000000000E+00 0.000000000000E+00 4 2.225165850000E-05 0.000000000000E+00 0.000000000000E+00 5 -2.813630850000E-05 0.000000000000E+00 0.000000000000E+00 6 8.679231940000E-06 0.000000000000E+00 0.000000000000E+00 7 -1.075372230000E-06 0.000000000000E+00 0.000000000000E+00 8 4.793672020000E-08 0.000000000000E+00 0.000000000000E+00 Max. rel. Error: 16.7 % Mean rel. Error: 5.09 % \end{verbatim}\end{small} \begin{figure} \label{3.2.3b} \epsfxsize=16truecm \epsffile{Amjuel_PS/ionconv3.eps} \end{figure} \newpage \subsection{ Reaction 3.3.1 $ p + He(1s^21S) \rightarrow H + He^+(1s) $ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.777393171216D+01 1.034570822224D+00 5.500659259212D-01 1 9.354555314272D+00 -1.691165109278D+00 -7.450052207738D-01 2 -4.235897398162D+00 1.383244831625D+00 3.396734449323D-01 3 1.350058534401D+00 -6.640009322644D-01 -2.562301717488D-02 4 -2.418149537330D-01 1.946040141373D-01 -2.712202677247D-02 5 1.747617790690D-02 -3.507141422752D-02 9.840686949146D-03 6 7.868843917720D-04 3.782419535260D-03 -1.470034129542D-03 7 -1.857520833749D-04 -2.234371833506D-04 1.049668682077D-04 8 7.419442223475D-06 5.549545840266D-06 -2.941631374324D-06 E-Index: 3 4 5 T-Index: 0 4.271707093128D-02 -5.858821491798D-02 1.392666257426D-02 1 1.174092828553D-02 1.114511012703D-01 -2.954831571871D-02 2 -6.307600501935D-02 -6.111443567710D-02 2.198175535806D-02 3 3.966559773589D-02 9.770353095467D-03 -6.712723502770D-03 4 -1.172231175354D-02 2.197390583445D-03 6.399497506338D-04 5 1.999302843269D-03 -1.106397155875D-03 9.894710667600D-05 6 -2.070618270598D-04 1.765303992000D-04 -2.889915777541D-05 7 1.226009237337D-05 -1.292057629192D-05 2.493401272590D-06 8 -3.182522175779D-07 3.665898328329D-07 -7.535980089596D-08 E-Index: 6 7 8 T-Index: 0 -1.826013734833D-03 1.338360116582D-04 -4.094793119826D-06 1 3.221947627445D-03 -1.596959700477D-04 2.851937035822D-06 2 -2.959465078436D-03 1.811254083073D-04 -4.188871522474D-06 3 1.199132836096D-03 -9.257540264113D-05 2.685063664954D-06 4 -2.155848545229D-04 2.170199383545D-05 -7.480430374938D-07 5 1.197406032871D-05 -2.356790229752D-06 1.014622773664D-07 6 1.233468768851D-06 8.575083472581D-08 -6.548641344013D-09 7 -1.868672214120D-07 3.144081097677D-09 1.518680425956D-10 8 6.598419439525D-09 -2.255951200310D-10 7.165455179223D-13 Max. rel. Error: 28.3918 % Mean rel. Error: 1.3778 % \end{verbatim}\end{small} \newpage This page is intentionally left blank \newpage \subsection{ Reaction 3.3.6a $ p + He^*(1s^12s^11S) \rightarrow H^*(2s) + He^+(1s) $ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.547454346557D+01 4.128640321938D-01 1.681364689904D-01 1 2.925159193919D+00 -4.482539906582D-01 -1.510618145526D-01 2 -2.632374609849D-01 1.498243646661D-01 4.224863000625D-02 3 -3.665347937696D-02 -4.030592366279D-03 -6.024374907107D-03 4 1.186624566602D-02 -7.264454630020D-03 1.759741131185D-03 5 -7.743098120973D-04 1.549566023754D-03 -5.251712659531D-04 6 -6.048032854477D-05 -1.303138256507D-04 7.489465754264D-05 7 9.567845819569D-06 4.491545385436D-06 -4.865196018372D-06 8 -3.240997611305D-07 -3.791720988961D-08 1.182380927243D-07 E-Index: 3 4 5 T-Index: 0 4.770799895182D-02 -4.589820198321D-03 -3.381658191835D-03 1 5.782833798276D-04 1.062966905109D-02 -1.000814684417D-03 2 -1.379424993966D-02 -4.799947755285D-03 2.003286792299D-03 3 3.861551147569D-03 8.428413708310D-04 -6.216316421045D-04 4 -5.418286557573D-04 -2.942217454245D-05 7.238789629847D-05 5 1.074828795860D-04 -1.693095034492D-05 -1.682620078098D-06 6 -1.905146446763D-05 3.627851762042D-06 -3.555921820186D-07 7 1.601618148499D-06 -3.021602782205D-07 3.224220197809D-08 8 -4.832611082122D-08 9.163386368269D-09 -8.754524349299D-10 E-Index: 6 7 8 T-Index: 0 7.216467750187D-04 -5.367354341527D-05 1.404882131093D-06 1 -1.026211922836D-04 1.753943422756D-05 -6.292768990258D-07 2 -2.604060260416D-04 1.473506727808D-05 -3.094165446584D-07 3 1.074723588583D-04 -7.721788090796D-06 2.030369344275D-07 4 -1.611312475612D-05 1.369478220738D-06 -4.100428990113D-08 5 1.009293380060D-06 -1.149043918048D-07 4.074816429488D-09 6 -1.512787587046D-08 5.066369422287D-09 -2.328387385602D-10 7 -7.878569805292D-10 -1.445940103849D-10 8.580766309466D-12 8 2.044140116707D-11 3.044550460011D-12 -1.768485828956D-13 Max. rel. Error: 7.6526 % Mean rel. Error: 1.0667 % \end{verbatim}\end{small} \newpage This page is intentionally left blank \newpage \subsection{ Reaction 3.3.6b $p + He^*(1s^12s^13S) \rightarrow H^*(2s) + He^+(1s) $ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.143965131590D+01 6.213651065042D-01 1.902530458816D-01 1 5.052041699363D+00 -7.148284765635D-01 -1.237588528705D-01 2 -1.123510624616D+00 5.432613921547D-01 8.782764771787D-02 3 5.348600593230D-01 -2.975038694390D-01 -7.480657433556D-02 4 -2.135986381612D-01 1.005463096676D-01 3.217845093386D-02 5 4.690491969254D-02 -1.984365278750D-02 -6.930272101671D-03 6 -5.582187291915D-03 2.224271972399D-03 7.806801953220D-04 7 3.414974814001D-04 -1.311003795110D-04 -4.398645721299D-05 8 -8.438843692321D-06 3.153343412371D-06 9.747101004706D-07 E-Index: 3 4 5 T-Index: 0 6.905094039815D-02 2.031144550828D-03 -5.216959360609D-03 1 -3.733697369694D-02 -4.284814988611D-04 8.393728104870D-03 2 -6.508591153825D-02 1.088127433701D-02 -1.741996511515D-03 3 6.989130699630D-02 -1.052805212797D-02 -1.083666162584D-03 4 -2.714253969913D-02 4.258559341854D-03 4.082988867720D-04 5 5.298275385423D-03 -9.198385408429D-04 -1.481408240559D-05 6 -5.526051789225D-04 1.111995316138D-04 -9.733079909866D-06 7 2.923449260993D-05 -7.085139465779D-06 1.368541840554D-06 8 -6.120199563565D-07 1.849580238681D-07 -5.378697856092D-08 E-Index: 6 7 8 T-Index: 0 6.870508923626D-04 -2.653292731940D-05 1.208474130385D-08 1 -1.989364522591D-03 1.753792411592D-04 -5.477952397515D-06 2 3.431473662601D-04 -3.592640513827D-05 1.335701974095D-06 3 4.316290417315D-04 -4.061169944387D-05 1.281804690424D-06 4 -1.790232068370D-04 1.771568491253D-05 -5.843104467181D-07 5 2.117076885890D-05 -2.256441586648D-06 7.622251547211D-08 6 2.956849458181D-07 6.754190895102D-09 -4.412084334419D-10 7 -2.054349022277D-07 1.712307554998D-08 -5.567694760593D-10 8 9.859620416969D-09 -8.710088226618D-10 2.871802269066D-11 Max. rel. Error: 34.6091 % Mean rel. Error: 1.4428 % \end{verbatim}\end{small} \newpage This page is intentionally left blank \newpage \section{H.4 : Fits for $\langle\sigma v \rangle (n_e,T)$}\label{sect4} \subsection{ Reaction 2.1.5JH $H + e \rightarrow H^+ + 2e $} Effective hydrogenic ionization rate. Data: L.C.Johnson \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.292647100524D+01 1.293481375348D-02 5.517562508468D-03 1 1.423977672396D+01 -1.173143955186D-02 1.063440108279D-03 2 -6.519438729039D+00 -7.189825749516D-03 9.247377414923D-04 3 2.009996151806D+00 1.275979740638D-02 -4.693479616874D-03 4 -4.289594424073D-01 -5.340866322754D-03 2.324582357388D-03 5 6.047834607038D-02 9.624900593359D-04 -4.182981184259D-04 6 -5.304737965836D-03 -7.854872454067D-05 2.735823803201D-05 7 2.606946949696D-04 2.317442253442D-06 5.148890779990D-08 8 -5.467903073834D-06 6.077380038450D-09 -4.712893073569D-08 E-Index: 3 4 5 T-Index: 0 -7.853816321645D-04 1.436128501544D-04 -3.883750282085D-07 1 -1.600053527730D-03 1.136554639958D-05 5.177662275946D-05 2 2.037026745547D-03 -3.668717204076D-04 5.368630315837D-06 3 -2.389224140310D-05 1.358069915666D-04 -1.454897555460D-05 4 -3.217228075879D-04 6.660581406632D-06 2.396531874534D-06 5 7.957230182146D-05 -7.447042563915D-06 1.849155263575D-07 6 -5.915348564130D-06 8.666302868477D-07 -6.115514821045D-08 7 -7.144182523188D-09 -2.540194754187D-08 4.097857835689D-09 8 1.086858755070D-08 -3.448417246175D-10 -8.714183216468D-11 E-Index: 6 7 8 T-Index: 0 -1.489774355194D-06 1.416361431167D-07 -3.890932078762D-09 1 -7.947999902838D-06 4.508505683240D-07 -8.952614093357D-09 2 3.713958914062D-06 -3.125764373429D-07 7.451213220623D-09 3 4.212031496989D-08 5.506044670830D-08 -1.852677638893D-09 4 -1.785208321244D-07 6.095649574151D-10 1.470204228549D-10 5 1.618233640838D-08 -8.182928298434D-10 4.835789623340D-12 6 1.075473174260D-09 4.118000674849D-11 -1.089323091222D-12 7 -2.048657335774D-10 3.027916374251D-12 1.155854020410D-14 8 8.023660696154D-12 -2.396518500447D-13 2.173645280354D-15 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: .8487 % Mean rel. Error: .2419 % \end{verbatim}\end{small} \begin{figure} \label{2.1.5} \epsfxsize=16truecm \epsffile{Amjuel_PS/hydi1_tr.ps} \end{figure} \newpage \subsection{ Reaction 2.1.5o $H + e \rightarrow H^+ + 2e $, Ly-opaque} Effective hydrogenic ionization rate. Data: L.C.Johnson, Ly-opaque \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.842625123610D+01 3.816926440645D-02 -2.093090374769D-02 1 1.212167851020D+01 -8.864661558973D-02 2.578404580790D-02 2 -6.815821411657D+00 1.136458676986D-01 -3.209328253150D-02 3 2.625844925126D+00 -7.176672848153D-02 2.221528694064D-02 4 -6.666700835468D-01 2.362874407172D-02 -7.539637780701D-03 5 1.063576010855D-01 -4.303004854934D-03 1.340877575599D-03 6 -1.019791186281D-02 4.388098086177D-04 -1.289968813905D-04 7 5.357498344762D-04 -2.353712235761D-05 6.392439908462D-06 8 -1.183601163067D-05 5.183054638931D-07 -1.286865471654D-07 E-Index: 3 4 5 T-Index: 0 1.173278205549D-02 -3.195307082806D-03 4.891090254225D-04 1 -1.125027025423D-02 3.132061119992D-03 -5.478419611750D-04 2 7.428129132200D-03 -1.359196323415D-03 2.455552537690D-04 3 -3.813499462891D-03 3.488231091499D-04 -5.136595197719D-05 4 1.139599698461D-03 -5.231484976569D-05 3.851106631395D-06 5 -1.830544200085D-04 3.418266263749D-06 2.695420674804D-07 6 1.595087521180D-05 -5.244682697928D-08 -4.069155577999D-08 7 -7.334538727835D-07 7.314879444968D-09 -1.321258886395D-09 8 1.468328421917D-08 -8.136369296580D-10 2.036456697308D-10 E-Index: 6 7 8 T-Index: 0 -3.972967626237D-05 1.591035727928D-06 -2.476205052687D-08 1 4.881508340119D-05 -2.055128753437D-06 3.275823973472D-08 2 -2.356276122712D-05 1.024674585628D-06 -1.635599873170D-08 3 5.236557713321D-06 -2.300633304095D-07 3.500516071428D-09 4 -4.712865883416D-07 2.015344675266D-08 -2.228472576727D-10 5 -1.533579453796D-09 2.312045651251D-10 -2.651886075183D-11 6 6.001489992879D-10 -5.139558636314D-11 3.525452470540D-12 7 3.249620872276D-10 -1.169248684183D-11 1.979747513777D-14 8 -2.321096956876D-11 9.053581287584D-13 -1.015243451999D-14 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 1.6436 % Mean rel. Error: .4360 % \end{verbatim}\end{small} \begin{figure} \label{2.1.5o} \epsfxsize=16truecm \epsffile{Amjuel_PS/hydi1_op.ps} \end{figure} \newpage \subsection{ Reaction 2.1.5 $H + e \rightarrow H^+ + 2e $ } Effective hydrogenic ionization rate Data: K. Sawada/T. Fujimoto (redone: 2016, extend Te range of fit validity from 0.1 -- 1e3 to 0.1 -- 2e4 eV) \cite{kn:Sawada} \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.248025330340D+01 -5.440669186583D-02 9.048888225109D-02 1 1.425332391510D+01 -3.594347160760D-02 -2.014729121556D-02 2 -6.632235026785D+00 9.255558353174D-02 -5.580210154625D-03 3 2.059544135448D+00 -7.562462086943D-02 1.519595967433D-02 4 -4.425370331410D-01 2.882634019199D-02 -7.285771485050D-03 5 6.309381861496D-02 -5.788686535780D-03 1.507382955250D-03 6 -5.620091829261D-03 6.329105568040D-04 -1.527777697951D-04 7 2.812016578355D-04 -3.564132950345D-05 7.222726811078D-06 8 -6.011143453374D-06 8.089651265488D-07 -1.186212683668D-07 E-Index: 3 4 5 T-Index: 0 -4.054078993576D-02 8.976513750477D-03 -1.060334011186D-03 1 1.039773615730D-02 -1.771792153042D-03 1.237467264294D-04 2 -5.902218748238D-03 1.295609806553D-03 -1.056721622588D-04 3 5.803498098354D-04 -3.527285012725D-04 3.201533740322D-05 4 4.643389885987D-04 1.145700685235D-06 8.493662724988D-07 5 -1.201550548662D-04 6.574487543511D-06 -9.678782818849D-07 6 8.270124691336D-06 3.224101773605D-08 4.377402649057D-08 7 1.433018694347D-07 -1.097431215601D-07 7.789031791949D-09 8 -2.381080756307D-08 6.271173694534D-09 -5.483010244930D-10 E-Index: 6 7 8 T-Index: 0 6.846238436472D-05 -2.242955329604D-06 2.890437688072D-08 1 -3.130184159149D-06 -3.051994601527D-08 1.888148175469D-09 2 4.646310029498D-06 -1.479612391848D-07 2.852251258320D-09 3 -1.835196889733D-06 9.474014343303D-08 -2.342505583774D-09 4 -1.001032516512D-08 -1.476839184318D-08 6.047700368169D-10 5 5.176265845225D-08 1.291551676860D-09 -9.685157340473D-11 6 -2.622921686955D-09 -2.259663431436D-10 1.161438990709D-11 7 -4.197728680251D-10 3.032260338723D-11 -8.911076930014D-13 8 3.064611702159D-11 -1.355903284487D-12 2.935080031599D-14 T1MIN = 0.10000D 00 EV T1MAX = 2.00000D 04 EV N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 1.98 % Mean rel. Error: 0.479 % \end{verbatim}\end{small} \begin{figure} \label{H4-2.1.5FU} \epsfxsize=16truecm \epsffile{Amjuel_PS/H4-2.1.5.eps} \end{figure} \newpage \subsection{ Reaction 2.1.8JH $ H^+ + e\rightarrow H(1s) $ } Effective hydrogenic recombination rate Data: L.C.Johnson, radiative + three-body contribution \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.855728479302D+01 3.488563234375D-02 -2.799644392058D-02 1 -7.664042607917D-01 -3.583233366133D-03 -7.452514292790D-03 2 -4.930424003280D-03 -3.620245352252D-03 6.958711963182D-03 3 -5.386830982777D-03 -9.532840484460D-04 4.631753807534D-04 4 -1.626039237665D-04 1.888048628708D-04 1.288577690147D-04 5 6.080907650243D-06 -1.014890683861D-05 -1.145028889459D-04 6 2.101102051942D-05 2.245676563601D-05 -2.245624273814D-06 7 -2.770717597683D-06 -4.695982369246D-06 3.250878872873D-06 8 1.038235939800D-07 2.523166611507D-07 -2.145390398476D-07 E-Index: 3 4 5 T-Index: 0 1.209545317879D-02 -2.436630799820D-03 2.837893719800D-04 1 2.709299760454D-03 -7.745129766167D-04 1.142444698207D-04 2 -2.139257298118D-03 4.603883706734D-04 -5.991636837395D-05 3 -5.371179699661D-04 1.543350502150D-04 -2.257565836876D-05 4 -1.634580516353D-05 -9.601036952725D-06 3.425262385387D-06 5 5.942193980802D-05 -1.211851723717D-05 1.118965496365D-06 6 -2.944873763540D-06 1.002105099354D-06 -1.291320799814D-07 7 -9.387290785993D-07 1.392391630459D-07 -1.139093288575D-08 8 7.381435237585D-08 -1.299713684966D-08 1.265189576423D-09 E-Index: 6 7 8 T-Index: 0 -1.886511169084D-05 6.752155602894D-07 -1.005893858779D-08 1 -9.382783518064D-06 3.902800099653D-07 -6.387411585521D-09 2 4.729262545726D-06 -1.993485395689D-07 3.352589865190D-09 3 1.730782954588D-06 -6.618240780594D-08 1.013364275013D-09 4 -4.077019941998D-07 2.042041097083D-08 -3.707977721109D-10 5 -4.275321573501D-08 3.708616111085D-10 7.068450112690D-12 6 7.786155463269D-09 -2.441127783437D-10 3.773208484020D-12 7 5.178505597480D-10 -9.452402157390D-12 -4.672724022059D-14 8 -6.854203970018D-11 1.836615031798D-12 -1.640492364811D-14 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 6.8962 % Mean rel. Error: .5559 % \end{verbatim}\end{small} \begin{figure} \label{2.1.8} \epsfxsize=16truecm \epsffile{Amjuel_PS/hydr1_tr.ps} \end{figure} \newpage \subsection{ Reaction 2.1.8o $ H^+ + e \rightarrow H(1s) $ Ly-opaque } Effective hydrogenic recombination rate Data: L.C.Johnson, radiative + three-body contribution all Lyman lines opaque, i.e. no radiative transition to ground state. \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.959696621207D+01 -2.370057688281D-01 2.485234780243D-01 1 -2.261509350573D+00 -3.916834765592D-01 4.175284638738D-01 2 -4.674937331875D-01 -5.569001933269D-03 1.424684098594D-02 3 2.507869795516D-01 2.497608379269D-02 -3.407068292654D-02 4 2.069706780864D-02 -6.227904899439D-03 7.567752788769D-03 5 -2.504106136665D-02 5.231970346733D-03 -4.961906824405D-03 6 4.740060719354D-03 -1.583429487117D-03 1.485117205295D-03 7 -3.716199599046D-04 1.790096302797D-04 -1.687816759412D-04 8 1.078074419507D-05 -6.889626133438D-06 6.523611088216D-06 E-Index: 3 4 5 T-Index: 0 -9.938245216461D-02 1.980881578608D-02 -2.122222479009D-03 1 -1.818480115491D-01 3.961587768727D-02 -4.770502751429D-03 2 -7.573368055249D-03 2.345252431484D-03 -3.903412960562D-04 3 1.848151065349D-02 -4.874151697039D-03 6.859699832287D-04 4 -3.519012590703D-03 7.900468003264D-04 -9.404610318098D-05 5 1.530766046402D-03 -1.980846746944D-04 7.679462128899D-06 6 -4.566472727887D-04 6.072295908223D-05 -2.912042904116D-06 7 5.315093984335D-05 -7.528931894689D-06 4.568686753692D-07 8 -2.087698447004D-06 3.070917297414D-07 -2.078805542480D-08 E-Index: 6 7 8 T-Index: 0 1.218203616198D-04 -3.464708585003D-06 3.763195232065D-08 1 3.183363649173D-04 -1.099361683574D-05 1.532076900830D-07 2 3.495619343912D-05 -1.549589929805D-06 2.649470795327D-08 3 -5.207997134901D-05 2.003342466410D-06 -3.056485646618D-08 4 5.971364301743D-06 -1.910514915873D-07 2.423960414424D-09 5 5.127742944183D-07 -5.042762997588D-08 1.117985320964D-09 6 -6.966012349475D-08 1.046266371637D-08 -2.448127591728D-10 7 -4.197741084618D-09 -6.390754230254D-10 1.836925499320D-11 8 4.554850332229D-10 1.165730429588D-11 -4.891755053806D-13 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 21.7976 % Mean rel. Error: 8.2471 % \end{verbatim}\end{small} \begin{figure} \label{2.1.8o} \epsfxsize=16truecm \epsffile{Amjuel_PS/hydr1_op.ps} \end{figure} \newpage \subsection{ Reaction 2.1.8 $ H^+ + e \rightarrow H(1s) $ } Effective hydrogenic recombination rate Data: K. Sawada, T.Fujimoto, radiative + three-body contribution, \cite{kn:Sawada} June17: Fit range extended from 0.1 -- 1e3 to 0.1 -- 2e4 \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.858858570847D+01 2.068671746773D-02 -7.868331504755D-03 1 -7.676413320499D-01 1.278006032590D-02 -1.870326896978D-02 2 2.823851790251D-03 -1.907812518731D-03 1.121251125171D-02 3 -1.062884273731D-02 -1.010719783828D-02 4.208412930611D-03 4 1.582701550903D-03 2.794099401979D-03 -2.024796037098D-03 5 -1.938012790522D-04 2.148453735781D-04 3.393285358049D-05 6 6.041794354114D-06 -1.421502819671D-04 6.143879076080D-05 7 1.742316850715D-06 1.595051038326D-05 -7.858419208668D-06 8 -1.384927774988D-07 -5.664673433879D-07 2.886857762387D-07 E-Index: 3 4 5 T-Index: 0 3.843362133859D-03 -7.411492158905D-04 9.273687892997D-05 1 3.828555048890D-03 -3.627770385335D-04 4.401007253801D-07 2 -3.711328186517D-03 6.617485083301D-04 -6.860774445002D-05 3 -1.005744410540D-03 1.013652422369D-04 -2.044691594727D-06 4 6.250304936976D-04 -9.224891301052D-05 7.546853961575D-06 5 -3.746423753955D-05 7.509176112468D-06 -8.688365258514D-07 6 -1.232549226121D-05 1.394562183496D-06 -6.434833988001D-08 7 1.774935420144D-06 -2.187584251561D-07 1.327090702659D-08 8 -6.591743182569D-08 8.008790343319D-09 -4.805837071646D-10 E-Index: 6 7 8 T-Index: 0 -7.063529824805D-06 3.026539277057D-07 -5.373940838104D-09 1 1.932701779173D-06 -1.176872895577D-07 2.215851843121D-09 2 4.508046989099D-06 -1.723423509284D-07 2.805361431741D-09 3 -4.431181498017D-07 3.457903389784D-08 -7.374639775683D-10 4 -3.682709551169D-07 1.035928615391D-08 -1.325312585168D-10 5 7.144767938783D-08 -3.367897014044D-09 6.250111099227D-11 6 -2.746804724917D-09 3.564291012995D-10 -8.551708197610D-12 7 -1.386720240985D-10 -1.946206688519D-11 5.745422385081D-13 8 6.459706573699D-12 5.510729582791D-13 -1.680871303639D-14 T1MIN = 0.10000D 00 EV T1MAX = 2.00000D 04 EV N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 0.931E+01 % Mean rel. Error: 0.745E+00 % \end{verbatim}\end{small} \begin{figure} \label{2.1.8FU} \epsfxsize=16truecm \epsffile{Amjuel_PS/H4-2.1.8.eps} \end{figure} \newpage \subsection{ Reaction 2.1.8a $H^+ + e \rightarrow H(1s) + hv $ } Effective hydrogenic recombination rate coefficient, $cm^3/s$ Data: L.C.Johnson, radiative contribution only \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.861779556590D+01 -1.786166918005D-02 6.391553337864D-04 1 -7.251997071478D-01 3.210966054964D-03 4.550251497787D-03 2 -1.735023322687D-02 -3.112517426840D-03 1.077863345492D-03 3 -3.557752804131D-03 1.558966107388D-03 -1.037331531958D-03 4 -2.777882255016D-04 -9.329932857673D-05 1.096331766957D-04 5 2.060295404466D-05 -1.283711654633D-04 7.312311894769D-05 6 1.593238392469D-05 3.705503401064D-05 -2.407235857913D-05 7 -2.116580756634D-06 -3.854172456142D-06 2.662392026941D-06 8 7.665990100168D-08 1.400789118322D-07 -1.008951470934D-07 E-Index: 3 4 5 T-Index: 0 -4.509415260040D-04 7.095459017274D-05 -5.660309928918D-06 1 -1.882306456891D-03 3.983133042462D-04 -4.851835293564D-05 2 -2.616958968739D-04 5.459332810644D-05 -8.635308675130D-06 3 2.817237174744D-04 -4.407815167942D-05 4.646017350681D-06 4 -4.567488387292D-05 8.495787235165D-06 -7.261076273040D-07 5 -1.064805149480D-05 -1.498776433806D-07 1.199087596048D-07 6 4.915213917257D-06 -3.346609397503D-07 -4.912753691671D-09 7 -6.120846201882D-07 5.663728215333D-08 -1.474221162308D-09 8 2.495214914834D-08 -2.678484130657D-09 1.170138331019D-10 E-Index: 6 7 8 T-Index: 0 1.160186631232D-07 7.564986067995D-09 -2.969815025786D-10 1 3.404834497087D-06 -1.280839994482D-07 1.982839967575D-09 2 8.383106368091D-07 -4.133352004945D-08 7.872491728981D-10 3 -3.365654551356D-07 1.428350791171D-08 -2.522153346435D-10 4 2.326992940046D-08 2.208089550616D-10 -1.989979386039D-11 5 -5.668079133507D-09 -1.018554043516D-10 7.766578964142D-12 6 1.302393677822D-09 -3.169013613822D-11 -1.783762758524D-13 7 -7.373095178045D-11 4.314457229158D-12 -4.791677504810D-14 8 -1.588254701759D-13 -1.226345218681D-13 2.329402447113D-15 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 2.5215 % Mean rel. Error: 0.1955 % \end{verbatim}\end{small} \begin{figure} \label{2.1.8a} \epsfxsize=16truecm \epsffile{Amjuel_PS/hydr1a.ps} \end{figure} \newpage \subsection{ Reaction 2.1.8b $H^+ + e + e \rightarrow H(1s) + e$ } Effective hydrogenic recombination rate coefficient, $cm^3/s$, i.e. one of the two electron density factors is already included. Data: L.C.Johnson, three-body contribution only \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.138669506796D+01 2.558074094965D-01 7.547564538159D-02 1 -1.417925704352D+00 -1.066708008069D-01 8.912699543671D-02 2 -3.966595205668D-02 1.064506076088D-01 -9.185507688379D-02 3 -2.739310162323D-03 1.071195586887D-02 -1.158499493255D-02 4 1.342474842019D-03 -1.404239147230D-02 1.282799910712D-02 5 -3.784959334108D-05 2.130406018949D-03 -1.795433974878D-03 6 -2.481473746256D-05 -2.906534460063D-05 4.381082887635D-07 7 3.022022778586D-06 -1.227016198396D-05 1.250237920569D-05 8 -1.059584647842D-07 5.895982135096D-07 -5.420516699864D-07 E-Index: 3 4 5 T-Index: 0 -3.195165302392D-02 5.993840007093D-03 -6.049665420516D-04 1 -3.076861794558D-02 5.170778601878D-03 -4.681886539105D-04 2 3.233942643372D-02 -5.730070151158D-03 5.639470554955D-04 3 4.028223463613D-03 -6.775275129877D-04 5.927342203251D-05 4 -4.343906483582D-03 7.330672175437D-04 -6.737562862785D-05 5 5.739582951694D-04 -9.301568592793D-05 8.339289670874D-06 6 4.646781534504D-06 -9.443082582766D-07 4.567269449835D-08 7 -4.231117608526D-06 6.309570737001D-07 -4.235798707450D-08 8 1.668808712577D-07 -2.180052385585D-08 1.047870711900D-09 E-Index: 6 7 8 T-Index: 0 3.390872601321D-05 -9.817548467947D-07 1.135964925849D-08 1 2.260490762610D-05 -5.312960958760D-07 4.417913806532D-09 2 -3.105931750375D-05 8.954284624235D-07 -1.053605286933D-08 3 -2.695731962799D-06 5.604944938198D-08 -3.081951853519D-10 4 3.406464134420D-06 -8.840559993869D-08 9.088416616843D-10 5 -4.195355464733D-07 1.130977058144D-08 -1.314879735454D-10 6 3.574490849965D-09 -4.342693823216D-10 1.186584611296D-11 7 7.775072659869D-10 4.164660123508D-11 -1.575223043337D-12 8 2.251635634963D-11 -3.743444984134D-12 9.336979510479D-14 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 6.0738 % Mean rel. Error: 0.8731 % \end{verbatim}\end{small} \begin{figure} \label{2.1.8b} \epsfxsize=16truecm \epsffile{Amjuel_PS/hydr1b.ps} \end{figure} \newpage \subsection{ Reaction 2.2.5 $e + H_2 \rightarrow e + H + H $ } H2 multi-step model Data: K. Sawada/Fujimoto ,\cite{kn:Sawada} coupling to reservoir of $ H(1), H_2, H_2^+, H^+ $ (``transported" species) $H_2$ is in vibrational ground state $v=0$, and the electronic levels in the molecules as discussed in \cite{kn:Sawada} are taken into account. \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.748251723699D+01 5.245554722385D-04 -2.978103958861D-04 1 1.032713102402D+01 -4.288853521030D-04 -4.899568733097D-04 2 -5.042872981718D+00 2.836621770958D-03 -3.043912367565D-03 3 1.608638174175D+00 -1.261120000328D-03 1.887422712154D-03 4 -4.314430346833D-01 -8.545622758573D-04 7.288308305238D-04 5 9.436567726730D-02 3.330555462733D-04 -3.941114594575D-04 6 -1.384992697339D-02 5.154637596963D-06 2.704571960637D-05 7 1.132016190295D-03 -1.288164830284D-05 7.769128981290D-06 8 -3.842014088368D-05 1.171737695451D-06 -9.017007769431D-07 E-Index: 3 4 5 T-Index: 0 -2.360275829176D-07 2.352410977770D-05 -4.997866180134D-06 1 4.986004995584D-04 -1.488915435909D-04 2.064670043755D-05 2 1.292894496252D-03 -2.905449411133D-04 3.788502709678D-05 3 -9.327238099803D-04 2.128634474527D-04 -2.509788157193D-05 4 -2.484715070595D-04 4.842155320136D-05 -6.186008058267D-06 5 1.711527657525D-04 -3.637820737985D-05 4.163286478680D-06 6 -2.084393307530D-05 5.401855723043D-06 -6.247464789742D-07 7 -1.221455182210D-06 -3.231445161484D-09 9.993216378891D-09 8 2.476534052706D-07 -3.367686347533D-08 2.869160964443D-09 E-Index: 6 7 8 T-Index: 0 4.276219304407D-07 -1.656742885479D-08 2.414039859152D-10 1 -1.483657661440D-06 5.231689914639D-08 -7.056262049968D-10 2 -2.892758625724D-06 1.174418148176D-07 -1.927933996765D-09 3 1.553010173585D-06 -4.703323705313D-08 5.371568383284D-10 4 5.102144895277D-07 -2.321199392340D-08 4.255457918971D-10 5 -2.597547413556D-07 8.256194712004D-09 -1.040875802194D-10 6 3.214084295485D-08 -5.485492350310D-10 -2.766340477990D-12 7 1.346287938920D-10 -7.497501425175D-11 2.502198014796D-12 8 -1.931319268617D-10 9.102276313210D-12 -1.872646131609D-13 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 1.7118 % Mean rel. Error: 0.4517 % \end{verbatim}\end{small} \begin{figure} \label{2.2.5} \epsfxsize=16truecm \epsffile{Amjuel_PS/hydh2d2.ps} \end{figure} \newpage \subsection{ Reaction 2.2.5g $e + H_2 \rightarrow e + H + H $ } H2 multi-step model, data: Sawada/Fujimoto/Greenland. $ H(1), H_2, H_2^+, H^+ $ transported (slow species). The $H_2(v)$ are in vibrational equilibrium (depends only upon $T_e$), and the electronic levels in the molecules as discussed in \cite{kn:Sawada} are taken into account. CX losses from vibr. distribution are computed assuming $T_e = T_i$, $n_e = n_p$, and an energy of $H_2$-Beam = 0.1 eV. \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.702372540584D+01 -3.152103191633D-03 5.990692171729D-03 1 1.081756417479D+01 -1.487216964825D-02 1.417396532101D-02 2 -5.368872027676D+00 5.419787589654D-03 -1.747268613395D-02 3 1.340684229143D+00 1.058157580038D-02 -3.446019122786D-03 4 -1.561644923145D-01 -3.847438570333D-03 3.571477356851D-03 5 -1.444731533894D-04 -3.194532513126D-04 -2.987368098475D-04 6 2.117693926546D-03 2.679309814780D-04 -1.037559373832D-04 7 -2.143738340207D-04 -3.539232757385D-05 1.909399233821D-05 8 6.979740947331D-06 1.462031952352D-06 -8.858634506391D-07 E-Index: 3 4 5 T-Index: 0 -3.151252835426D-03 7.457309144890D-04 -9.238664007853D-05 1 -4.689911797083D-03 7.180338663163D-04 -5.502798587526D-05 2 9.532963297450D-03 -2.196705622859D-03 2.611447288152D-04 3 -7.032769815599D-04 4.427959286553D-04 -7.370484189164D-05 4 -1.103305795473D-03 1.476712517858D-04 -8.461162952132D-06 5 2.092094838648D-04 -4.339352509941D-05 4.009328699469D-06 6 7.297053580368D-06 1.454171585421D-06 -2.251616910293D-07 7 -3.819368125069D-06 3.754063159414D-07 -2.441872829462D-08 8 2.099830142707D-07 -2.606862169776D-08 2.039813579349D-09 E-Index: 6 7 8 T-Index: 0 6.222557542845D-06 -2.160024578659D-07 3.028755759836D-09 1 1.983066081752D-06 -2.207639762507D-08 -2.116339335271D-10 2 -1.695536960581D-05 5.737375510694D-07 -7.940900078995D-09 3 5.746786010618D-06 -2.182085196303D-07 3.264045809897D-09 4 9.757111870171D-08 8.130014050833D-09 -2.234996157750D-10 5 -1.762651912129D-07 3.357860444624D-09 -1.857322587267D-11 6 9.191700327811D-09 -2.052366968228D-11 -3.567738654108D-12 7 1.437490161488D-09 -6.172308568891D-11 1.104905484620D-12 8 -1.113483084607D-10 3.859777100010D-12 -5.909099891913D-14 T1MIN = 0.10000D 00 EV T1MAX = 1.00000D 03 EV N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 11.6439 % Mean rel. Error: 2.6169 % \end{verbatim}\end{small} \begin{figure} \label{2.2.5g} \epsfxsize=16truecm \epsffile{Amjuel_PS/green4.ps} \end{figure} \newpage \subsection{ Reaction 2.2.9 $ e + H_2 \rightarrow 2e + H_2^+ $ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.574773783577D+01 3.470247049909D-01 -9.683166540937D-02 1 1.769208985507D+01 -1.311169841222D+00 4.700486215943D-01 2 -8.291764008409D+00 1.591701525694D+00 -5.814996025336D-01 3 2.555712347240D+00 -8.625268584825D-01 2.612076696684D-01 4 -5.370404654062D-01 2.375816996323D-01 -4.165908778170D-02 5 7.443307905391D-02 -3.322214182214D-02 -2.351235556666D-03 6 -6.391785721973D-03 1.862554278190D-03 1.540632467396D-03 7 3.001729098239D-04 3.497202259366D-05 -1.742029226138D-04 8 -5.607182991432D-06 -5.779550092391D-06 6.495742927455D-06 E-Index: 3 4 5 T-Index: 0 1.959576276250D-03 2.479361119190D-03 -1.196632952666D-04 1 -5.521175478827D-02 -2.689651616933D-03 7.308915874002D-04 2 9.160898084105D-02 -4.770789631868D-03 1.994775632224D-05 3 -3.686525285376D-02 1.945480608139D-03 -3.690918356665D-05 4 1.732469114063D-03 3.693513203529D-04 -4.931268184607D-05 5 1.723053881691D-03 -2.096625925098D-04 1.358575558294D-05 6 -3.547150770477D-04 1.392157055273D-05 1.047463944093D-06 7 2.296551698214D-05 2.357520372192D-06 -5.306085513950D-07 8 -3.040011333889D-07 -2.361542565281D-07 3.655056080262D-08 E-Index: 6 7 8 T-Index: 0 -1.862956119592D-05 1.669867158509D-06 -3.673736278200D-08 1 -2.920560755694D-05 -3.148831240316D-07 2.514856386324D-08 2 -7.511552245648D-06 1.089689676313D-06 -2.920863498031D-08 3 4.836340453567D-06 -4.165748666929D-07 9.265898224345D-09 4 2.727501534044D-06 -1.081027384449D-07 2.420509440644D-09 5 -1.041586202167D-06 6.928574330531D-08 -1.746656185835D-09 6 1.513510667993D-08 -9.915499708242D-09 3.298173891188D-10 7 2.223137028418D-08 3.340169309800D-10 -2.560542889504D-11 8 -1.771478792301D-09 1.334615260635D-11 6.831564719957D-13 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 3.1001 % Mean rel. Error: .4740 % \end{verbatim}\end{small} \begin{figure} \label{2.2.9} \epsfxsize=16truecm \epsffile{Amjuel_PS/hydh2i.ps} \end{figure} \newpage \subsection{ Reaction 2.2.10 $ e + H_2 \rightarrow 2e + H + H^+ $ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.793749300315D+01 -3.333162972531D-01 1.849601203843D-01 1 1.280249398154D+01 1.028969438485D+00 -3.271855492638D-01 2 -3.778148553140D+00 -1.415561059533D+00 2.928509524911D-01 3 2.499987501522D-01 1.032922656537D+00 -1.580288004759D-01 4 2.480574522949D-01 -4.372934216955D-01 6.448433196301D-02 5 -9.960628182831D-02 1.092652428162D-01 -1.782307798975D-02 6 1.709129400742D-02 -1.574889001363D-02 2.865310743302D-03 7 -1.435304503973D-03 1.203823111704D-03 -2.350465388313D-04 8 4.808639828229D-05 -3.761591649539D-05 7.490531472388D-06 E-Index: 3 4 5 T-Index: 0 -8.803945197107D-02 2.205180180735D-02 -2.852568161901D-03 1 1.305597441611D-01 -3.408439821910D-02 4.591924060066D-03 2 -7.425165688158D-02 2.028424685287D-02 -3.042376564749D-03 3 9.934702707539D-03 -2.450845732158D-03 5.716646876513D-04 4 1.229222932630D-03 -9.281410519553D-04 5.946235618034D-05 5 1.192181214757D-04 2.310636556641D-04 -2.492990725967D-05 6 -1.700396064727D-04 -1.502644504654D-06 3.297869416435D-07 7 2.507288189894D-05 -3.077975735212D-06 3.748299687254D-07 8 -1.077314971617D-06 1.950247963978D-07 -2.569729600929D-08 E-Index: 6 7 8 T-Index: 0 1.942314738448D-04 -6.597388255594D-06 8.798544848606D-08 1 -3.167471002157D-04 1.070920193931D-05 -1.408139742113D-07 2 2.279124955373D-04 -8.197224564797D-06 1.130682076163D-07 3 -5.339115778704D-05 2.135848413694D-06 -3.072223247387D-08 4 -8.758032156912D-08 -7.270955072707D-08 1.100087131523D-09 5 1.217600444191D-06 -3.624263301602D-08 6.139167092128D-10 6 6.572135289627D-10 4.269190108005D-10 -3.666090917669D-11 7 -2.613600078122D-08 8.263175463927D-10 -8.509179497022D-12 8 1.804377780165D-09 -6.031847199601D-11 7.416020205748D-13 T1MIN = 0.05000D 00 EV T1MAX = 1.00000D 03 EV N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 1.2041 % Mean rel. Error: .4804 % \end{verbatim}\end{small} \begin{figure} \label{2.2.10} \epsfxsize=16truecm \epsffile{Amjuel_PS/hydh2d1.ps} \end{figure} \newpage \subsection{ Reaction 2.2.11 $e + H_2^+ \rightarrow 2e + H^+ + H^+ $ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.708803769397D+01 9.784233987341D-02 -7.200361272130D-03 1 1.561780529774D+01 -1.673256230592D-02 2.743322772895D-02 2 -6.874406034117D+00 -7.782929961315D-03 -6.888773684846D-03 3 2.010540060675D+00 -3.226785148562D-03 -6.181192193854D-03 4 -3.614768906120D-01 3.710098881765D-03 2.045814599796D-03 5 2.956861321735D-02 -5.524443504504D-04 -2.457951062112D-05 6 9.662490252868D-04 -1.548556801431D-04 1.417215042439D-05 7 -3.543571865464D-04 4.662969089421D-05 -1.471117766355D-05 8 1.827109843671D-05 -3.179895716088D-06 1.432429412413D-06 E-Index: 3 4 5 T-Index: 0 6.496843022778D-03 -1.420590818760D-03 1.703620321164D-04 1 -1.026956102747D-02 1.999561527383D-03 -2.043607814503D-04 2 2.306107197863D-03 -4.029222834436D-04 3.932152471491D-05 3 2.388146990238D-03 -5.018901320009D-04 5.520233512352D-05 4 -8.523935993991D-04 1.751295192861D-04 -1.944203941844D-05 5 3.433179945503D-05 -1.450208898992D-06 -2.447566480782D-07 6 -6.444863591678D-06 -1.566028729499D-06 4.152486680818D-07 7 5.235585096328D-06 -5.779667826854D-07 2.139729421817D-08 8 -5.141065080107D-07 7.734387173369D-08 -6.163336831045D-09 E-Index: 6 7 8 T-Index: 0 -1.160738946400D-05 4.148222302162D-07 -6.007853385325D-09 1 1.084177127603D-05 -2.671800995803D-07 2.093182411476D-09 2 -2.094907364150D-06 5.682907060010D-08 -6.320752545610D-10 3 -3.080798536641D-06 7.864770315002D-08 -6.357395371638D-10 4 1.138888354831D-06 -3.256303793266D-08 3.501794038444D-10 5 1.375679100044D-08 4.863880510459D-10 -3.004374374556D-11 6 -2.855068942744D-08 6.081804811000D-10 9.512865901179D-13 7 -3.656048425230D-10 3.759866326965D-11 -1.486151370215D-12 8 3.128313515842D-10 -1.061842444216D-11 1.771099769640D-13 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 1.0209 % Mean rel. Error: 0.3164 % \end{verbatim}\end{small} \begin{figure} \label{2.2.11} \epsfxsize=16truecm \epsffile{Amjuel_PS/hydh2p0.ps} \end{figure} \newpage \subsection{ Reaction 2.2.12 $ e + H_2^+ \rightarrow e + H + H^+ $ } Effective dissociative excitation of H$_2^+$ to H and H$^+$, including the component $e+H_2^+ \rightarrow H + H^* \rightarrow H + H^+$ from dissociative recombination of H$_2^+$ with excited products. \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -1.793443274600D+01 -4.932783688604D-02 1.039088280849D-01 1 2.236108757681D+00 -2.545406018621D-02 -1.160421006835D-01 2 -3.620018994703D-01 6.721527680150D-02 1.564387124002D-02 3 -4.353922258965D-01 -3.051033606589D-02 3.512861172521D-02 4 1.580381801957D-01 2.493654957203D-03 -1.601970998119D-02 5 1.697880687685D-02 2.106675963900D-03 4.521983358170D-04 6 -1.521914651109D-02 -7.527862162788D-04 9.095551479381D-04 7 2.406276368070D-03 9.971361856278D-05 -1.760978402353D-04 8 -1.219469579955D-04 -4.785505675232D-06 9.858840337511D-06 E-Index: 3 4 5 T-Index: 0 -4.375935166008D-02 9.196691651936D-03 -1.043378648769D-03 1 4.407846563362D-02 -8.192521304984D-03 8.200277386433D-04 2 -4.939045440424D-03 4.263195867947D-04 1.034216805418D-05 3 -1.179504564265D-02 2.091772760029D-03 -1.991100044575D-04 4 5.346709597939D-03 -8.711870134835D-04 7.542066727545D-05 5 -3.017151690655D-04 6.209239389357D-05 -7.598119096817D-06 6 -2.372576223034D-04 3.018561480848D-05 -1.365255868731D-06 7 4.877659148871D-05 -6.477358351729D-06 3.541106430252D-07 8 -2.779210878533D-06 3.720379996058D-07 -2.110289928486D-08 E-Index: 6 7 8 T-Index: 0 6.600342421838D-05 -2.198466460165D-06 3.004145701249D-08 1 -4.508284363534D-05 1.282824614809D-06 -1.474719350236D-08 2 -3.975028601900D-06 2.322116289258D-07 -4.381217154470D-09 3 1.018080238045D-05 -2.597941866088D-07 2.524118386011D-09 4 -3.410778344979D-06 7.120460603822D-08 -4.412295474522D-10 5 5.523273241689D-07 -2.130508249251D-08 3.319099650589D-10 6 -4.604769733903D-08 5.867910270430D-09 -1.357779142836D-10 7 1.309772899670D-09 -8.072907334230D-10 2.074669430611D-11 8 3.753875073646D-11 4.024906665497D-11 -1.075990572574D-12 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 15.8263 % Mean rel. Error: 3.9031 % \end{verbatim}\end{small} \begin{figure} \label{2.2.12} \epsfxsize=16truecm \epsffile{Amjuel_PS/hydh2p1.eps} \end{figure} \newpage \subsection{ Reaction 2.2.14 $ e + H_2^+ \rightarrow H + H $ } Effective dissociative recombination of H$_2^+$ to H and H, subtracting the ionising component $e+H_2^+ \rightarrow H + H^* \rightarrow H + H^+$ from dissociative recombination of H$_2^+$ with excited products. \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -1.664335253647D+01 8.953780953631D-02 -1.056411030518D-01 1 -6.005444031657D-01 4.063933992726D-02 -4.753947846841D-02 2 4.494812032769D-04 7.884508616595D-05 3.688007562485D-04 3 1.632894866655D-04 3.108116177617D-04 -3.521552580917D-04 4 -7.234142549752D-05 -1.316311320262D-03 1.643509328764D-03 5 -1.504085050039D-05 1.315865970237D-04 -1.025653773999D-04 6 1.113923667684D-05 2.711411525392D-05 -8.495922363727D-05 7 -1.843926162250D-06 -1.663674537499D-06 1.308069926896D-05 8 9.864173150662D-08 -2.212261708468D-07 -4.431749501051D-07 E-Index: 3 4 5 T-Index: 0 4.477000808690D-02 -9.729945434357D-03 1.174456882002D-03 1 2.188304031377D-02 -5.201085606791D-03 6.866340394051D-04 2 -4.659255785539D-04 1.907115980400D-04 -3.434324710145D-05 3 -2.233169775063D-04 1.869415236037D-04 -4.329991211511D-05 4 -6.412764282779D-04 1.048891053765D-04 -7.018555173322D-06 5 5.310324781249D-05 -1.831888048039D-05 3.423755373077D-06 6 4.026487801017D-05 -6.289324474240D-06 1.911447036702D-07 7 -7.324021449032D-06 1.431739868187D-06 -1.085644779665D-07 8 3.270530731011D-07 -7.282085521177D-08 6.578253567957D-09 E-Index: 6 7 8 T-Index: 0 -7.987743820637D-05 2.842957892768D-06 -4.104508608435D-08 1 -5.059940013116D-05 1.930213882205D-06 -2.963966822809D-08 2 3.067651560323D-06 -1.325689465590D-07 2.212493073620D-09 3 4.465256901322D-06 -2.136296167564D-07 3.873085368404D-09 4 4.776213235854D-08 1.380537343974D-08 -4.199397846492D-10 5 -3.303384352061D-07 1.551627097700D-08 -2.809391819541D-10 6 3.638198230235D-08 -3.235540606394D-09 7.605442050634D-11 7 1.143164983367D-09 2.151595003971D-10 -7.052562220005D-12 8 -1.925258267827D-10 -4.217474167519D-12 2.364754029318D-13 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 3.3331 % Mean rel. Error: 0.3010 % \end{verbatim}\end{small} \begin{figure} \label{2.2.14} \epsfxsize=16truecm \epsffile{Amjuel_PS/hydh2p2.eps} \end{figure} \newpage \subsection{ Reaction 2.3.9a $e + He(1s^21S) \rightarrow e + He^+(1s) + e $ } Helium multi-step model, here ionization, Eth=24.56 eV Fujimoto Formulation II, meta-stable unresolved, (only ground level transported, no meta-stables kept explicit), \cite{kn:Fujimoto} \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -4.227118452798D+01 1.294554451998D-01 -8.433979538052D-02 1 2.411668100975D+01 -8.121999208281D-02 4.052570160482D-02 2 -1.203181133667D+01 -3.998282970932D-03 -2.819919193060D-03 3 3.829444688521D+00 2.546414073266D-02 2.654490306111D-03 4 -7.945839257175D-01 -1.493597874850D-02 -1.018320076497D-03 5 1.054334178555D-01 4.338821244147D-03 -1.483560478208D-04 6 -8.578643565653D-03 -6.689202603525D-04 9.084162487421D-05 7 3.886232727181D-04 5.180805123476D-05 -1.125453787291D-05 8 -7.487575233223D-06 -1.582977433740D-06 4.413792107083D-07 E-Index: 3 4 5 T-Index: 0 4.910721979375D-02 -1.454047282438D-02 2.178105605879D-03 1 -2.367924962508D-02 8.488392041366D-03 -1.452752408581D-03 2 -1.904887727240D-03 -2.390948585334D-04 1.844484422285D-04 3 1.087493205419D-03 -4.469192206896D-04 3.715538155590D-05 4 2.821927325759D-04 3.269264854581D-05 -5.937518354028D-06 5 -6.901574689672D-05 6.350490312899D-06 -4.414167358057D-07 6 -4.184111347149D-06 1.153919327151D-07 3.797435455934D-08 7 1.536214841434D-06 -1.632601398517D-07 8.948177075796D-09 8 -7.832095176637D-08 9.586974774950D-09 -6.739076170810D-10 E-Index: 6 7 8 T-Index: 0 -1.657512355348D-04 6.161429564793D-06 -8.910615590909D-08 1 1.170902182939D-04 -4.410479245308D-06 6.297315949647D-08 2 -1.972728027860D-05 7.779440219801D-07 -1.033814145233D-08 3 -1.595144154431D-06 6.311039124056D-08 -1.485989166680D-09 4 4.714656637197D-07 -2.433462923993D-08 5.307423532159D-10 5 1.266603603049D-08 8.049435558339D-10 -3.807796193572D-11 6 -4.123383037275D-09 1.095960078746D-10 -5.109801608123D-14 7 -1.853674996294D-10 1.342166707999D-14 1.184569645146D-14 8 2.565598443992D-11 -4.994625098807D-13 4.124048804450D-15 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 1.4966 % Mean rel. Error: .1241 % \end{verbatim}\end{small} \begin{figure} \label{2.3.9a} \epsfxsize=16truecm \epsffile{Amjuel_PS/helia.ps} \end{figure} \newpage \subsection{ Reaction 2.3.9b $e + He(1s^21S;r) \rightarrow e + He^+(1s) + e $ } Eth=24.588 eV Fujimoto Formulation I (meta-stable resolved, i.e., ground level and 2 meta-stable levels transported) \cite{kn:Fujimoto} \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -4.465926038712D+01 2.779089377769D-01 -1.924882766567D-01 1 2.525835077281D+01 -3.615923725584D-01 1.317375998510D-01 2 -1.209203690110D+01 2.546508612886D-01 -4.865271188617D-02 3 3.800524426932D+00 -1.050334429568D-01 1.534747997056D-02 4 -8.039502806290D-01 2.383460807262D-02 -2.453115299067D-03 5 1.113782505171D-01 -2.736570987242D-03 -1.204111477713D-04 6 -9.620115283603D-03 1.170152671250D-04 8.499825475516D-05 7 4.684217843660D-04 2.993567258600D-06 -9.064004864288D-06 8 -9.803749599678D-06 -2.872558504737D-07 3.052211397578D-07 E-Index: 3 4 5 T-Index: 0 8.206249637969D-02 -1.857913019533D-02 2.303280474362D-03 1 -3.756327901158D-02 7.553859741475D-03 -9.078039556264D-04 2 3.019270415903D-03 6.079717185636D-05 -1.971883028916D-05 3 -1.216174535037D-04 -1.789202918039D-04 2.652901470795D-05 4 1.469571845580D-04 -3.672662632973D-05 3.283809863879D-06 5 1.895504949459D-05 9.915856648703D-06 -1.080542155973D-06 6 -1.228789754131D-05 -2.775942493726D-07 3.600949456643D-08 7 1.331783826572D-06 -3.482200586084D-08 3.023300632995D-09 8 -4.228344440471D-08 1.047078160211D-09 -7.325236965794D-11 E-Index: 6 7 8 T-Index: 0 -1.557492713615D-04 5.412603196390D-06 -7.592974771773D-08 1 6.285196169828D-05 -2.363737361863D-06 3.748123629849D-08 2 -1.284093049142D-06 2.768704515392D-07 -9.149600770688D-09 3 -7.430360191467D-07 -7.771887920734D-08 3.535086119528D-09 4 -3.318791946233D-07 3.208524419469D-08 -1.011210049359D-09 5 5.266320143919D-08 -3.383189536291D-09 1.132832454025D-10 6 3.748617077019D-09 -1.897621201127D-10 -6.405513953940D-13 7 -7.781196082881D-10 4.279614523560D-11 -6.119815491934D-13 8 2.391497281895D-11 -1.495486439356D-12 2.587685854804D-14 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 1.3886 % Mean rel. Error: .1520 % \end{verbatim}\end{small} \begin{figure} \label{2.3.9b} \epsfxsize=16truecm \epsffile{Amjuel_PS/helib.ps} \end{figure} \newpage \subsection{ Reaction 2.3.9c $e + He(1s^21S;r) \rightarrow e + He(1s^12s^11S;r) $ } Eth=20.614 \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -4.046178452435D+01 2.793780023801D-02 -2.636827236275D-02 1 2.021782349890D+01 -8.168151009006D-02 6.137459348454D-02 2 -9.976409627529D+00 7.203017486249D-02 -4.594744469839D-02 3 3.121941621264D+00 -3.252368776384D-02 1.838136188172D-02 4 -6.605740116932D-01 7.971710032974D-03 -3.491501531484D-03 5 9.314429433629D-02 -1.237053221067D-03 3.539330238278D-04 6 -8.331619915042D-03 1.280998359531D-04 -2.164671094364D-05 7 4.255343291630D-04 -7.951439218420D-06 7.965320643996D-07 8 -9.415940442146D-06 2.158374132954D-07 -1.212346927674D-08 E-Index: 3 4 5 T-Index: 0 9.966974050192D-03 -1.925058189572D-03 2.074618402408D-04 1 -1.789108699037D-02 2.499301042347D-03 -1.708164459820D-04 2 1.099110619333D-02 -1.123236352791D-03 2.768319881512D-05 3 -4.067150951400D-03 4.169742301105D-04 -1.424941738587D-05 4 5.821208934666D-04 -4.623802427724D-05 8.865908638099D-07 5 -1.693003577039D-05 -2.195524273463D-06 2.451445678475D-07 6 -3.496132235049D-06 7.607387051093D-07 -2.643851478727D-08 7 4.015715517122D-07 -6.690887808842D-08 2.045934897132D-09 8 -1.496923652893D-08 2.594682285097D-09 -1.399655571965D-10 E-Index: 6 7 8 T-Index: 0 -1.262053793968D-05 4.055587151672D-07 -5.348263576276D-09 1 4.628208806209D-06 2.791547274449D-08 -2.554662311089D-09 2 3.397787872961D-06 -2.546734368181D-07 5.048596843802D-09 3 -7.637600844108D-07 7.190678272390D-08 -1.515996656096D-09 4 1.543470779365D-07 -1.154851629261D-08 2.413115266566D-10 5 -1.466182203352D-08 7.285294206745D-10 -1.706462195600D-11 6 -1.132975723190D-09 6.492076232833D-11 -3.972506213491D-13 7 1.178546445834D-10 -6.482775463755D-12 5.122149685044D-14 8 2.346036357946D-12 -3.268745663823D-14 1.995604762061D-15 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 1.9207 % Mean rel. Error: .5914 % \end{verbatim}\end{small} \begin{figure} \label{2.3.9c} \epsfxsize=16truecm \epsffile{Amjuel_PS/helic.ps} \end{figure} \newpage \subsection{ Reaction 2.3.9d $ e + He(1s^21S;r) \rightarrow e + He(1s^12s^13S;r) $ } Eth=19.818 eV \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.886266644950D+01 7.019809942099D-04 -4.884086339705D-03 1 1.929521258283D+01 -2.357936604103D-02 -1.328300789738D-02 2 -9.046404053855D+00 8.666192442035D-02 5.474654335859D-02 3 2.673018107253D+00 -1.398928491802D-01 3.218710988103D-03 4 -5.548107653535D-01 7.465434423573D-02 -1.179392922571D-02 5 7.774830542594D-02 -1.905817901709D-02 3.638331146570D-03 6 -6.848256427157D-03 2.528446995280D-03 -4.700217870527D-04 7 3.400854043835D-04 -1.673888466652D-04 2.614365787435D-05 8 -7.262673007156D-06 4.357192276102D-06 -4.506225745622D-07 E-Index: 3 4 5 T-Index: 0 4.394808572685D-03 -1.302054032826D-03 1.826711561551D-04 1 1.082410659623D-03 8.797507874605D-04 -1.904140538432D-04 2 -2.932730590755D-02 5.819861355501D-03 -6.211677015176D-04 3 7.586337950327D-03 -1.674705131468D-03 1.745859315455D-04 4 2.158501813724D-04 7.916139470987D-05 -6.470261758484D-06 5 -2.830357834958D-04 2.090178740450D-05 -2.905940657585D-06 6 2.610671874389D-05 -7.317822457225D-07 2.937506973332D-07 7 9.223198907867D-07 -4.349863908454D-07 1.893279869199D-08 8 -1.418436717966D-07 3.344143189525D-08 -2.438361820942D-09 E-Index: 6 7 8 T-Index: 0 -1.338147384862D-05 4.944420378156D-07 -7.274738213340D-09 1 1.572144633422D-05 -5.949713883471D-07 8.661413444821D-09 2 3.751189894835D-05 -1.205285676422D-06 1.596181856159D-08 3 -1.072392282940D-05 3.817775426074D-07 -5.941731934892D-09 4 5.703111011170D-07 -4.610054978455D-08 1.257685434225D-09 5 1.376224572390D-07 3.158742833521D-09 -2.256374221221D-10 6 -2.123916588197D-08 -1.342964777517D-10 2.534904955517D-11 7 2.438015393047D-11 2.825944427401D-11 -1.724540860429D-12 8 8.609576897508D-11 -2.649053786615D-12 6.205443362599D-14 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 4.7040 % Mean rel. Error: 1.6362 % \end{verbatim}\end{small} \begin{figure} \label{2.3.9d} \epsfxsize=16truecm \epsffile{Amjuel_PS/helid.ps} \end{figure} \newpage \subsection{ Reaction 2.3.9e $e + He(1s^12s^11S;r) \rightarrow e + He(1s^21S;r) $ } Exotherm by -20.614 eV \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -1.206284357030D+01 -9.395741200722D-01 8.941559006967D-02 1 1.001413279976D-01 1.092169776728D-01 1.368198258579D-01 2 7.586400083695D-02 -3.795422777009D-03 -4.592861987024D-02 3 -6.305941229397D-02 -1.344397679189D-02 5.918300497317D-03 4 1.769150254942D-02 3.790811280315D-03 -6.656861914400D-06 5 -2.649142451670D-03 -4.390182739385D-04 -1.378634631707D-04 6 2.286216360493D-04 1.421107391865D-05 2.727632307001D-05 7 -1.081890897336D-05 1.614465895521D-06 -2.798379357036D-06 8 2.194368384994D-07 -1.169587182544D-07 1.178226546132D-07 E-Index: 3 4 5 T-Index: 0 2.236104074143D-02 -6.491279005972D-03 6.949727832958D-04 1 -5.565930009734D-02 1.010402473629D-02 -1.046827564504D-03 2 1.258334121198D-02 -1.876085557457D-03 1.902110155531D-04 3 6.956902121898D-04 -2.605824960044D-04 1.950702712776D-05 4 -5.678513919575D-04 9.916918467853D-05 -5.461700671234D-06 5 9.155083108892D-05 -9.582108792123D-06 -4.823548954286D-08 6 -8.973643720110D-06 5.015822067600D-07 4.733355630355D-08 7 7.315416774742D-07 -6.070951170683D-08 2.496749755159D-09 8 -3.205208905129D-08 4.211868482308D-09 -4.146419126420D-10 E-Index: 6 7 8 T-Index: 0 -3.798849551595D-05 1.060426073614D-06 -1.221792772705D-08 1 6.343654833533D-05 -2.081812227589D-06 2.840825118625D-08 2 -1.235336841503D-05 4.391737031475D-07 -6.361146384328D-09 3 -2.609090338780D-07 -2.035332888490D-08 5.697468968308D-10 4 9.584672975523D-09 7.522667390232D-09 -1.643595153340D-10 5 4.899977333096D-08 -2.232347489472D-09 2.900728952005D-11 6 -4.956007021108D-09 1.036072591263D-10 5.476491421305D-13 7 -2.464346448050D-10 1.983186245349D-11 -4.977113923684D-13 8 3.334367936705D-11 -1.585718526609D-12 2.983699805655D-14 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 1.4647 % Mean rel. Error: .6179 % \end{verbatim}\end{small} \begin{figure} \label{2.3.9e} \epsfxsize=16truecm \epsffile{Amjuel_PS/helie.ps} \end{figure} \newpage \subsection{ Reaction 2.3.9f $e + He(1s^12s^11S;r) \rightarrow e + He^+(1s) + e $ } Eth=24.588-20.614 eV= 3.974 eV \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.041118707850D+01 2.064277904192D-01 -2.301314111088D-01 1 4.734415747558D+00 -2.552828703588D-01 2.342297501453D-01 2 -2.031119990372D+00 1.324170464675D-01 -4.709002494788D-02 3 6.371388191840D-01 -6.485323499659D-02 -1.318105876403D-02 4 -1.606102572000D-01 3.031094673577D-02 4.353315277834D-03 5 2.869498856933D-02 -8.594657926314D-03 1.245406154419D-04 6 -3.217835269221D-03 1.298813772998D-03 -1.446399013109D-04 7 1.992406567281D-04 -9.756034343132D-05 1.558038205391D-05 8 -5.162497860818D-06 2.873135417997D-06 -5.121082856413D-07 E-Index: 3 4 5 T-Index: 0 1.064846554112D-01 -2.384946202844D-02 2.875360842310D-03 1 -1.009365349705D-01 2.154424500834D-02 -2.450397986314D-03 2 1.965251665219D-02 -4.861043898033D-03 5.741139338224D-04 3 6.274439358726D-03 -5.336599826346D-04 6.766527255195D-06 4 -2.730895337646D-03 2.879856399739D-04 -8.539443051056D-06 5 3.376848227155D-04 -2.761034449494D-05 -1.226863119476D-06 6 -1.429851963639D-05 8.564331543394D-07 2.266756951926D-07 7 1.313034465605D-07 -1.155540500016D-07 8.907397769803D-09 8 -9.429070218568D-09 1.043211307579D-08 -1.547549446017D-09 E-Index: 6 7 8 T-Index: 0 -1.875978041743D-04 6.245347035980D-06 -8.331988072406D-08 1 1.492018825102D-04 -4.569691982094D-06 5.506673096644D-08 2 -3.190474508863D-05 7.544465168586D-07 -4.738153009264D-09 3 -4.524848313611D-07 1.101272889478D-07 -3.647448463620D-09 4 1.327453253122D-07 -2.364732558216D-08 8.985219510628D-10 5 1.509448581903D-07 -1.051090322975D-09 -1.035749496501D-10 6 -1.493652619657D-08 -1.728825755255D-10 1.851526257919D-11 7 -1.266737591814D-09 1.032899830898D-10 -2.632477381331D-12 8 1.383817472027D-10 -6.759540208869D-12 1.300020937903D-13 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 3.1668 % Mean rel. Error: .5043 % \end{verbatim}\end{small} \begin{figure} \label{2.3.9f} \epsfxsize=16truecm \epsffile{Amjuel_PS/helif.ps} \end{figure} \newpage \subsection{ Reaction 2.3.9g $ e + He(1s^12s^11S;r) \rightarrow e + He(1s^12s^13S;r) $ } Exotherm by -20.614 + 19.818 eV = -0.796 eV \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -1.511346543847D+01 -8.315548974761D-03 1.043755302803D-03 1 2.080755731664D-02 -1.438655344675D-02 3.050387143129D-02 2 -1.559881223335D-01 -4.819070749165D-03 5.469768725333D-03 3 3.593311746308D-02 -3.264350393911D-03 -2.797070666582D-03 4 -7.539069188132D-03 2.816838207584D-03 1.209358979731D-04 5 1.249554266705D-03 -6.865425821712D-04 4.394712468238D-05 6 -1.346691563985D-04 7.711126608572D-05 -3.761880439834D-06 7 8.141009386823D-06 -4.262318558331D-06 -5.160666241730D-08 8 -2.101701177702D-07 1.010890135509D-07 3.792122360486D-09 E-Index: 3 4 5 T-Index: 0 2.642487583410D-03 -1.141726366943D-03 1.946543332558D-04 1 -1.854158470475D-02 4.594389089735D-03 -5.599959861484D-04 2 2.070413057149D-04 -3.457506453968D-04 4.738780926722D-05 3 8.235312574359D-04 -9.572690868675D-05 8.428282893341D-06 4 -1.330419686348D-04 1.899203210608D-05 -1.396220087820D-06 5 1.494981666075D-05 -3.053826052126D-06 2.132092797921D-07 6 -2.368299001887D-06 4.919560666227D-07 -3.450359185228D-08 7 2.216347288940D-07 -4.134834676754D-08 2.800553268281D-09 8 -5.585637013718D-09 9.462594289102D-10 -4.980912274284D-11 E-Index: 6 7 8 T-Index: 0 -1.635057730275D-05 6.698344020218D-07 -1.065235099548D-08 1 3.560438313422D-05 -1.132594240133D-06 1.422148875942D-08 2 -2.442018698579D-06 4.281026474337D-08 5.902980719683D-11 3 -6.289242286208D-07 2.809710863001D-08 -4.986421098936D-10 4 5.944783491030D-08 -1.403317455776D-09 1.466091168551D-11 5 -2.812985305069D-09 -2.643823395694D-10 7.873039688058D-12 6 3.288755762988D-10 5.309244160943D-11 -1.497810114810D-12 7 -2.188207542114D-11 -4.594641184965D-12 1.274835520030D-13 8 -1.490478001851D-12 2.101409635615D-13 -4.858731679885D-15 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 3.2971 % Mean rel. Error: .9554 % \end{verbatim}\end{small} \begin{figure} \label{2.3.9g} \epsfxsize=16truecm \epsffile{Amjuel_PS/helig.ps} \end{figure} \newpage \subsection{ Reaction 2.3.9h $e + He(1s^12s^13S;r) \rightarrow e + He(1s^21S;r) $ } Exotherm by = -19.818 eV \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -1.830459498604D+01 1.680944192322D-01 -1.907710632311D-01 1 1.261631206881D+00 -3.697196539108D-01 3.033207775574D-01 2 -6.559878055182D-01 3.061935618408D-01 -1.782153223733D-01 3 1.697614445868D-01 -1.342126595676D-01 5.676221077284D-02 4 -3.176415719557D-02 3.126025766778D-02 -1.011584147746D-02 5 3.950262828345D-03 -3.455627026606D-03 6.079929754617D-04 6 -2.881881569143D-04 1.125950976085D-04 5.069359855193D-05 7 1.022634571062D-05 7.797965660632D-06 -7.903959237155D-06 8 -1.046204166475D-07 -5.060676841045D-07 2.672428957821D-07 E-Index: 3 4 5 T-Index: 0 7.870000493965D-02 -1.578049324901D-02 1.693793556658D-03 1 -1.021849055299D-01 1.773149558150D-02 -1.726009071069D-03 2 4.310244321027D-02 -5.236106415441D-03 3.417399063180D-04 3 -8.861603178392D-03 3.398799078845D-04 4.431709264967D-05 4 1.152839986316D-03 9.136542557803D-06 -9.999842824089D-06 5 -1.259483668399D-05 -8.845662317330D-06 8.897275861513D-07 6 -1.194283431812D-05 8.912124314893D-07 -4.132333818961D-08 7 7.631517909210D-07 5.811563274232D-08 -6.834989323422D-09 8 -3.354009675567D-09 -6.847471248575D-09 6.066678972621D-10 E-Index: 6 7 8 T-Index: 0 -9.871776235813D-05 2.943212020081D-06 -3.527779579573D-08 1 9.567692855718D-05 -2.834877407571D-06 3.493434187484D-08 2 -1.237776471579D-05 2.515470587336D-07 -2.566899239887D-09 3 -4.572811804993D-06 1.335801462225D-07 -8.926601447859D-10 4 3.785048727116D-07 1.570413745481D-08 -7.805586685406D-10 5 3.807398587262D-08 -7.209735737750D-09 2.098640072212D-10 6 -2.405215414685D-09 4.468725637555D-10 -1.423750029854D-11 7 -9.649173073383D-12 1.030982426102D-11 -1.042452128502D-13 8 -2.881700207187D-12 -1.158584840686D-12 2.909357590574D-14 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 6.5233 % Mean rel. Error: 1.8951 % \end{verbatim}\end{small} \begin{figure} \label{2.3.9h} \epsfxsize=16truecm \epsffile{Amjuel_PS/helih.ps} \end{figure} \newpage \subsection{ Reaction 2.3.9i $ e + He(1s^12s^13S;r) \rightarrow e + He(1s^12s^11S;r) $ } Eth = 20.614 - 19.818 eV = 0.796 eV \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -1.745844276703D+01 8.157573269596D-02 -8.846137669182D-02 1 7.481807449876D-01 -8.855888981396D-02 6.895575898405D-02 2 -4.821059764779D-01 4.679324654447D-02 -3.297751569188D-02 3 1.178180871789D-01 -6.059351136561D-03 6.707641671282D-03 4 -1.832266433398D-02 -3.019133239406D-03 -4.072864365252D-06 5 1.619689578381D-03 1.226840796832D-03 -1.633059618549D-04 6 -5.423530837755D-05 -1.774072691416D-04 1.112445681671D-05 7 -1.967026987940D-06 1.153537885107D-05 9.730921470847D-07 8 1.471829150856D-07 -2.811554762172D-07 -8.690862477419D-08 E-Index: 3 4 5 T-Index: 0 3.729534986051D-02 -7.748150218997D-03 8.681073774233D-04 1 -2.009477611517D-02 2.695260975948D-03 -1.670023006117D-04 2 7.266340675294D-03 -5.231546959702D-04 -1.405113747904D-05 3 -1.185084843308D-03 -7.521294935444D-06 1.345383423264D-05 4 -3.463344438708D-06 2.717377734542D-05 -3.273238480292D-06 5 5.881112042281D-06 -3.089656478315D-06 4.514505533598D-07 6 6.093509408469D-06 -8.020661101230D-07 1.087961936931D-08 7 -1.135225653662D-06 1.679703656220D-07 -7.767824389490D-09 8 5.404365621466D-08 -8.134516470380D-09 4.439057728063D-10 E-Index: 6 7 8 T-Index: 0 -5.326368279955D-05 1.687247391834D-06 -2.160318603760D-08 1 3.273035637060D-06 9.077935253350D-08 -3.430880317364D-09 2 3.581367863934D-06 -1.600203938605D-07 2.265889575361D-09 3 -7.627838979440D-07 1.599025715771D-09 4.761644881308D-10 4 1.521655610951D-08 1.078364608775D-08 -3.386106465918D-10 5 -8.083755569905D-09 -1.161692326935D-09 4.153576692338D-11 6 2.280605076008D-09 -9.703614416875D-11 8.269006530832D-13 7 -1.272866644000D-10 1.985460981397D-11 -4.226560743702D-13 8 1.412497774809D-13 -8.003922930542D-13 1.975681079140D-14 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 1.8916 % Mean rel. Error: .4888 % \end{verbatim}\end{small} \begin{figure} \label{2.3.9i} \epsfxsize=16truecm \epsffile{Amjuel_PS/helii.ps} \end{figure} \newpage \subsection{ Reaction 2.3.9j $e + He(1s^12s^13S;r) \rightarrow e + He^+(1s) + e $ } Eth = 24.588 - 19.818 eV = 4.770 eV \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.055363233340D+01 4.495119087580D-01 -5.238622256836D-01 1 5.210334391329D+00 -2.968974679742D-01 2.779506719390D-01 2 -2.250469356935D+00 7.010500442526D-02 -1.213577735853D-01 3 5.852050404826D-01 8.921407862649D-02 4.101964952741D-03 4 -9.522800090383D-02 -6.623026789339D-02 1.426598675675D-02 5 8.361746435674D-03 1.876265413172D-02 -4.938987966830D-03 6 -2.082000823695D-04 -2.653612987499D-03 7.235705862418D-04 7 -1.971223241071D-05 1.866108873151D-04 -5.008080286294D-05 8 1.129438144977D-06 -5.204161575593D-06 1.341100873190D-06 E-Index: 3 4 5 T-Index: 0 2.389768266075D-01 -5.282830816524D-02 6.225525677663D-03 1 -9.544309562602D-02 1.574089888139D-02 -1.373029882004D-03 2 3.981143589359D-02 -5.552464406897D-03 4.010663176656D-04 3 -6.610103528390D-03 9.857909449549D-04 -6.826906017552D-05 4 -7.969610821575D-04 -1.713086806983D-05 3.192882264529D-06 5 4.727105277550D-04 -1.892061941621D-05 5.709120517813D-07 6 -6.875356963100D-05 2.067400657772D-06 -4.852278760689D-08 7 4.145701518111D-06 -3.688167910326D-09 -5.119123986569D-09 8 -8.570742834160D-08 -5.179756344998D-09 4.745066997076D-10 E-Index: 6 7 8 T-Index: 0 -3.959446131986D-04 1.281892887943D-05 -1.658021134736D-07 1 6.228002425783D-05 -1.303442479359D-06 8.322300537481D-09 2 -1.588204879114D-05 3.456291200468D-07 -3.614686328664D-09 3 3.402964809821D-06 -1.409141853759D-07 2.865103804351D-09 4 -3.264060374187D-07 2.446519428773D-08 -6.273758803879D-10 5 -3.265134644505D-08 8.398689087309D-10 1.744587191452D-12 6 1.231197186211D-08 -8.532974556790D-10 1.733410572003D-11 7 -1.110937956560D-09 9.978997213312D-11 -2.217674451730D-12 8 3.268128548473D-11 -3.678837719391D-12 8.560132404451D-14 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 7.0831 % Mean rel. Error: 2.2103 % \end{verbatim}\end{small} \begin{figure} \label{2.3.9j} \epsfxsize=16truecm \epsffile{Amjuel_PS/helij.ps} \end{figure} \newpage \subsection{ Reaction 2.3.13a $e + He^+(1s) \rightarrow He(1s^21S) $ } Helium multi-step model, here recombination: radiative + threebody + dielectronic Fujimoto Formulation II (only ground level transported, no metastables kept explicit), \cite{kn:Fujimoto} \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.872754373123D+01 -6.171082987797D-03 2.414548639597D-02 1 1.564233603544D+00 -3.972220721457D-02 -4.466712599181D-02 2 -6.182140631482D+00 1.626641668186D-01 3.366589582541D-02 3 5.459428677778D+00 -1.700323494998D-01 -1.540106384088D-02 4 -2.128115924661D+00 7.233939709414D-02 5.819196258503D-03 5 4.373730373037D-01 -1.574917019835D-02 -1.456253436544D-03 6 -4.972257208732D-02 1.866175274689D-03 2.047337498511D-04 7 2.967287371427D-03 -1.147811325052D-04 -1.460813593905D-05 8 -7.271204747116D-05 2.874049670122D-06 4.124421172202D-07 E-Index: 3 4 5 T-Index: 0 -7.188662067622D-03 9.481268604767D-04 -1.958887458637D-05 1 1.247359158796D-02 -1.660591942878D-03 6.019181402025D-05 2 -7.413737965595D-03 1.220189896183D-03 -9.505295724750D-05 3 9.524545793262D-04 -8.734341535385D-05 -2.796027477899D-06 4 -7.655935845761D-05 -1.837949067050D-05 4.725789832980D-06 5 4.772491845078D-05 -1.827059132463D-06 -6.941163292710D-08 6 -1.004438052808D-05 7.590734865850D-07 -6.771179147667D-08 7 7.422385993164D-07 -3.281946488134D-08 2.164459880579D-09 8 -1.689203971933D-08 -9.071172814458D-10 1.844295219334D-10 E-Index: 6 7 8 T-Index: 0 -5.507786383328D-06 4.358288686930D-07 -9.503272091010D-09 1 3.800156798817D-06 -3.377807793756D-07 6.828447501225D-09 2 4.459492214068D-06 -1.552772441333D-07 2.866586118879D-09 3 4.561981097438D-07 4.940311502014D-09 -6.525725010760D-10 4 -3.997782411860D-07 1.036731541123D-08 -3.373845712183D-11 5 2.716740135949D-08 -1.143121626264D-09 1.295139027087D-11 6 1.218720257518D-09 6.787024479540D-11 -2.432253541918D-12 7 1.113868237282D-10 -1.513922678655D-11 3.951084520871D-13 8 -2.055023511556D-11 1.101902611511D-12 -2.206082129473D-14 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 16.4494 % Mean rel. Error: 3.2360 % \end{verbatim}\end{small} \begin{figure} \label{2.3.13a} \epsfxsize=16truecm \epsffile{Amjuel_PS/helra.ps} \end{figure} \newpage \subsection{ Reaction 2.3.13b $e + He^+(1s) \rightarrow He(1s^21S;r) $ } Helium multi-step model, here recombination: radiative + threebody + dielectronic Fujimoto Formulation I (ground level and 2 meta-stable levels transported), effective recombination into ground state $(1|1S)$ \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.932450239883D+01 -1.725214936087D-02 4.209507397331D-02 1 1.368459463821D+00 -7.548584212824D-02 -3.321889449021D-02 2 -5.057940093488D+00 2.531332526084D-01 -1.925988688740D-02 3 4.437755591817D+00 -2.369773678428D-01 2.411850401784D-02 4 -1.704236205062D+00 9.630485149239D-02 -6.971157814419D-03 5 3.430644471030D-01 -2.061167258227D-02 7.487855629993D-04 6 -3.809452269361D-02 2.434745940239D-03 -1.722706965522D-06 7 2.218026788496D-03 -1.502211895379D-04 -5.165559630643D-06 8 -5.301589276464D-05 3.780661493099D-06 2.647213620732D-07 E-Index: 3 4 5 T-Index: 0 -1.843883199649D-02 4.330069861940D-03 -5.571398183907D-04 1 2.246769961570D-02 -6.920109284335D-03 1.034704067336D-03 2 -1.562041938975D-03 2.844891620769D-03 -5.840417169956D-04 3 -6.245247150004D-03 1.707788608782D-04 8.828047075521D-05 4 2.150122229030D-03 -1.997306644340D-04 2.987453868437D-06 5 -2.352870835454D-04 2.321396939441D-05 -1.669051074965D-06 6 -1.929788529702D-06 1.001774243168D-06 7.435769683477D-08 7 1.999043007214D-06 -3.211502011021D-07 8.114609805127D-09 8 -9.897241177277D-08 1.504658532546D-08 -5.883462440247D-10 E-Index: 6 7 8 T-Index: 0 4.006413547865D-05 -1.488766590351D-06 2.211904689519D-08 1 -8.066726007499D-05 3.137222500010D-06 -4.796687278784D-08 2 5.166332348737D-05 -2.133727041895D-06 3.362146796114D-08 3 -1.099721749926D-05 5.014979395019D-07 -8.105197770220D-09 4 4.904814231191D-07 -2.358575243153D-08 2.498171028400D-10 5 1.745034668357D-07 -1.128396994326D-08 2.586295673609D-10 6 -3.342032519922D-08 2.451263340785D-09 -5.477602284810D-11 7 2.414625764231D-09 -2.022906627308D-10 4.590099192405D-12 8 -6.465233005227D-11 6.181507714121D-12 -1.430061439345D-13 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 15.0191 % Mean rel. Error: 3.1731 % \end{verbatim}\end{small} \begin{figure} \label{2.3.13b} \epsfxsize=16truecm \epsffile{Amjuel_PS/helrb.ps} \end{figure} \newpage \subsection{ Reaction 2.3.13c $ e + He^+(1s) \rightarrow He(1s^12s^11S;r) + hv$ } \cite{kn:Fujimoto}. Here: effective recombination into meta-stable level $(2|1S)$. \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.290594969157D+01 5.936377204270D-01 -5.786568026984D-01 1 1.289118555318D+00 -7.322821510173D-01 5.216313908016D-01 2 -4.581116130605D+00 4.359234826400D-01 -1.879684009591D-01 3 3.975023080430D+00 -1.135607337249D-01 -2.093787195291D-02 4 -1.511744296191D+00 9.273954721890D-03 3.091151170807D-02 5 3.006694544045D-01 -7.098672020828D-04 -6.524345786670D-03 6 -3.291282273842D-02 4.674323034046D-04 3.252758528411D-04 7 1.885862263038D-03 -7.894912660673D-05 3.023350709086D-05 8 -4.430501809351D-05 3.801909601518D-06 -2.522313594898D-06 E-Index: 3 4 5 T-Index: 0 2.219812747147D-01 -4.301992587218D-02 4.645717376756D-03 1 -1.469524854136D-01 1.758178948996D-02 -6.553480315101D-04 2 4.156489474989D-02 -1.653580474529D-03 -5.740235177360D-04 3 4.449510483711D-03 -7.099391762833D-04 1.140482945563D-04 4 -6.447934562370D-03 5.521339815402D-04 -1.215385049113D-05 5 1.190208632381D-03 -8.535844740287D-05 1.100343069640D-06 6 7.662178711899D-06 -1.003394753061D-05 9.133676744341D-07 7 -1.693836511335D-05 2.998300023499D-06 -2.134268520285D-07 8 1.008933043477D-06 -1.637662372864D-07 1.194860574397D-08 E-Index: 6 7 8 T-Index: 0 -2.827549938027D-04 9.098967864743D-06 -1.204212130817D-07 1 -3.911503234413D-05 3.838699392781D-06 -8.432388008514D-08 2 8.252435318894D-05 -4.174329959264D-06 7.461274593602D-08 3 -1.015903498277D-05 4.067368927608D-07 -5.956193776494D-09 4 -1.743597814483D-06 1.504881645494D-07 -3.516856295239D-09 5 3.283228084253D-07 -2.777357769656D-08 6.855090395029D-10 6 -3.246510016651D-08 1.021166636920D-09 -2.826061022812D-11 7 5.448904749550D-09 1.026064555133D-11 -1.372295711583D-12 8 -3.572199625876D-10 1.353028569150D-12 7.810473188768D-14 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 12.8697 % Mean rel. Error: 4.3370 % \end{verbatim}\end{small} \begin{figure} \label{2.3.13c} \epsfxsize=16truecm \epsffile{Amjuel_PS/helrc.ps} \end{figure} \newpage \subsection{ Reaction 2.3.13d $e + He^+(1s) \rightarrow He(1s^12s^13S;r) + hv $ } \cite{kn:Fujimoto}. Here: effective recombination into meta-stable level $(2|3S)$. \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.956247006586D+01 4.857379877013D-01 -4.698385090723D-01 1 2.226655583858D+00 -5.008925977592D-01 4.409072277517D-01 2 -8.386271074322D+00 -6.680555751755D-02 1.358293373473D-01 3 7.802551872732D+00 1.513454163302D-01 -2.382523353494D-01 4 -3.176066118073D+00 -2.915513853670D-02 8.389442053277D-02 5 6.790403187679D-01 -8.583336134054D-03 -8.339355078342D-03 6 -8.005018693268D-02 3.501616009283D-03 -8.108811483383D-04 7 4.936833057738D-03 -4.038202701566D-04 1.917972012272D-04 8 -1.245931475232D-04 1.550754095349D-05 -8.944775549284D-06 E-Index: 3 4 5 T-Index: 0 1.816491812551D-01 -3.584007722558D-02 4.008582628581D-03 1 -1.490076771833D-01 2.428208422290D-02 -2.197248681202D-03 2 -4.192264845130D-02 6.681287810863D-03 -3.474715517406D-04 3 7.034251548002D-02 -9.653541471324D-03 3.950052472624D-04 4 -2.594911934917D-02 3.785834072023D-03 -1.721024156646D-04 5 3.100772841149D-03 -5.641898835295D-04 3.146400786804D-05 6 1.226453809803D-04 9.772361084934D-06 -1.220791337288D-06 7 -4.737671071626D-05 4.334084847132D-06 -1.862385782715D-07 8 2.364380548912D-06 -2.583267263336D-07 1.313403535033D-08 E-Index: 6 7 8 T-Index: 0 -2.562289391561D-04 8.707904177549D-06 -1.215806872260D-07 1 1.109906018249D-04 -2.900632901582D-06 3.027934182965D-08 2 -1.076950834118D-05 1.529234802310D-06 -3.663757563702D-08 3 2.408158683211D-05 -2.450750101163D-06 5.482201735529D-08 4 -8.229247133546D-06 9.351454862581D-07 -2.147970339341D-08 5 1.022459855218D-06 -1.480508733520D-07 3.599099499020D-09 6 -8.112983260770D-08 1.090170350156D-08 -2.777349026055D-10 7 6.415033848685D-09 -3.093185955060D-10 7.625408371264D-12 8 -2.624838999683D-10 -6.850467836445D-13 5.598594440202D-14 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 21.5948 % Mean rel. Error: 5.8841 % \end{verbatim}\end{small} \begin{figure} \label{2.3.13d} \epsfxsize=16truecm \epsffile{Amjuel_PS/helrd.ps} \end{figure} \newpage \subsection{ Reaction 2.2C $e + He^+(1s) \rightarrow He^{++} + e + e $ } Ionization Rates for singly charged helium ions COLRAD (McWhirter), hydrogen-like approximation \cite{kn:McWhirter} $ \langle sigma*vrel \rangle(Te,ne) $(cm**3/s) \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -7.504895618885D+01 2.201465463709D-02 -5.069769253639D-03 1 5.475513292431D+01 -5.417589714886D-02 3.775044165759D-02 2 -2.693028880068D+01 3.774947998557D-02 -2.411882491817D-02 3 8.660359434783D+00 -1.764877195580D-02 7.243690204418D-03 4 -1.955813859940D+00 8.202168146805D-03 -3.070056924124D-03 5 3.098090672677D-01 -2.771730559069D-03 1.297834186151D-03 6 -3.271260113212D-02 5.325112160328D-04 -2.929485587655D-04 7 2.050483088051D-03 -5.190809564237D-05 3.145856505861D-05 8 -5.719259025474D-05 2.004313708534D-06 -1.292078319547D-06 E-Index: 3 4 5 T-Index: 0 3.915543748345D-03 -1.031132793821D-03 1.654691798718D-04 1 -1.633041262280D-02 3.459931210677D-03 -4.194602018842D-04 2 8.989971506710D-03 -1.829622573856D-03 2.164276869595D-04 3 -1.273168299077D-03 1.763624435402D-04 -2.479535228702D-05 4 9.752207930721D-05 6.251121832296D-05 -6.640018325938D-06 5 -1.296242864408D-04 -8.805176355814D-06 1.717983972172D-06 6 4.563001069981D-05 -1.836358658149D-06 -6.237635823497D-08 7 -5.886932297134D-06 4.277584502763D-07 -1.234530993035D-08 8 2.657229485598D-07 -2.298984920724D-08 9.125550698905D-10 E-Index: 6 7 8 T-Index: 0 -1.471360785546D-05 6.823504501535D-07 -1.247427417560D-08 1 2.861803302953D-05 -1.036298188456D-06 1.553321018673D-08 2 -1.391926980686D-05 4.512942119697D-07 -5.904011561947D-09 3 1.882628114227D-06 -6.323064673756D-08 8.275404429978D-10 4 1.952370344224D-07 1.751264412799D-09 -1.622640470420D-10 5 -5.793682625805D-08 -1.220451186228D-09 7.819729115572D-11 6 1.020925549512D-09 4.417455780936D-10 -1.689115024159D-11 7 4.669160272059D-10 -4.606556580267D-11 1.506577519668D-12 8 -2.598750073326D-11 1.464529452448D-12 -4.669913022501D-14 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: .3141 % Mean rel. Error: .1103 % \end{verbatim}\end{small} \begin{figure} \label{2.2C} \epsfxsize=16truecm \epsffile{Amjuel_PS/heli.ps} \end{figure} \newpage \subsection{ Reaction 2.6A0 $e + C \rightarrow C^+ + 2e $ } Ionization Rates for singly charged carbon, ADAS 93 $ \langle sigma*vrel \rangle(Te,ne) $(cm**3/s) \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.971457639565D+01 1.107810794514D+00 -4.929092425558D-01 1 1.499806652944D+01 -2.549991583370D+00 9.026830825116D-01 2 -7.145949073329D+00 6.664487958895D-01 -1.727631701810D-01 3 2.340511256186D+00 -1.160562412201D-01 1.411445363827D-02 4 -5.249343322780D-01 2.135356892092D-02 -1.638667443530D-03 5 7.562193210612D-02 -2.918522374196D-03 1.286365870759D-04 6 -6.679478578836D-03 3.000723261637D-04 -1.608459495742D-05 7 3.270945618657D-04 -1.883054084198D-05 1.732029469888D-06 8 -6.675613055770D-06 4.142784144247D-07 -3.486309036661D-08 E-Index: 3 4 5 T-Index: 0 1.300116911300D-01 -2.066054730760D-02 2.042310400958D-03 1 -1.879920996407D-01 2.431269610957D-02 -2.004879563783D-03 2 2.797274709016D-02 -2.903521270254D-03 1.995997150157D-04 3 -5.971983093427D-04 -7.377767439216D-05 1.267367125997D-05 4 6.910190376581D-05 -5.464445143303D-06 5.674562003155D-07 5 -7.001250033151D-07 7.855848854211D-07 -8.856533728232D-08 6 4.049976855256D-07 -2.088187353775D-08 -6.089302275674D-09 7 -1.675345958159D-07 1.579162356473D-08 -6.994965968869D-10 8 2.814990023664D-09 -2.947061589979D-10 2.418389203250D-11 E-Index: 6 7 8 T-Index: 0 -1.198777580517D-04 3.797623457774D-06 -5.001748956830D-08 1 1.013724485054D-04 -2.844335907618D-06 3.386548334244D-08 2 -8.259361032307D-06 1.731145419218D-07 -1.270740802103D-09 3 -1.039751082795D-06 4.599752398553D-08 -7.953804201299D-10 4 1.653887367244D-08 -3.425776625948D-09 8.586728657030D-11 5 -4.099151298763D-09 5.982763605144D-10 -1.370643938638D-11 6 1.485858394226D-09 -8.987472676089D-11 1.616606601615D-12 7 -1.867411789486D-11 2.235327393834D-12 -3.862181485750D-14 8 -1.188451034508D-12 4.216699821614D-14 -9.477595087316D-16 T1MIN = 1.00000D 00 EV T1MAX = 5.00000D 04 EV N2MIN = 1.00000D 10 1/CM3 N2MAX = 1.00000D 15 1/CM3 Max. rel. Error: 1.2246 % Mean rel. Error: .2748 % \end{verbatim}\end{small} \begin{figure} \label{2.6A0} \epsfxsize=16truecm \epsffile{Amjuel_PS/carbi.ps} \end{figure} \newpage \subsection{ Reaction 2.7A0 $e + N \rightarrow N^+ + 2e $ } Ionization Rates for neutral nitrogen, ADAS 96 $ \langle sigma*vrel \rangle(Te,ne) $(cm**3/s) \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.125599079514D+01 8.881344790721D-02 3.875689690924D-02 1 1.501972942719D+01 -2.245019983323D-01 -1.170266566017D-01 2 -8.563505396323D+00 2.563611550679D-01 5.993043917730D-02 3 3.259172785778D+00 -1.459562059574D-01 -3.629785517504D-03 4 -8.028485847461D-01 4.560133800137D-02 -3.579706539679D-03 5 1.239955993583D-01 -8.202838629323D-03 9.221893790607D-04 6 -1.152891908930D-02 8.472922768697D-04 -8.914562423314D-05 7 5.889464965188D-04 -4.669795084986D-05 3.515034526935D-06 8 -1.269186213968D-05 1.064343317380D-06 -3.611292369142D-08 E-Index: 3 4 5 T-Index: 0 -7.367355926910D-03 -8.933351435213D-04 1.937451469905D-04 1 4.426863655734D-02 -4.430861799571D-03 3.253064203736D-05 2 -3.020399271227D-02 3.927234491519D-03 -1.959177270882D-04 3 6.189975576309D-03 -7.279341465385D-04 2.546794744614D-05 4 -2.466055005611D-04 -1.287111351337D-05 7.621210137952D-06 5 -3.039643456169D-05 9.491026278127D-06 -1.535906103316D-06 6 -2.900624448150D-06 3.745360666294D-07 3.692979682516D-08 7 8.586152612035D-07 -1.356120392220D-07 4.747296972249D-09 8 -3.812958439511D-08 5.487542777793D-09 -1.437006614531D-10 E-Index: 6 7 8 T-Index: 0 -4.302425039372D-06 -4.449062046116D-07 1.641092601069D-08 1 1.829955290678D-05 -1.088030063258D-06 2.060046531889D-08 2 1.624638825366D-06 2.150911835291D-07 -6.785152839285D-09 3 -1.935192712324D-07 -2.396214128585D-10 1.822600582381D-10 4 -2.751092797923D-07 -9.878792756722D-09 3.880864455805D-10 5 3.342842434144D-08 3.080573580529D-09 -1.004120274888D-10 6 5.903820424145D-10 -3.124143842671D-10 8.467756187765D-12 7 3.173842995092D-11 -2.659413955852D-12 4.729814633051D-14 8 -1.577918732137D-11 1.171782749066D-12 -2.466359817399D-14 T1MIN = 0.20000D 00 1/CM3 T1MAX = 1.50000D 04 1/CM3 N2MIN = 5.00000D 07 1/CM3 N2MAX = 2.00000D 15 1/CM3 Max. rel. Error: 2.9930 % Mean rel. Error: 0.7199 % \end{verbatim}\end{small} \begin{figure} \label{2.7A0} \epsfxsize=16truecm \epsffile{Amjuel_PS/niti-rate.eps} \end{figure} \newpage \subsection{ Reaction 2.8A0 $e + O \rightarrow O^+ + 2e $ } Ionization Rates for neutral oxygen, ADAS 96 $ \langle sigma*vrel \rangle(Te,ne) $(cm**3/s) \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.328362393733D+01 -4.484395495461D-01 6.167722720177D-01 1 1.655302385400D+01 9.070420476255D-01 -7.492202987359D-01 2 -9.246899232716D+00 -6.861308571709D-01 3.853130674026D-01 3 3.468152479829D+00 2.653279717129D-01 -9.503130449306D-02 4 -8.532829072212D-01 -5.834222497364D-02 9.030518658158D-03 5 1.333834015615D-01 7.496194087446D-03 4.753498599348D-04 6 -1.265465442757D-02 -5.453745857810D-04 -1.638438870269D-04 7 6.624459298778D-04 2.000567259474D-05 1.131325208597D-05 8 -1.465832842295D-05 -2.619665824220D-07 -2.369684156977D-07 E-Index: 3 4 5 T-Index: 0 -2.589961397492D-01 4.118976653137D-02 -1.959950990473D-03 1 2.638779663615D-01 -3.490775262239D-02 5.793136771074D-04 2 -1.247067819410D-01 1.680118594677D-02 -5.089127052875D-04 3 2.929033903989D-02 -4.430118646918D-03 2.507450743683D-04 4 -2.550710866039D-03 4.693149835285D-04 -3.225531357806D-05 5 -1.298585181626D-04 -1.260782059434D-06 -6.674084144123D-07 6 3.005970684014D-05 -2.808693744681D-07 3.437325607970D-08 7 -5.378571580338D-07 -4.142319433039D-07 5.148458125516D-08 8 -5.436002215866D-08 2.927695957962D-08 -3.654799869508D-09 E-Index: 6 7 8 T-Index: 0 -9.739946501376D-05 1.139459064885D-05 -2.689494629827D-07 1 2.088106459889D-04 -1.507734725052D-05 3.066201565961D-07 2 -5.644498060513D-05 4.238399098405D-06 -7.745613330596D-08 3 -3.986851509525D-06 7.226554994339D-08 -6.046272342238D-09 4 1.782158795226D-06 -1.325057610801D-07 4.204627741204D-09 5 2.320632028445D-08 9.646974765235D-09 -4.535319182284D-10 6 -1.080831526075D-08 1.525797006183D-10 1.266728082419D-11 7 -2.138597283955D-09 3.312940600087D-11 -2.535541525696D-13 8 1.982722701483D-10 -4.851782342710D-12 4.242787336605D-14 T1MIN = 0.20000D 00 1/CM3 T1MAX = 1.50000D 04 1/CM3 N2MIN = 5.00000D 07 1/CM3 N2MAX = 2.00000D 15 1/CM3 Max. rel. Error: 8.8515 % Mean rel. Error: 0.9745 % \end{verbatim}\end{small} \begin{figure} \label{2.8A0} \epsfxsize=16truecm \epsffile{Amjuel_PS/oxyi-rate.eps} \end{figure} \newpage \subsection{ Reaction 2.3.2B0 $e + He^+(1s) \rightarrow He(1s^21S) + hv$ } Data from impurity transport code ``STRAHL'', \cite{kn:Behringer} Recombination Rates for single charged Helium Ions (w/o three-body) \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.898866818182D+01 -3.068735204957D-02 7.818231657785D-02 1 1.816504622984D+00 -1.996644882484D-01 -2.022934910684D-01 2 -5.957620306977D+00 5.564226839342D-01 2.720939045109D-01 3 4.883356392367D+00 -5.504736532364D-01 -1.589729887673D-01 4 -1.785690784875D+00 2.554161096465D-01 4.391044966362D-02 5 3.443976158874D-01 -6.304562647473D-02 -6.048646045521D-03 6 -3.666670180913D-02 8.499875301084D-03 4.080124220783D-04 7 2.042474095540D-03 -5.896220272289D-04 -1.226466093436D-05 8 -4.653873125342D-05 1.644314326566D-05 1.520073468241D-07 E-Index: 3 4 5 T-Index: 0 -4.360289476744D-02 1.088616122909D-02 -1.442780146671D-03 1 1.057079914763D-01 -2.358570776702D-02 2.968485844589D-03 2 -1.235076579967D-01 2.248324096678D-02 -2.497067848696D-03 3 6.635551763548D-02 -9.269476706908D-03 8.089219419856D-04 4 -1.831174182029D-02 1.752848228102D-03 -7.418643102963D-05 5 2.905705534546D-03 -1.678595996471D-04 -7.790745301776D-06 6 -2.926914092439D-04 1.437277876918D-05 1.085106848461D-06 7 1.894207582471D-05 -1.612501983994D-06 6.632343028157D-08 8 -5.989406850464D-07 8.425772893569D-08 -8.367921447451D-09 E-Index: 6 7 8 T-Index: 0 1.043554466513D-04 -3.878190225512D-06 5.783675088058D-08 1 -2.149050424333D-04 8.207356509792D-06 -1.268150915732D-07 2 1.779838048026D-04 -7.127873717134D-06 1.175164928521D-07 3 -5.675497459272D-05 2.589770454486D-06 -4.902088171680D-08 4 5.561292499931D-06 -4.363201173962D-07 1.122814678532D-08 5 2.465992165628D-07 5.016603759447D-08 -1.901239672341D-09 6 -4.188299784450D-09 -8.149167953030D-09 2.753349347791D-10 7 -1.167337552792D-08 1.023904862606D-09 -2.578964505694D-11 8 8.321169431770D-10 -4.756050161152D-11 9.973991458967D-13 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 16.6458 % Mean rel. Error: 6.0389 % \end{verbatim}\end{small} \begin{figure} \label{2.3.2B0} \epsfxsize=16truecm \epsffile{Amjuel_PS/helir1.ps} \end{figure} \newpage \subsection{ Reaction 2.3.2B1 $e + He^{++} \rightarrow He^+(1s) + hv$ } Recombination Rates for double charged Helium Ions (w/o three-body) \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.689730745452D+01 -4.189774474235D-02 3.907009691550D-02 1 -6.433874222932D-01 3.299308672728D-02 -2.112564779272D-02 2 -1.779312827872D-02 -2.784310132407D-02 3.756334628555D-03 3 -2.941208629331D-03 2.348797955174D-02 -3.603044725903D-03 4 -1.097079440712D-04 -1.041386945451D-02 2.110484002085D-03 5 3.627190561298D-05 2.454594288891D-03 -5.469934610104D-04 6 -2.051498433274D-06 -3.182066464328D-04 7.445181597104D-05 7 9.049897913059D-08 2.153132862082D-05 -5.311099451965D-06 8 -2.589196837551D-09 -5.949628493511D-07 1.570204824882D-07 E-Index: 3 4 5 T-Index: 0 -1.856976066463D-02 4.225395376848D-03 -5.189796861077D-04 1 9.361575704851D-03 -2.096884296496D-03 2.460978351345D-04 2 -1.500786464745D-05 -5.281337256827D-05 1.822688274176D-05 3 -1.199741248527D-04 7.729105625058D-05 -1.292571216711D-05 4 -1.215394704492D-04 8.835563507260D-07 2.346139078670D-07 5 3.717841775232D-05 -4.659128130528D-07 2.336659134693D-08 6 -4.784046635653D-06 -1.879150864927D-07 3.484666707655D-08 7 3.629533941682D-07 1.916572317480D-08 -4.026763260489D-09 8 -1.317789208085D-08 -1.808855222707D-10 9.539953463992D-11 E-Index: 6 7 8 T-Index: 0 3.509533525807D-05 -1.228955181999D-06 1.739986570439D-08 1 -1.534423152274D-05 4.789360346264D-07 -5.852399019136D-09 2 -2.723344400799D-06 1.665540778802D-07 -3.521640501579D-09 3 1.408094932910D-06 -7.805738049487D-08 1.598423694616D-09 4 -8.824848629130D-08 8.227207653809D-09 -2.131061531618D-10 5 2.250976512907D-10 -4.235527036624D-10 1.550066068535D-11 6 -2.041471088674D-09 8.365367756013D-11 -1.652661621540D-12 7 2.600592567487D-10 -9.155241214856D-12 1.419133004850D-13 8 -6.933726687326D-12 2.503906957552D-13 -3.798372386466D-15 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 4.5211 % Mean rel. Error: 0.3321 % \end{verbatim}\end{small} \begin{figure} \label{2.3.2B1} \epsfxsize=16truecm \epsffile{Amjuel_PS/helir2.ps} \end{figure} \newpage \subsection{ Reaction 2.3.2C $\ e + He^{++} \rightarrow He^+(1s) + hv$ } McWhirter's COLRAD (Hydrogen-like-ion) code: \cite{kn:McWhirter} \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.689214714131D+01 3.841692092650D-02 -2.151460046121D-02 1 -7.416684284021D-01 -5.199553857553D-02 3.438416388654D-02 2 1.549811628148D-02 1.921849237497D-02 -8.089751449111D-03 3 -5.022643137206D-03 1.540629050827D-03 -7.848453879802D-03 4 -2.966821161678D-03 -1.893539924742D-03 4.846354316088D-03 5 1.716018223894D-03 6.468052386412D-06 -9.304158014361D-04 6 -4.229257398810D-04 1.430545146021D-04 2.720980715002D-05 7 4.855298100008D-05 -2.713103018793D-05 1.061403221125D-05 8 -2.091379921301D-06 1.529918299298D-06 -8.819776625245D-07 E-Index: 3 4 5 T-Index: 0 1.113251929355D-02 -2.612008568492D-03 3.555115960397D-04 1 -1.649709408021D-02 3.745035825507D-03 -4.770050113400D-04 2 5.051466915107D-03 -1.400888615025D-03 1.945119633833D-04 3 2.248785870746D-03 -1.593097934071D-04 -1.072827330359D-05 4 -1.751184149675D-03 2.311213551980D-04 -1.261592043312D-05 5 3.966217825812D-04 -5.599522857044D-05 3.206357069410D-06 6 -2.835692554212D-05 3.986381335434D-06 -1.237526859045D-07 7 -1.563313372280D-06 2.625959470738D-07 -3.940819818057D-08 8 2.172325347358D-07 -3.473325519567D-08 3.579469680317D-09 E-Index: 6 7 8 T-Index: 0 -2.731753894771D-05 1.106668461341D-06 -1.811175295207D-08 1 3.368532716741D-05 -1.237223053047D-06 1.842374272400D-08 2 -1.349677736259D-05 4.458107763508D-07 -5.616195641425D-09 3 1.549801888675D-06 -4.466672928817D-08 1.764795248975D-10 4 2.970110443204D-07 -7.035453496351D-09 1.847001891274D-10 5 -7.282619416548D-08 9.859256161271D-10 -1.965913679526D-11 6 -6.579575377692D-09 3.713367646234D-10 -4.389109805641D-12 7 2.919813070386D-09 -9.345142710166D-11 1.091816211559D-12 8 -2.087578972278D-10 6.033495076188D-12 -6.834858440297D-14 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: .2915 % Mean rel. Error: .0363 % \end{verbatim}\end{small} \begin{figure} \label{2.3.2C} \epsfxsize=16truecm \epsffile{Amjuel_PS/helr.ps} \end{figure} \newpage Data from impurity transport code ``STRAHL'', \cite{kn:Behringer} Recombination Rates for single charged Be Ions (w/o three-body) \subsection{ Reaction 2.3.4B0 $e + Be^+ \rightarrow Be + hv$ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.725929462038D+01 -1.296055365219D-01 2.245292514899D-02 1 1.598632576296D+00 1.302182159333D-04 -2.924508048254D-02 2 -7.069733638623D-02 1.301621002137D-02 1.388489192201D-02 3 -2.067343201215D-01 1.279607652398D-02 -8.226493898105D-03 4 2.796219393914D-02 -1.144848913448D-02 3.649484551890D-03 5 5.780534740910D-03 3.235328959441D-03 -7.482336928187D-04 6 -1.791370907134D-03 -4.230924884959D-04 5.874787455135D-05 7 1.653534958925D-04 2.595221480786D-05 -2.868950341068D-08 8 -5.311684839816D-06 -5.924897096316D-07 -1.331690294260D-07 E-Index: 3 4 5 T-Index: 0 -1.244235177506D-02 3.352082223981D-03 -4.750321394261D-04 1 1.419746473600D-02 -4.100011934711D-03 6.269202287880D-04 2 -4.288663227065D-03 1.247934273073D-03 -2.322360688726D-04 3 2.497646037590D-04 4.417198058647D-05 1.716710307904D-05 4 2.490565857171D-05 -6.848577114910D-05 3.867029384089D-06 5 -2.697562238180D-05 1.387239687374D-05 -4.925211191787D-07 6 1.287864123306D-05 -2.354269427799D-06 3.073587970762D-08 7 -1.972411742335D-06 2.825061118192D-07 -7.702743784611D-09 8 9.449990775297D-08 -1.322880879849D-08 5.884617340207D-10 E-Index: 6 7 8 T-Index: 0 3.617661866105D-05 -1.399725603339D-06 2.156930157877D-08 1 -5.003180914560D-05 1.985020029777D-06 -3.097413546292D-08 2 2.077646031907D-05 -8.667756318377D-07 1.374149193674D-08 3 -2.600090567970D-06 1.170403862720D-07 -1.712303962785D-09 4 -4.054013167812D-08 3.807690920711D-09 -2.098135936009D-10 5 -7.568193559820D-09 -9.343144402500D-10 6.008228504862D-11 6 6.869621840242D-09 -1.575414388099D-10 -3.255005891524D-12 7 -5.010735365600D-10 2.217617931435D-11 -5.017068152436D-14 8 2.010217590918D-12 -5.523345073293D-13 4.450782184771D-15 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 6.2699 % Mean rel. Error: 1.0385 % \end{verbatim}\end{small} \begin{figure} \label{2.3.4B0} \epsfxsize=16truecm \epsffile{Amjuel_PS/beryr1.ps} \end{figure} \newpage Data from impurity transport code ``STRAHL'', \cite{kn:Behringer} Recombination Rates for doubly charged Be Ions (w/o three-body) \subsection{ Reaction 2.3.4B1 $e + Be^{++} \rightarrow Be^+ + hv$ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.728409454363D+01 -1.241811114602D-01 1.328174994693D-01 1 -2.299481340923D+00 1.889049385273D-01 -2.096802695556D-01 2 4.885685671195D+00 -2.008764876827D-01 1.648701897617D-01 3 -5.251357791035D+00 1.631486837681D-01 -7.503508975743D-02 4 2.543387065980D+00 -7.665832661210D-02 1.818184962498D-02 5 -6.269100539052D-01 1.928103605570D-02 -2.110079141475D-03 6 8.249496717063D-02 -2.610043486921D-03 7.049607917706D-05 7 -5.541301207997D-03 1.802133911336D-04 5.702189021974D-06 8 1.496309096538D-04 -4.989437255700D-06 -3.793346968439D-07 E-Index: 3 4 5 T-Index: 0 -5.910214948004D-02 1.285989947336D-02 -1.526818134096D-03 1 7.862010247287D-02 -1.449011071235D-02 1.461947439599D-03 2 -5.176172885669D-02 7.317236286761D-03 -5.006068297333D-04 3 2.174133611107D-02 -2.589246910885D-03 1.224743194508D-04 4 -5.098247822369D-03 5.664018911361D-04 -2.623256825779D-05 5 5.566735359374D-04 -5.584858194143D-05 3.211048838419D-06 6 -1.070413228691D-05 -3.231789926435D-07 -9.263670040464D-08 7 -2.513802136711D-06 4.313606598236D-07 -1.345931063116D-08 8 1.390196607821D-07 -2.084300790388D-08 8.301747763811D-10 E-Index: 6 7 8 T-Index: 0 1.005202819403D-04 -3.444000702166D-06 4.788161890026D-08 1 -8.097933215082D-05 2.286740613012D-06 -2.544219441065D-08 2 1.209066466730D-05 2.327109476167D-07 -1.143146298073D-08 3 1.794422803392D-06 -3.537707361735D-07 8.456876614023D-09 4 -2.156876176312D-07 6.001245421502D-08 -1.405872631137D-09 5 -1.162693902875D-07 2.839971828955D-09 -4.787146737233D-11 6 2.652307178112D-08 -1.756949577531D-09 3.793381075708D-11 7 -2.115315858957D-09 1.781987654521D-10 -3.982036996716D-12 8 6.140791320298D-11 -5.995928373217D-12 1.365597034534D-13 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 19.0670 % Mean rel. Error: 6.8000 % \end{verbatim}\end{small} \begin{figure} \label{2.3.4B1} \epsfxsize=16truecm \epsffile{Amjuel_PS/beryr2.ps} \end{figure} \newpage Data from impurity transport code ``STRAHL'', \cite{kn:Behringer} Recombination Rates for singly charged B Ions (w/o three-body) \subsection{ Reaction 2.3.5B0 $ e + B^+ \rightarrow B + hv $ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.918956305904D+01 3.267550103394D-02 -4.823066950210D-02 1 8.901372275414D-01 -3.397383703545D-01 1.289852726858D-01 2 3.343506939285D+00 2.282515642460D-01 -9.103783258930D-02 3 -3.008679922076D+00 -5.388342232412D-02 2.167553199906D-02 4 1.112964165086D+00 1.260534666317D-03 -7.052258987157D-04 5 -2.245854583458D-01 1.232228819204D-03 -1.977243930068D-04 6 2.569483673112D-02 -1.483676372126D-04 -3.653164425984D-05 7 -1.563882824177D-03 2.300571590825D-06 1.068539912027D-05 8 3.933351235932D-05 2.450506888590D-07 -5.790374711265D-07 E-Index: 3 4 5 T-Index: 0 1.084235624678D-02 4.281860869234D-05 -3.006985941012D-04 1 -3.793909504492D-02 4.214381437312D-03 5.910871725608D-06 2 2.943514986182D-02 -4.396644202855D-03 2.457154873853D-04 3 -7.736046881343D-03 1.441634147933D-03 -1.205002465319D-04 4 3.041197053727D-04 -1.227481836109D-04 1.626382262962D-05 5 1.177319584913D-04 -1.388326649605D-05 3.987367591191D-07 6 -2.705344470187D-06 1.266769783662D-06 -1.190611163202D-07 7 -2.136704633704D-06 2.158430175622D-07 -1.198466851774D-08 8 1.462074438369D-07 -1.888327232304D-08 1.358886807026D-09 E-Index: 6 7 8 T-Index: 0 3.913363201372D-05 -1.987487775013D-06 3.630009838447D-08 1 -3.407335594737D-05 2.302780682573D-06 -4.724118588530D-08 2 3.689509356594D-06 -8.271291751691D-07 2.110278755964D-08 3 3.252526057299D-06 7.531658549775D-08 -3.753147142803D-09 4 -7.584147771365D-07 5.617754775370D-09 2.618328829288D-10 5 1.169505739833D-09 4.403213913778D-10 -2.082516311551D-11 6 6.928958657672D-09 -2.614080202244D-10 3.949718599255D-12 7 2.061339771948D-10 7.658743006289D-12 -2.294692069099D-13 8 -5.021219740097D-11 7.599476609801D-13 -1.699102278262D-15 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 15.7065 % Mean rel. Error: 2.2281 % \end{verbatim}\end{small} \newpage This page is intentionally left blank \newpage Data from impurity transport code ``STRAHL'', \cite{kn:Behringer} Recombination Rates for doubly charged B Ions (w/o three-body) \subsection{ Reaction 2.3.5B1 $e + B^{++} \rightarrow B^+ + hv$ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.696271008275D+01 -7.423987167527D-02 3.571997357107D-02 1 2.025499561046D+00 -2.017543096490D-01 3.889732429633D-02 2 -4.525788140577D-01 1.968460159120D-01 -6.412952427778D-02 3 -3.570127232580D-01 -7.677034125200D-02 2.458200773053D-02 4 2.176453653579D-01 1.757254624302D-02 -4.002911937506D-03 5 -5.551419899407D-02 -2.867264920419D-03 3.695449702619D-04 6 7.441747604883D-03 3.370916489954D-04 -3.534397855198D-05 7 -5.097962423085D-04 -2.392639746135D-05 3.307875064213D-06 8 1.405770163082D-05 7.241258048176D-07 -1.324815003798D-07 E-Index: 3 4 5 T-Index: 0 -1.957405255310D-02 4.910268684892D-03 -6.464476031989D-04 1 -5.508972762098D-03 -4.103038628528D-04 1.902830434350D-04 2 1.585484361226D-02 -2.177399186175D-03 1.563169407076D-04 3 -4.639868259732D-03 6.167716090045D-04 -4.549330605404D-05 4 4.476991372525D-05 2.476330393040D-05 -4.315071827987D-06 5 1.274740751517D-04 -2.134889461534D-05 1.854544233927D-06 6 -1.479662046092D-05 1.581279654885D-06 -5.641458092706D-08 7 3.704493921569D-07 4.734791626350D-08 -1.455285738785D-08 8 1.013413641304D-08 -5.639914715196D-09 8.778548005120D-10 E-Index: 6 7 8 T-Index: 0 4.608213097181D-05 -1.682328343662D-06 2.462552849920D-08 1 -1.936931659635D-05 8.242354232962D-07 -1.278778364027D-08 2 -5.717563499079D-06 1.159226451051D-07 -1.577559627995D-09 3 1.710077304240D-06 -4.608894528959D-08 1.034076249492D-09 4 4.279304514899D-07 -1.372870923770D-08 1.655700973007D-11 5 -1.249051804766D-07 3.972618831455D-09 -2.392056598119D-11 6 3.662805039340D-09 -1.410127247126D-10 -5.284190509036D-13 7 8.814048276934D-10 -2.379651723043D-11 3.923946846891D-13 8 -5.221503829879D-11 1.455883950215D-12 -1.921453513095D-14 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 7.5135 % Mean rel. Error: 2.0952 % \end{verbatim}\end{small} \newpage This page is intentionally left blank \newpage Data from impurity transport code ``STRAHL'', \cite{kn:Behringer} Recombination Rates for singly charged C Ions (w/o three-body) \subsection{ Reaction 2.3.6B0 $e + C^{+} \rightarrow C + hv$ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.923411311232D+01 1.678337974062D-01 -1.269890700218D-01 1 -1.749378923698D+00 -5.867508813696D-01 3.397276446168D-01 2 6.127446343098D+00 3.513770163224D-01 -3.131110083174D-01 3 -4.441560794072D+00 -3.036137429391D-02 1.289084037863D-01 4 1.527841448611D+00 -3.932152302666D-02 -2.579185039826D-02 5 -2.957532224524D-01 1.516783137012D-02 2.555395039340D-03 6 3.288049698838D-02 -2.329750940307D-03 -1.325353309286D-04 7 -1.958690224903D-03 1.660871088628D-04 6.019220191601D-06 8 4.844127251791D-05 -4.535654544518D-06 -2.688488538169D-07 E-Index: 3 4 5 T-Index: 0 2.720437652981D-02 -1.111631011430D-03 -3.480216080173D-04 1 -6.886574322654D-02 3.439645295541D-03 5.751243071725D-04 2 6.328287422211D-02 -4.081409017151D-03 -2.359905542867D-04 3 -2.671202258246D-02 2.108719776241D-03 -7.726681822181D-06 4 5.571312305715D-03 -4.818176068215D-04 1.334742280902D-05 5 -6.449949817748D-04 5.958291545901D-05 -1.609837915859D-06 6 5.723823810059D-05 -6.760386887666D-06 1.723115899471D-07 7 -4.762486550175D-06 7.317966975006D-07 -3.186790226580D-08 8 2.051810131854D-07 -3.486630219212D-08 2.049817590722D-09 E-Index: 6 7 8 T-Index: 0 5.022696584875D-05 -2.548461445798D-06 4.576047167523D-08 1 -8.585218474052D-05 4.198580036578D-06 -7.219262965042D-08 2 4.464512662440D-05 -2.122412913024D-06 3.430797320366D-08 3 -6.790151469405D-06 2.960526415072D-07 -3.591611206495D-09 4 -8.898179366602D-08 2.113053977058D-08 -8.335017960966D-10 5 1.948025779931D-08 -3.879062320437D-09 1.297193866948D-10 6 1.158556735339D-08 -6.938508364472D-10 1.200809450653D-11 7 -9.678693700555D-10 1.166071387136D-10 -2.726800105081D-12 8 -8.574281546240D-13 -4.129172667888D-12 1.141324130890D-13 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 20.1006 % Mean rel. Error: 2.5839 % \end{verbatim}\end{small} \newpage this page is intentionally left blank \newpage \subsection{ Reaction 2.3.6A0 $e + C^{+} \rightarrow C + hv$ } Recombination Rates for single charged Carbon Ions, ADAS 93, lower valid density range than in Behringer rate, 1e9 --4e15, i.e. also wrong low ne (Corona) limit. \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.386015899408D+01 -3.910955838564D+00 1.552770970883D+00 1 -5.659678700923D+00 3.273571762123D+00 -1.226359264263D+00 2 5.390501265589D+00 -2.355302777087D-01 -5.195368951742D-02 3 -3.714328835667D+00 3.628845439540D-01 -2.200031489025D-02 4 1.135859606525D+00 -1.186644208284D-01 5.551341663448D-03 5 -1.869372950502D-01 1.628631987628D-02 6.410015500816D-04 6 1.780826701298D-02 -1.478766722313D-03 -8.533991517766D-05 7 -9.287327719634D-04 9.071133960815D-05 -1.095758224111D-06 8 2.035725216911D-05 -2.414914230400D-06 1.597295024608D-07 E-Index: 3 4 5 T-Index: 0 -3.450187675134D-01 4.712272970491D-02 -4.042671286872D-03 1 2.600531850861D-01 -3.341908339155D-02 2.682578223051D-03 2 1.011059953763D-02 -1.169563926566D-03 6.667572788661D-05 3 3.526377986446D-03 -3.427847110389D-04 1.835504781865D-05 4 -8.838264136732D-04 8.565268990423D-05 -1.066175819677D-06 5 -8.593821289931D-05 5.272524686958D-06 -1.224520162331D-06 6 2.660975471746D-06 1.089822895916D-06 -2.890683271478D-09 7 1.203297067573D-06 -2.099731716273D-07 6.174132427111D-09 8 -4.421659538874D-08 4.310876850464D-09 2.079113580150D-10 E-Index: 6 7 8 T-Index: 0 2.122032361962D-04 -6.207489360202D-06 7.739602341370D-08 1 -1.336715470333D-04 3.811224434825D-06 -4.747119054140D-08 2 1.856735987460D-06 -3.458187396125D-07 9.391749990270D-09 3 -2.365613863260D-06 2.014784469522D-07 -5.309278460907D-09 4 2.407496723541D-07 -4.228290011762D-08 1.385165315494D-09 5 3.962428233835D-08 4.764982812388D-09 -2.132127641260D-10 6 -8.202254054789D-10 -4.541903480422D-10 2.006990579325D-11 7 2.277931530317D-10 3.545967143036D-12 -6.419790552377D-13 8 -4.192645662630D-11 1.557121980135D-12 -1.271691932014D-14 N2MIN = 1.00000D 09 1/CM3 N2MAX = 4.00000D 15 1/CM3 Max. rel. Error: 7.2475 % Mean rel. Error: 1.9064 % \end{verbatim}\end{small} \begin{figure} \label{2.3.6A0} \epsfxsize=16truecm \epsffile{Amjuel_PS/carbr-rate.eps} \end{figure} \newpage \subsection{ Reaction 2.3.7A0 $e + N^{+} \rightarrow N + hv$ } Recombination Rates for single charged Nitrogen Ions, ADAS 96 lower valid density range than in Behringer rate: 1e8 --4e15 \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.890979447961D+01 3.404781058304D-02 3.109171343385D-02 1 -1.174542935934D-01 -6.300786378143D-02 1.285451136251D-02 2 1.062396631545D+00 -4.594988800022D-02 -2.144355651778D-02 3 -1.281784857503D-01 1.750663794712D-02 -4.218563857410D-04 4 -1.778575430266D-01 7.578877787156D-03 3.404271527997D-03 5 6.798785783958D-02 -4.597105849322D-03 -4.739820114489D-04 6 -1.028526325632D-02 8.617482106535D-04 -6.225202836732D-05 7 7.268082281380D-04 -7.084122217378D-05 1.512785518009D-05 8 -1.988053691842D-05 2.183474002160D-06 -7.348547415367D-07 E-Index: 3 4 5 T-Index: 0 -2.959597171711D-02 9.972437524383D-03 -1.611047280109D-03 1 -3.284720599538D-03 -3.277710167038D-04 1.453494237233D-04 2 1.590875283251D-02 -4.416788978628D-03 6.137394728855D-04 3 -4.267873772733D-03 1.898156366712D-03 -3.376326628079D-04 4 -9.522209957584D-04 9.592101950028D-06 2.643190197805D-05 5 2.795617403751D-04 -5.664874714649D-05 5.086981091994D-06 6 1.044379154837D-05 1.194568825982D-07 -2.192339608178D-07 7 -5.854382133761D-06 1.051704842577D-06 -9.578564349722D-08 8 3.249656113647D-07 -6.545647058295D-08 6.814062555229D-09 E-Index: 6 7 8 T-Index: 0 1.362263347704D-04 -5.786235879715D-06 9.750444797037D-08 1 -1.452433975975D-05 5.648617057221D-07 -7.117648875509D-09 2 -4.553987913630D-05 1.730678240365D-06 -2.652544738754D-08 3 2.933958065856D-05 -1.240562994480D-06 2.045493282478D-08 4 -3.634440120548D-06 1.885575439239D-07 -3.485971868424D-09 5 -1.949862893743D-07 2.024442443875D-09 2.630734008273D-11 6 2.521164443225D-08 -1.296752613661D-09 2.627656129565D-11 7 4.358665026882D-09 -7.347981360072D-11 -2.477653636206D-13 8 -3.772451802902D-10 1.008260868721D-11 -9.316575573714D-14 N2MIN = 1.00000D 08 1/CM3 N2MAX = 4.00000D 15 1/CM3 Max. rel. Error: 21.5715 % Mean rel. Error: 6.5304 % \end{verbatim}\end{small} \begin{figure} \label{2.3.7A0} \epsfxsize=16truecm \epsffile{Amjuel_PS/nitr-rate.eps} \end{figure} \newpage \subsection{ Reaction 2.3.8A0 $e + O^{+} \rightarrow O + hv$ } Recombination Rates for single charged Oxygen Ions, ADAS 96 lower valid density range than in Behringer rate \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.950202333277D+01 3.417421048652D-02 5.550176406244D-04 1 -3.905878105714D-01 -3.366885804101D-02 5.611644267242D-03 2 8.142161905922D-01 -2.619980609301D-02 1.119917102498D-02 3 -6.314301870760D-02 -6.677833838048D-04 -4.595557614154D-03 4 -1.300209551942D-01 7.344464113626D-03 1.010388603060D-03 5 4.543327490228D-02 -2.431608679889D-03 -1.605807371797D-04 6 -6.551209458023D-03 3.385675498043D-04 1.776299449335D-05 7 4.487444713804D-04 -2.208733089758D-05 -1.188982868102D-06 8 -1.202054123175D-05 5.549447564031D-07 3.573244244320D-08 E-Index: 3 4 5 T-Index: 0 -4.878404722759D-03 2.496704857025D-03 -4.801811432048D-04 1 -6.846315928181D-03 1.781404680449D-03 -2.299350278961D-04 2 -7.650465593431D-03 2.291477501261D-03 -3.428663325456D-04 3 3.319766657887D-03 -8.305632223570D-04 9.687240430638D-05 4 -7.429595897823D-04 1.597082088291D-04 -1.586721570563D-05 5 9.174847318131D-05 -1.791485541629D-05 2.557912304553D-06 6 -3.656971171905D-06 4.415203015131D-07 -2.729885842433D-07 7 -2.390420213573D-07 8.850471294306D-08 1.320290015666D-08 8 1.760145190417D-08 -5.311149778654D-09 -1.932208107521D-10 E-Index: 6 7 8 T-Index: 0 4.414828976029D-05 -1.913653761986D-06 3.169334833101D-08 1 1.629563730611D-05 -6.508094947057D-07 1.168016914799D-08 2 2.801630724815D-05 -1.195893028045D-06 2.066069583201D-08 3 -5.817227023091D-06 1.815236921961D-07 -2.440874713720D-09 4 6.876080976925D-07 -7.143508700482D-09 -1.579410946829D-10 5 -2.191883763675D-07 9.084875748335D-09 -1.438945391695D-10 6 4.429673221310D-08 -2.592667144327D-09 5.218677785470D-11 7 -3.785422204476D-09 2.552603164217D-10 -5.520425235115D-12 8 1.170863046694D-10 -8.639504027193D-12 1.945039811844D-13 N2MIN = 1.00000D 08 1/CM3 N2MAX = 4.00000D 15 1/CM3 Max. rel. Error: 17.6166 % Mean rel. Error: 5.7730 % \end{verbatim}\end{small} \begin{figure} \label{2.3.8A0} \epsfxsize=16truecm \epsffile{Amjuel_PS/oxyr-rate.eps} \end{figure} \newpage \subsection{ Reaction 2.3.10B0 $e + Ne^+ \rightarrow Ne + hv$ } Data from impurity transport code ``STRAHL'', \cite{kn:Behringer} Recombination Rates for singly charged Ne Ions (w/o threebody) \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.950007003885D+01 3.491651842120D-01 -4.526729152358D-01 1 -6.520457077063D-01 7.213904325098D-02 3.658011914091D-01 2 -2.555722669669D+00 -7.475436856707D-01 9.738719342931D-02 3 3.661205101651D+00 5.765147468133D-01 -1.604649380940D-01 4 -1.748125063014D+00 -2.102066448685D-01 6.321986952859D-02 5 4.075296845781D-01 4.352555184156D-02 -1.311266215655D-02 6 -5.084544478774D-02 -5.232558963021D-03 1.582205007651D-03 7 3.267745768343D-03 3.392758114186D-04 -1.046424800738D-04 8 -8.515144644683D-05 -9.147101439320D-06 2.913148029419D-06 E-Index: 3 4 5 T-Index: 0 1.822526019576D-01 -3.440093707612D-02 3.365607055965D-03 1 -1.925738935529D-01 4.196008186724D-02 -4.824821656521D-03 2 2.722985240177D-02 -9.973812872134D-03 1.461560737391D-03 3 1.878485303345D-02 -1.385285413951D-03 9.295164050536D-06 4 -7.774293016035D-03 7.843935223543D-04 -5.991856389796D-05 5 1.332124081154D-03 -1.033638922199D-04 8.612183709508D-06 6 -1.337988184391D-04 5.636490415762D-06 -4.121413995158D-07 7 8.230405845512D-06 -1.571454512161D-07 3.845854426768D-09 8 -2.383823550795D-07 4.365491330109D-09 2.073873285125D-12 E-Index: 6 7 8 T-Index: 0 -1.720328845594D-04 4.174907414363D-06 -3.433683135382D-08 1 3.088521584980D-04 -1.043623699368D-05 1.452433604004D-07 2 -1.188366580476D-04 5.102874363441D-06 -8.840074619382D-08 3 1.172576233056D-05 -9.701778130960D-07 2.315053595109D-08 4 1.480911313552D-06 7.311631221035D-08 -3.231110770367D-09 5 -3.779888128247D-07 1.120723303371D-09 2.214485537742D-10 6 2.901125564163D-08 -7.405559613471D-10 1.446032893388D-12 7 -1.213848594721D-09 7.298790343151D-11 -1.305351788753D-12 8 3.400354319444D-11 -2.737297017901D-12 6.063188511756D-14 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 54.9736 % Mean rel. Error: 6.6709 % \end{verbatim}\end{small} \begin{figure} \label{2.3.10B0} \epsfxsize=16truecm \epsffile{Amjuel_PS/neonr1.ps} \end{figure} \newpage Data from impurity transport code ``STRAHL'', \cite{kn:Behringer} Recombination Rates for doubly charged Ne Ions (w/o three-body) \subsection{ Reaction 2.3.10B1 $e + Ne^{++}\rightarrow Ne^+ + hv$ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.764720323935D+01 -1.955655877647D-01 1.671527355799D-01 1 1.118894063339D+00 3.129124651555D-01 -1.009059388068D-01 2 -5.807229758743D+00 -4.303560193277D-01 5.147902079014D-02 3 5.906119436289D+00 2.908074868726D-01 -3.504756895839D-02 4 -2.486369699756D+00 -1.066677872724D-01 1.675054599333D-02 5 5.400218712330D-01 2.285969690928D-02 -4.685542119686D-03 6 -6.423019855816D-02 -2.860087284730D-03 7.328508385727D-04 7 3.984332639562D-03 1.927287799126D-04 -5.887153870896D-05 8 -1.009911047233D-04 -5.380432470580D-06 1.881736675497D-06 E-Index: 3 4 5 T-Index: 0 -7.260114126178D-02 1.583009936797D-02 -1.898589530133D-03 1 3.746533708965D-02 -8.655894421673D-03 1.099661830628D-03 2 -6.718805346046D-03 1.999612428280D-03 -3.290996365052D-04 3 -4.526057371154D-04 -1.450332583776D-05 6.267094921401D-05 4 4.734615609031D-04 -1.872293739068D-04 1.215375414502D-06 5 -1.215606626036D-05 5.132159918071D-05 -2.379109789101D-06 6 -2.422737859678D-05 -4.568253290882D-06 2.259728294625D-07 7 3.940458387139D-06 2.917180971670D-08 6.379283743551D-09 8 -1.800023588704D-07 9.209746135240D-09 -1.047238386420D-09 E-Index: 6 7 8 T-Index: 0 1.268000506338D-04 -4.414136321690D-06 6.233135264975D-08 1 -7.507106502001D-05 2.542756842488D-06 -3.303898330923D-08 2 2.397963779263D-05 -6.716878731698D-07 3.568810796685D-09 3 -6.220521674696D-06 1.257734260178D-07 2.204442932049D-09 4 9.599983583142D-07 -1.352244273881D-08 -1.106786869688D-09 5 -1.008039023067D-07 1.880168166012D-09 2.080209442599D-10 6 1.781190939483D-08 -6.447382343471D-10 -1.518762965124D-11 7 -2.457175556170D-09 9.557839810920D-11 1.286224146698D-14 8 1.179856275948D-10 -4.471022550637D-12 3.079250396313D-14 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 21.1204 % Mean rel. Error: 6.0132 % \end{verbatim}\end{small} \begin{figure} \label{2.3.10B1} \epsfxsize=16truecm \epsffile{Amjuel_PS/neonr2.ps} \end{figure} \newpage Data from impurity transport code ``STRAHL'', \cite{kn:Behringer} Recombination Rates for singly charged Ar Ions (w/o three-body) \subsection{ Reaction 2.3.18B0 $ e + Ar^+ \rightarrow Ar + hv $ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.961523714505D+01 -3.466294797008D-01 3.739734228058D-01 1 -9.700717663678D-01 3.174213911999D-01 -2.690300717347D-01 2 2.733587493672D-01 -3.157221881515D-01 6.974859201463D-02 3 -2.623209601735D-01 2.934758215827D-01 -5.501202052884D-02 4 1.121844963088D-01 -1.406901237239D-01 3.460910634739D-02 5 -2.608050847276D-02 3.514232816083D-02 -9.818421888710D-03 6 3.353322712511D-03 -4.716045851013D-03 1.375466865468D-03 7 -2.241669321389D-04 3.232299270856D-04 -9.397908348434D-05 8 6.083901388792D-06 -8.888872233070D-06 2.502839044441D-06 E-Index: 3 4 5 T-Index: 0 -1.677610771210D-01 3.629620906444D-02 -4.200257817954D-03 1 1.288420244186D-01 -3.161715324237D-02 4.057456599586D-03 2 -1.580414272181D-02 5.471732050209D-03 -8.980424488739D-04 3 -9.482732378151D-04 4.606867303099D-04 7.340402374160D-06 4 -1.908249918710D-03 -8.498577198828D-05 9.702094170437D-06 5 8.582053824339D-04 -2.071529296492D-05 -1.272108567719D-07 6 -1.258112651082D-04 1.949277321810D-06 2.643262514781D-07 7 7.448923978325D-06 2.740906796410D-07 -7.103042442755D-08 8 -1.383359038597D-07 -2.541568324398D-08 4.131280999373D-09 E-Index: 6 7 8 T-Index: 0 2.648330614117D-04 -8.569045126425D-06 1.113597041124D-07 1 -2.773372679142D-04 9.588925395704D-06 -1.320334721938D-07 2 6.859512197435D-05 -2.469218146406D-06 3.413301196731D-08 3 -3.175389000213D-06 1.354114675747D-07 -1.709524073729D-09 4 -1.895926857712D-07 -4.275832820919D-09 1.814552488433D-10 5 -7.124015966833D-08 7.365306362028D-09 -1.907511087995D-10 6 -3.822283871117D-09 -9.046050010004D-10 3.169432383695D-11 7 3.382667208777D-09 -1.902820234583D-11 -1.500255342391D-12 8 -2.249462681920D-10 4.358044610945D-12 -5.630369486130D-16 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 21.9156 % Mean rel. Error: 2.3347 % \end{verbatim}\end{small} \begin{figure} \label{2.3.18B0} \epsfxsize=16truecm \epsffile{Amjuel_PS/argr1.ps} \end{figure} \newpage Data from impurity transport code ``STRAHL'', \cite{kn:Behringer} Recombination Rates for doubly charged Ar Ions (w/o three-body) \subsection{ Reaction 2.3.18B1 $ e + Ar^{++} \rightarrow Ar^+ + hv$ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.772725546092D+01 -1.964508067762D-01 2.324627102422D-01 1 -6.978601807006D-01 -3.079561336369D-02 -2.145381507914D-02 2 -1.450309406042D-01 1.046307484649D-01 -4.369629888000D-02 3 7.260838315993D-02 -3.466094766036D-02 -7.255991015237D-04 4 -2.582804347800D-02 1.815351628023D-03 6.871280269968D-03 5 5.160665923838D-03 1.395970098141D-03 -2.114054789289D-03 6 -5.799496412067D-04 -3.699751917053D-04 3.252016165358D-04 7 3.420248521929D-05 3.736066138991D-05 -2.707472572922D-05 8 -8.205975768535D-07 -1.373593769853D-06 9.391881125204D-07 E-Index: 3 4 5 T-Index: 0 -1.121363406353D-01 2.586067808011D-02 -3.210690057370D-03 1 1.781324636009D-02 -4.150064170275D-03 4.491490678296D-04 2 1.565988829654D-02 -4.208889079256D-03 6.472110597204D-04 3 -1.979769358644D-04 6.722846983901D-04 -1.476650287912D-04 4 -1.629081885435D-03 7.839217315971D-05 5.746848866889D-06 5 3.607110982734D-04 -3.524282842463D-06 -1.878125337156D-06 6 -4.180965183796D-05 -2.409133311107D-06 5.593232200934D-07 7 3.500759466355D-06 1.374491446170D-07 -3.705743160513D-08 8 -1.463187124936D-07 4.107894379819D-09 1.824159518664D-10 E-Index: 6 7 8 T-Index: 0 2.193249820474D-04 -7.757566204730D-06 1.108985082330D-07 1 -2.393877794814D-05 5.679271788812D-07 -3.900827694763D-09 2 -5.394011848597D-05 2.272796732271D-06 -3.777889093261D-08 3 1.363319474233D-05 -5.936164719619D-07 9.957385133643D-09 4 -6.009177241892D-07 1.485983255077D-08 -3.099011150065D-11 5 1.007709629207D-08 8.232051597397D-09 -2.668448723973D-10 6 -1.251252096167D-08 -1.153506022137D-09 4.325526291510D-11 7 5.438054847774D-10 1.039015370714D-10 -3.543703207540D-12 8 4.191847861623D-11 -5.007688195721D-12 1.309659229521D-13 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 25.0141 % Mean rel. Error: 1.9704 % \end{verbatim}\end{small} \begin{figure} \label{2.3.18B1} \epsfxsize=16truecm \epsffile{Amjuel_PS/argr2.ps} \end{figure} \newpage \subsection{ Reaction 3.2.3r $p + H_2 (+e) \rightarrow H + H + H $ (MAR via $H_2^+$, cold $H_2$) } $H_2$ multi-step model, MAR rate coefficient $cm^3/s$. Data: Sawada/Fujimoto \cite{kn:Sawada} $H_2(v=0)$ transported, $H_2^+$ in QSS with $H_2$, $E_{H_2}=0.1$ eV $H_2(v\geq 1)$ is also in QSS with $H_2(v=0)$. Vibrational distribution $P(v)$ as fct. of $T_e~(=T_p)$ only (assuming $n_e=n_p$, so density cancels here). The MAR rate coefficient is a fct. of $n_e$ and $T (T_e=T_p)$, and must be multiplied with density $n_p$ to turn it into a collision rate $1/s$, and then with $n_{H_2(v=0)}$ to turn it into a volumetric reaction rate ($cm^{-3}s^{-1}$). This is consistent with underlying $P(v)$ only for $n_e=n_p$. \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.191302446846D+01 2.201979359177D-02 -5.084127804366D-02 1 2.515287131029D+00 -1.951782673829D-03 1.210559594877D-02 2 -3.739165027129D+00 -5.039990032868D-03 5.156475880767D-02 3 1.460287495804D+00 -1.902427777619D-02 -2.653691460740D-03 4 -3.613420054183D-01 -9.136720216773D-03 -4.776315047524D-03 5 1.022097226981D-01 1.430112787487D-02 -2.068159413388D-03 6 -2.326509820253D-02 -4.698557490053D-03 1.350601458627D-03 7 2.755718181169D-03 6.183157753063D-04 -2.180157674348D-04 8 -1.245440617856D-04 -2.916396705941D-05 1.131212737957D-05 E-Index: 3 4 5 T-Index: 0 2.725675449247D-02 -6.821140812496D-03 8.984277627487D-04 1 -1.056465122608D-02 3.268414282907D-03 -4.770499814477D-04 2 -3.005896796044D-02 7.117618884301D-03 -8.640595844451D-04 3 8.718387627078D-03 -3.083275129564D-03 4.690013186619D-04 4 2.274299170449D-03 -8.429380778242D-05 -5.166724308864D-05 5 -8.581335425960D-04 2.018790326947D-04 -9.377832906111D-06 6 9.091464941954D-06 -3.214048434350D-05 2.476622604418D-06 7 1.640987010283D-05 1.594693278851D-06 -1.857150815035D-07 8 -1.227368784843D-06 -6.059729362682D-09 4.830770876395D-09 E-Index: 6 7 8 T-Index: 0 -6.471300739878D-05 2.392339469853D-06 -3.542871296534D-08 1 3.555893312434D-05 -1.316695158693D-06 1.915346495446D-08 2 5.696582068003D-05 -1.943708118398D-06 2.693231032650D-08 3 -3.587259258804D-05 1.355091397789D-06 -2.009854793386D-08 4 7.313297805130D-06 -3.673160516940D-07 6.439394992510D-09 5 -6.689618689827D-07 6.721794871158D-08 -1.490826423672D-09 6 4.829313987833D-08 -1.004736504929D-08 2.534364634180D-10 7 -4.842242342991D-09 9.541230138142D-10 -2.466137348591D-11 8 2.201416000842D-10 -3.685384915056D-11 9.608086847565D-13 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 12.2399 % Mean rel. Error: 5.5197 % \end{verbatim}\end{small} \begin{figure} \label{2.2.5mar} \epsfxsize=16truecm \epsffile{Amjuel_PS/mar-H2+.ps} \end{figure} \newpage \subsection{ Reaction 3.2.3d $p + H_2 (+e) \rightarrow p + H + H (+e) $ (MAD via $H_2^+$, cold $H_2$) } $H_2$ multi-step model, MAD rate coefficient $cm^3/s$, same conditions as for effective MAR rate coefficient: $n_e=n_p$ to remove $n_e$ and $n_p$ dependence in $P(v)$, $T_e=T_p$ to remove $T_p$ dependence in $P(v)$, $E_{H_2}=0.1$ eV. \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.305748927979D+01 5.724038174456D-02 -5.615862094751D-02 1 5.292904264798D+00 -1.292700263854D-01 3.199290063730D-02 2 -4.589002200888D+00 1.035141485454D-01 4.245746723064D-02 3 1.282553627472D+00 8.228634639144D-03 -6.982329836971D-02 4 -5.768335357015D-02 -4.231280575573D-02 4.520570788253D-02 5 -1.762738366359D-02 1.754153736792D-02 -1.333930685945D-02 6 -6.220461405830D-04 -2.841940983105D-03 1.674562107704D-03 7 6.413295998688D-04 1.777701087291D-04 -5.286124278229D-05 8 -4.623793560750D-05 -2.110102637934D-06 -2.826184196637D-06 E-Index: 3 4 5 T-Index: 0 2.580537345185D-02 -5.187638531338D-03 5.591824235916D-04 1 -1.411097510416D-03 -1.861670137347D-03 3.728807776936D-04 2 -2.833978655627D-02 6.680453562388D-03 -7.508030455334D-04 3 2.197499638706D-02 -2.786872754376D-03 1.536533061795D-04 4 -9.850360398006D-03 5.824809680428D-04 2.282005339391D-05 5 2.328857648314D-03 -4.906664256889D-05 -9.488057748931D-06 6 -1.644016839248D-04 -2.447100861104D-05 2.465487188700D-06 7 -1.933715475610D-05 7.307909083302D-06 -5.218713324203D-07 8 2.372770563877D-06 -5.341529037052D-07 3.931259348181D-08 E-Index: 6 7 8 T-Index: 0 -3.282931512925D-05 9.814853142975D-07 -1.164322982242D-08 1 -3.011576633244D-05 1.138828160076D-06 -1.667604512176D-08 2 4.303656667760D-05 -1.201510983254D-06 1.269878029776D-08 3 -1.336438693130D-06 -1.902010802533D-07 5.308752951539D-09 4 -3.734435698157D-06 1.331754413945D-07 -1.412895213605D-09 5 1.096115694138D-07 3.997691612605D-08 -1.319357291444D-09 6 1.527860379159D-07 -2.055626589064D-08 5.202352548656D-10 7 -1.441930896339D-08 2.541011510181D-09 -6.500006263746D-11 8 -7.928979184194D-11 -9.515229004763D-11 2.697745453159D-12 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 11.3558 % Mean rel. Error: 5.3396 % \end{verbatim}\end{small} \begin{figure} \label{2.2.5mad} \epsfxsize=16truecm \epsffile{Amjuel_PS/marmad-H2+.ps} \end{figure} \newpage \subsection{ Reaction 3.2.3i $p + H_2 (+e) \rightarrow p + p + H +e (+e) $ (MAI via $H_2^+$, cold $H_2$) } $H_2$ multi-step model, MAI rate coefficient $cm^3/s$, Data: Sawada/Fujimoto ,\cite{kn:Sawada} same conditions as for effective MAR rate coefficient: $n_e=n_p$ to remove $n_e$ and $n_p$ dependence in $P(v)$, $T_e=T_p$ to remove $T_p$ dependence in $P(v)$, $E_{H_2}=0.1$ eV. \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -4.373131541734D+01 6.718149393827D-01 -3.867837685625D-01 1 2.174689987798D+01 -1.191104354839D+00 7.378457372332D-01 2 -1.162182756359D+01 7.756604222360D-01 -4.321461052143D-01 3 1.837003210284D+00 -1.537238550557D-01 8.022138313912D-02 4 8.791715928275D-01 -6.293664899458D-02 2.407530624100D-02 5 -4.701697036505D-01 4.136103649916D-02 -1.573783289950D-02 6 9.146891578771D-02 -9.230394630199D-03 3.397451000676D-03 7 -8.352940909550D-03 9.482379346865D-04 -3.411244141755D-04 8 2.983980601563D-04 -3.758192682764D-05 1.332532546790D-05 E-Index: 3 4 5 T-Index: 0 1.350532623779D-01 -2.606290252421D-02 2.960623240635D-03 1 -2.337897758691D-01 4.249920373347D-02 -4.710792852313D-03 2 1.244024912859D-01 -1.991554109544D-02 2.092199411332D-03 3 -2.768133389852D-02 3.798880238692D-03 -3.638596889044D-04 4 4.582163407263D-04 -2.026711273229D-04 1.801057292473D-05 5 1.179264114144D-03 -1.870608178594D-05 -1.181360244394D-06 6 -2.827540980953D-04 8.280496335764D-07 8.876306183255D-07 7 2.896154172252D-05 2.341967770730D-07 -1.335324508242D-07 8 -1.146002829775D-06 -1.521564259490D-08 5.973795729243D-09 E-Index: 6 7 8 T-Index: 0 -1.932912896769D-04 6.651475974023D-06 -9.311652407600D-08 1 3.059747667206D-04 -1.054165293122D-05 1.478357492460D-07 2 -1.374611007871D-04 4.927217261940D-06 -7.245875668840D-08 3 2.590722791448D-05 -1.080909364087D-06 1.850940055128D-08 4 -1.952361813207D-06 1.287993215397D-07 -3.006990415615D-09 5 1.194038887873D-07 -1.002354431841D-08 3.112143515737D-10 6 -3.422331996712D-08 3.799710153845D-10 -6.935765606162D-12 7 4.289635494443D-09 5.061843256637D-11 -2.503981294990D-12 8 -1.601724546314D-10 -5.336350859656D-12 1.956601576452D-13 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 3.7214 % Mean rel. Error: 1.4562 % \end{verbatim}\end{small} \begin{figure} \label{2.2.5mai} \epsfxsize=16truecm \epsffile{Amjuel_PS/mar-compare-H2+.eps} \end{figure} \newpage \subsection{ Reaction 7.2.3a $ p + H^{-} \rightarrow H + H$ (for cold $H^-$) } CX multistep recombination rate for $H^-$ ions, \cite{kn:Sawada} Rate p + $H^- \rightarrow H + H^*$ followed by $H^* \rightarrow H(1)$ $ \langle \sigma*v_{rel} \rangle(T_e,n_e) (cm^3/s)$ Assume low energy of projectile, $E(H^-)=0.1$ eV, $T_e = T_i$. $H^*$ production based on HYDHEL 7.2.2, 7.2.3. \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -1.690146932812D+01 7.569370314490D-02 -1.118661556236D-01 1 -2.301580195362D-01 2.981364856606D-03 -1.296888142995D-02 2 2.124304411230D-02 -4.585972147659D-02 7.447057284991D-02 3 7.720995917466D-03 3.504507942086D-03 1.734371731330D-04 4 1.331695301990D-02 -9.042026807455D-04 -4.764566765886D-03 5 3.536238349067D-04 -8.011930719727D-04 1.101704458636D-03 6 -1.446558546363D-03 1.152532160685D-03 -8.305881275354D-04 7 2.479021261394D-04 -2.773890711262D-04 2.167753172783D-04 8 -1.248597948333D-05 1.903633250451D-05 -1.590752591530D-05 E-Index: 3 4 5 T-Index: 0 5.784649204408D-02 -1.430206446825D-02 1.883300059210D-03 1 9.188878355062D-03 -2.795985155376D-03 4.355473614802D-04 2 -3.922380885092D-02 9.609624588460D-03 -1.240136716983D-03 3 -1.347164354237D-03 5.423527604759D-04 -9.468953600274D-05 4 3.858570576628D-03 -1.128426542832D-03 1.607204158523D-04 5 -5.449050513405D-04 1.255763496307D-04 -1.495920840346D-05 6 2.084267816803D-04 -1.903417990674D-05 -2.796205484739D-07 7 -6.195779421732D-05 7.927649861583D-06 -4.211576616550D-07 8 4.992428048704D-06 -7.522431288906D-07 5.827438308119D-08 E-Index: 6 7 8 T-Index: 0 -1.346209157175D-04 4.900081433053D-06 -7.105742130265D-08 1 -3.579321024690D-05 1.457520878645D-06 -2.319369078632D-08 2 8.671653962517D-05 -3.101461653370D-06 4.442783018453D-08 3 8.309512179236D-06 -3.552667688177D-07 5.887954953357D-09 4 -1.197915401674D-05 4.484319353024D-07 -6.656156226037D-09 5 9.441566217674D-07 -2.989807912656D-08 3.717785721362D-10 6 1.584268580014D-07 -9.504026475042D-09 1.811886563961D-10 7 2.531413590874D-10 7.572949322455D-10 -1.937737123063D-11 8 -2.220813567852D-09 3.174650814148D-11 6.296020826533D-14 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 4.1781 % Mean rel. Error: .9694 % \end{verbatim}\end{small} \begin{figure} \label{7.2.3a} \epsfxsize=16truecm \epsffile{Amjuel_PS/hmrc.ps} \end{figure} \newpage \subsection{ Reaction 7.2.3b $ p + H^{-} \rightarrow H + H^+ + 2e$ (for cold $H^-$) } CX multistep ionization rate for $H^-$ ions, \cite{kn:Sawada} Rate p + $H^- \rightarrow H + H^*$ followed by $H^* \rightarrow H^+ +e$ $ \langle \sigma*v_{rel} \rangle(T_e,n_e) (cm^3/s)$ \\ Assume low energy of projectile, $E(H^-)=0.1$ eV, $T_e = T_i$. $H^*$ production based on HYHDEL 7.2.2, 7.2.3 (not included: process 7.2.1 of proton impact electron detachment). \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.274642366537D+01 1.055347808907D+00 -8.644168315786D-02 1 1.594755262357D+00 -1.134505488332D-01 1.193838572515D-01 2 -7.947374319647D-01 5.372231672557D-02 -1.798104638021D-02 3 2.774560684070D-01 -3.731637924945D-02 1.249720348407D-02 4 -9.340115304254D-02 7.824080188667D-03 -7.880149239516D-05 5 2.404236598616D-02 8.348790303724D-04 -1.947217396578D-03 6 -3.635353640159D-03 -4.379659530212D-04 4.542431412762D-04 7 2.758341263855D-04 4.578696899777D-05 -3.345082277318D-05 8 -7.995248003067D-06 -1.405530335553D-06 4.938572628097D-07 E-Index: 3 4 5 T-Index: 0 5.770739917980D-02 -1.651543971724D-02 2.426926977738D-03 1 -4.779741494751D-02 9.036602994533D-03 -8.828786882875D-04 2 -2.492326178844D-04 1.070003818666D-03 -1.975024076418D-04 3 -2.377802775838D-03 3.185245795525D-04 -3.766701342971D-05 4 2.730699348365D-04 -1.613682461379D-04 2.956305967893D-05 5 4.228772072344D-04 -3.061264744513D-05 -4.412707867464D-07 6 -8.943967815733D-05 7.191065760263D-06 -2.516431736865D-07 7 3.040805346315D-06 4.037034921179D-07 -7.745783067338D-08 8 2.407555731254D-07 -8.580821961541D-08 1.001281190560D-08 E-Index: 6 7 8 T-Index: 0 -1.852128922021D-04 6.948553416066D-06 -1.014917161032D-07 1 4.408052942176D-05 -1.018626285421D-06 7.671244985570D-09 2 1.598210863669D-05 -6.159714930603D-07 9.185228515472D-09 3 3.135633075387D-06 -1.383905482846D-07 2.380265714001D-09 4 -2.493019966708D-06 1.000180106519D-07 -1.546520999798D-09 5 1.760055762971D-07 -8.605767550690D-09 1.338507166605D-10 6 5.049361112014D-09 -2.841033281170D-10 9.491816236733D-12 7 4.107873810473D-09 -5.899534309929D-11 -6.502135074988D-13 8 -5.295286447696D-10 1.196080372249D-11 -7.019149004762D-14 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 4.7342 % Mean rel. Error: 1.9827 % \end{verbatim}\end{small} \begin{figure} \label{7.2.3b} \epsfxsize=16truecm \epsffile{Amjuel_PS/hmio.ps} \end{figure} \newpage \subsection{ Reaction 2.2.17r $e + H_2 (+p) \rightarrow H + H + H $ (MAR via $H^-$, cold $H_2$) } $H_2$ multi-step model, intermediate H$^-$ condensed MAR rate coefficient $cm^3/s$. Data: Sawada/Fujimoto/Greenland \cite{kn:Sawada} $H_2(v=0)$ transported, $H-$ in QSS with $H_2$, $E_{H_2}=0.1$ eV $H_2(v\geq 1)$ is also in QSS with $H_2(v=0)$. Vibrational distribution $P(v)$ as fct. of $T_e$ only (assuming $n_e=n_p$, so density cancels here). The MAR rate coefficient is a fct. of $n_e$ and $T (T_e=T_p)$, and must be multiplied with density $n_e$ to turn it into a collision rate $1/s$, and then with $n_{H_2(v=0)}$ to turn it into a volumetric reaction rate ($cm^{-3}s^{-1}$). \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.297800283146D+01 6.534592113445D-02 -9.544034335177D-02 1 3.255752862650D-01 -4.609955130788D-02 5.098906708830D-02 2 -2.786114306651D+00 -1.546214758321D-02 2.847577356774D-02 3 5.451071688762D-01 1.247241020831D-02 -1.353760272178D-02 4 -6.286158855226D-02 -4.389219885290D-03 3.206993381146D-03 5 4.602307315406D-02 -3.365073093686D-04 4.783138611752D-04 6 -1.377583511277D-02 6.740788490537D-04 -6.551863726515D-04 7 1.527262955311D-03 -1.450720501257D-04 1.431871130747D-04 8 -5.704031483864D-05 9.223227686785D-06 -9.308552409010D-06 E-Index: 3 4 5 T-Index: 0 4.970735210679D-02 -1.243141252556D-02 1.655580726220D-03 1 -1.954797928578D-02 3.399801537594D-03 -2.849051225621D-04 2 -1.678956104784D-02 4.504025971793D-03 -6.240461921076D-04 3 5.119377169125D-03 -8.773390579671D-04 7.144457352822D-05 4 -5.136674287472D-04 -7.768096468037D-05 3.000125315688D-05 5 -2.297027336534D-04 4.978316796624D-05 -5.355797001723D-06 6 2.206810315147D-04 -3.303528206775D-05 2.195396861484D-06 7 -4.980757484889D-05 8.014816441375D-06 -6.397577372929D-07 8 3.352896292336D-06 -5.723489499349D-07 5.088071892707D-08 E-Index: 6 7 8 T-Index: 0 -1.194692428627D-04 4.379565825329D-06 -6.383725114244D-08 1 1.051829766407D-05 -9.154397761809D-08 -2.152692619811D-09 2 4.608932334537D-05 -1.718655992974D-06 2.542645887393D-08 3 -2.388410284649D-06 2.655768446028D-09 1.025732328009D-09 4 -3.192832412396D-06 1.454747252965D-07 -2.454086710166D-09 5 2.865878646518D-07 -6.904361734587D-09 5.002886041869D-11 6 -3.785101515696D-08 -2.050241512510D-09 7.102693831116D-11 7 2.367506961773D-08 -2.530033040264D-10 -3.372527364917D-12 8 -2.359337617271D-09 5.134816267193D-11 -3.545642487622D-13 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 0.234E+02 % Mean rel. Error: 0.116E+02 % \end{verbatim}\end{small} \begin{figure} \label{2.2.17mar} \epsfxsize=16truecm \epsffile{Amjuel_PS/mar-H-.eps} \end{figure} \newpage \subsection{ Reaction 2.2.17d $e + H_2 (+p) \rightarrow p + H + H $ (MAD via $H^-$, cold $H_2$) } $H_2$ multi-step model, H$^-$ condensed MAD rate coefficient $cm^3/s$, same conditions as for effective MAR rate coefficient: $n_e=n_p, T_e=T_p$ to remove $n_p,T_p$ dependence in second step, $E_{H_2}=0.1$ eV. \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.882083547683D+01 1.095791921388D+00 -1.230711293981D-01 1 2.151709312342D+00 -4.168827415549D-02 4.892315481992D-02 2 -3.595143998663D+00 -2.412908863509D-02 3.295635167166D-02 3 7.775259996676D-01 -6.068712552241D-03 3.634654300394D-03 4 -1.395293276372D-01 4.544589777558D-03 -4.066643547905D-03 5 6.013775491272D-02 -1.839703814205D-04 3.051477843336D-04 6 -1.461016120534D-02 -6.880568170969D-05 -5.434943913724D-05 7 1.482124097593D-03 -1.816234384924D-06 2.631936396542D-05 8 -5.220871340356D-05 9.259820722261D-07 -2.405390251053D-06 E-Index: 3 4 5 T-Index: 0 7.156191553995D-02 -1.924429230749D-02 2.729436304739D-03 1 -2.163365368372D-02 4.090487899919D-03 -3.583331242137D-04 2 -1.528766675405D-02 3.561575456573D-03 -4.454863057078D-04 3 -1.214281149023D-03 2.441534541113D-04 -3.652079252543D-05 4 1.744404381785D-03 -3.908220370889D-04 5.014932056722D-05 5 -2.160937153726D-04 5.731455836804D-05 -7.513434462406D-06 6 5.747785604281D-05 -1.494808974427D-05 1.694028119666D-06 7 -1.618482069160D-05 3.709442120281D-06 -4.001502419799D-07 8 1.271263892578D-06 -2.787472368647D-07 2.994682318717D-08 E-Index: 6 7 8 T-Index: 0 -2.041720297851D-04 7.573899339820D-06 -1.099140704569D-07 1 1.252069523769D-05 -1.374650112152D-08 -5.466351407287D-09 2 3.063903823423D-05 -1.087318819599D-06 1.550671864150D-08 3 3.268697767939D-06 -1.457925944423D-07 2.490300520343D-09 4 -3.621341085954D-06 1.350800086799D-07 -2.014614269650D-09 5 5.230899431395D-07 -1.841979478877D-08 2.572500353175D-10 6 -9.509188594474D-08 2.540647702443D-09 -2.460554994619D-11 7 2.191691514991D-08 -5.803874517021D-10 5.695004783405D-12 8 -1.671204190850D-09 4.617233523173D-11 -4.914469012752D-13 N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 0.250E+02 % Mean rel. Error: 0.108E+02 % \end{verbatim}\end{small} \begin{figure} \label{2.2.17mad} \epsfxsize=16truecm \epsffile{Amjuel_PS/mad-H-.eps} \end{figure} \newpage \section{H.5 : Fits for $\langle\sigma \cdot v \cdot momentum \rangle (T) $} to be written \newpage \section{H.6 : Fits for $\langle\sigma \cdot v \cdot momentum \rangle (E,T) $ } to be written \newpage \section{H.7 : Fits for $\langle\sigma \cdot v \cdot momentum \rangle (n_e,T) $ } \newpage This page is intentionally left blank \newpage \section{H.8 : Fits for $\langle\sigma \cdot v \cdot E_p \rangle (T_b) \ [cm^3/s \cdot eV]$} $E_p$ is a relevant energy related to the process, e.g. it may be the impacting electron or ion in eV, or the radiation energy loss per reaction, etc. In the present section the energy-weighted rate is a function of temperature [eV] of the impacting electron or ion \subsection{ Reaction 2.2.14 $e + H_2^+(v) \rightarrow H(1s) + H^*(n) (v=0-9, n \ge 2) $ } The energy weighting in this rate coefficient is done with the kinetic energy of impacting electron. The general expression for this type of incident particle energy-weighted rate, in which the second particle is at rest, reads: $\langle\sigma v_e E_{elec}\rangle(T_e) = kT_e \cdot \langle\sigma v_e\rangle \cdot \left(3/2 + \frac{d \ln \langle\sigma v_e\rangle}{d \ln(kT_e)}\right)$ The fit for the particular process in this paragraph should result in $\langle\sigma v_e E_{elec}\rangle(T_e) \approx 0.896 ~kT_e ~\langle\sigma v_e\rangle$, i.e. low energy electrons are preferred in this reaction, over the average electrons with $3/2~kT_e$ \begin{small}\begin{verbatim} h0 -1.681368547011e+01 h1 3.964355004318e-01 h2 0.000000000000e+00 h3 0.000000000000e+00 h4 0.000000000000e+00 h5 0.000000000000e+00 h6 0.000000000000e+00 h7 0.000000000000e+00 h8 0.000000000000e+00 \end{verbatim}\end{small} \subsection{ Reaction 2.7.14 $e + N_2^+ \rightarrow N + N^*(n) $ } The energy weighting in this rate coefficient is done with the kinetic energy of impacting electron. The same procedure is applied as for $H_2^+$ dissociative recombination, see above in this section. \begin{small}\begin{verbatim} h0 -1.650010000000e+01 h1 0.700000000000e+00 h2 0.000000000000e+00 h3 0.000000000000e+00 h4 0.000000000000e+00 h5 0.000000000000e+00 h6 0.000000000000e+00 h7 0.000000000000e+00 h8 0.000000000000e+00 \end{verbatim}\end{small} \newpage This page is intentionally left blank \newpage \subsection{ Reaction 2.2B0 $e + He(1s^21S) \rightarrow e + He^+(1s) + e $ 11/94 update } \begin{small}\begin{verbatim} h0 -3.294427070846D+01 h1 2.058485983359D+01 h2 -1.018663912043D+01 h3 3.072113276309D+00 h4 -6.121540418115D-01 h5 8.135920959426D-02 h6 -6.956871247682D-03 h7 3.454933903445D-04 h8 -7.541153102380D-06 \end{verbatim}\end{small} \subsection{ Reaction 2.2B1 $e + He^+(1s) \rightarrow e + He^{++} + e$ 11/94 update } \begin{small}\begin{verbatim} h0 -5.355348236978D+01 h1 4.009715623653D+01 h2 -1.981585158765D+01 h3 6.148719835529D+00 h4 -1.288397616745D+00 h5 1.817351838759D-01 h6 -1.642324160178D-02 h7 8.519919601377D-04 h8 -1.917188865674D-05 \end{verbatim}\end{small} \begin{figure} \label{e2.2B} \epsfxsize=16truecm \epsffile{Amjuel_PS/fige2_2B.ps} \end{figure} \newpage \subsection{ Reaction 2.4B0 $e + Be \rightarrow e + Be^+ + e $ 1/96 update } Electron cooling rates for neutral Beryllium Atoms $ \langle de*sigma*vrel \rangle(T_e) (eV*cm**3/s), Be \rightarrow Be^*$ \begin{small}\begin{verbatim} h0 -1.600797819812D+01 h1 4.801721310374D+00 h2 -2.546377115756D+00 h3 7.688590079004D-01 h4 -1.502880642117D-01 h5 1.910668947476D-02 h6 -1.528566911077D-03 h7 6.997210970692D-05 h8 -1.398145303385D-06 Max. rel. Error: .1477 % Mean rel. Error: .0376 % \end{verbatim}\end{small} \subsection{ Reaction 2.4B1 $e + Be^+ \rightarrow e + Be^{++} + e $ 1/96 update } Electron cooling rates for single charged Beryllium Ions $ \langle de*sigma*vrel \rangle(T_e) (eV*cm**3/s), Be^+ \rightarrow Be^{+*} $ \begin{small}\begin{verbatim} h0 -1.570117098474D+01 h1 3.492073280813D+00 h2 -1.988895527002D+00 h3 6.770887182178D-01 h4 -1.567537912034D-01 h5 2.416405226747D-02 h6 -2.343329470312D-03 h7 1.280666147623D-04 h8 -2.989849097428D-06 Max. rel. Error: .1400 % Mean rel. Error: .0783 % \end{verbatim}\end{small} \begin{figure} \label{2.4Bl} \epsfxsize=16truecm \epsffile{Amjuel_PS/beryl.ps} \end{figure} \newpage \subsection{ Reaction 2.5B0 $e + B \rightarrow e + B^+ + e $ 1/96 update } Electron cooling rates for neutral Boron Particles $ \langle de*sigma*vrel \rangle(T_e) (eV*cm**3/s), B \rightarrow B^* $ \begin{small}\begin{verbatim} h0 -1.854307390504D+01 h1 6.477147013729D+00 h2 -3.012265953316D+00 h3 7.443204571714D-01 h4 -9.875163519457D-02 h5 4.879302715434D-03 h6 3.317004129594D-04 h7 -5.135297123379D-05 h8 1.774782835741D-06 \end{verbatim}\end{small} \subsection{ Reaction 2.5B1 $e + B^+ \rightarrow e + B^{++} + e $ 1/96 update } Electron cooling rates for single charged Boron Particles $ \langle de*sigma*vrel \rangle(T_e) (eV*cm**3/s), B^+ \rightarrow B^{+*} $ \begin{small}\begin{verbatim} h0 -2.025375436381D+01 h1 8.540697000676D+00 h2 -4.378249188138D+00 h3 1.324025185106D+00 h4 -2.627439468179D-01 h5 3.472998074572D-02 h6 -2.959016392102D-03 h7 1.467662520364D-04 h8 -3.204537616409D-06 \end{verbatim}\end{small} \newpage This page is intentionally left blank \newpage \subsection{ Reaction 2.6B0 $e + C \rightarrow e + C^+ + e $ 1/98 update } Electron cooling rates for neutral Carbon Particles. Here: use $\Delta E_e = I_p = const = 11.30$ constant multiplier to corresp. ionisation fit. $ \langle de*sigma*vrel \rangle(T_e) (eV*cm**3/s), C \rightarrow C^* $ \begin{small}\begin{verbatim} h0 -2.712642477000D+01 h1 1.180604026361D+01 h2 -5.438799573749D+00 h3 1.750648117869D+00 h4 -3.946542606866D-01 h5 5.887749368990D-02 h6 -5.469027807326D-03 h7 2.850693136991D-04 h8 -6.354758903485D-06 \end{verbatim}\end{small} \subsection{ Reaction 2.6B1 $e + C^+ \rightarrow e + C^{++} + e $ 1/98 update } Electron cooling rates for single charged Carbon Particles $ \langle de*sigma*vrel \rangle(T_e) (eV*cm**3/s), C^+ \rightarrow C^{+*} $ \begin{small}\begin{verbatim} h0 -2.182881258910D+01 h1 8.721441032283D+00 h2 -3.874718527697D+00 h3 9.883761525498D-01 h4 -1.611584081736D-01 h5 1.774337558846D-02 h6 -1.355435656870D-03 h7 6.703143691651D-05 h8 -1.588682523808D-06 Max. rel. Error: 1.0056 % Mean rel. Error: .3730 % \end{verbatim}\end{small} \newpage This page is intentionally left blank \newpage \subsection{ Reaction 2.7B0 $e + N \rightarrow e + N^{+} + e $ } Electron cooling rates for neutral Nitrogen atoms due to ionisation. here: use $\Delta E_e = I_p = const = 14.535$ $ \langle de*sigma*vrel \rangle(T_e) (eV*cm**3/s), N \rightarrow N^{*} $ \begin{small}\begin{verbatim} h0 -3.000278067000D+01 h1 1.487745850177D+01 h2 -7.393982038208D+00 h3 2.552657836634D+00 h4 -6.031414732283D-01 h5 9.299608313666D-02 h6 -8.862541230616D-03 h7 4.718778196780D-04 h8 -1.071093371002D-05 \end{verbatim}\end{small} \newpage This page is intentionally left blank \newpage \subsection{ Reaction 2.10B0 $e + Ne \rightarrow e + Ne^+ + e $ 1/96 update } Electron cooling rates for neutral and single charged Neon Particles $ \langle de*sigma*vrel \rangle(T_e) (eV*cm**3/s), Ne \rightarrow Ne^*$ \begin{small}\begin{verbatim} h0 -3.296011717683D+01 h1 2.090175238087D+01 h2 -1.260497269687D+01 h3 4.703674520432D+00 h4 -1.084256841690D+00 h5 1.545011409578D-01 h6 -1.329678439752D-02 h7 6.349448203560D-04 h8 -1.293944291911D-05 Max. rel. Error: .0768 % Mean rel. Error: .0448 % \end{verbatim}\end{small} \subsection{ Reaction 2.10B1 $ e + Ne^+ \rightarrow e + Ne^{++} + e $ 1/96 update } Electron cooling rates for neutral and single charged Neon Particles $ \langle de*sigma*v-rel \rangle(T_e) (eV*cm**3/s), Ne^+ \rightarrow Ne^{+*} $ \begin{small}\begin{verbatim} h0 -4.016425730032D+01 h1 2.721204153637D+01 h2 -1.284168864085D+01 h3 3.355303591105D+00 h4 -4.850926860273D-01 h5 3.324128846263D-02 h6 -7.385513932230D-05 h7 -1.193933246957D-04 h8 4.774152004995D-06 Max. rel. Error: .3700 % Mean rel. Error: .2182 % \end{verbatim}\end{small} \begin{figure} \label{2.10l} \epsfxsize=16truecm \epsffile{Amjuel_PS/neonl.ps} \end{figure} \newpage \subsection{ Reaction 2.18B0 $e + Ar \rightarrow e + Ar^+ + e$ 1/96 update } Electron cooling rates for neutral and single charged Argon Particles here: use $\Delta E_e = I_p = const = 15.7596$, constant multiplier to corresp. ionisation fit. $ \langle de*sigma*vrel \rangle(T_e) (eV*cm**3/s), Ar \rightarrow Ar^* $ \begin{small}\begin{verbatim} h0 -3.054602443000D+01 h1 1.627861918393D+01 h2 -7.765170847889D+00 h3 2.446384994382D+00 h4 -5.186581624286D-01 h5 7.184868450814D-02 h6 -6.200405891186D-03 h7 3.018464732517D-04 h8 -6.325074170944D-06 \end{verbatim}\end{small} \subsection{ Reaction 2.18B1 $e + Ar^+ \rightarrow e + Ar^{++} + e$ 1/96 update } Electron cooling rates for neutral and single charged Argon Particles $ \langle de*sigma*vrel \rangle(T_e) (eV*cm**3/s), Ar^+ \rightarrow Ar^{+*} $ \begin{small}\begin{verbatim} h0 -4.165898540334D+01 h1 2.608109647112D+01 h2 -1.166949407607D+01 h3 3.280473403465D+00 h4 -6.113171083108D-01 h5 7.504889391247D-02 h6 -5.828589448772D-03 h7 2.593634229260D-04 h8 -5.035811848208D-06 Max. rel. Error: .0697 % Mean rel. Error: .0288 % \end{verbatim}\end{small} \begin{figure} \label{2.18Bl} \epsfxsize=16truecm \epsffile{Amjuel_PS/argl.ps} \end{figure} \newpage \subsection{ Reaction 2.26B0 $e + Fe \rightarrow e + Fe^+ + e$ 2/06 update } Electron cooling rates for neutral and single charged Iron Particles $ \langle de*sigma*vrel \rangle(T_e) (eV*cm**3/s), Fe \rightarrow Fe^* $ \begin{small}\begin{verbatim} h0 -2.251653573541D+01 h1 8.433391246873D+00 h2 -3.846892917152D+00 h3 1.185977478850D+00 h4 -2.459331954696D-01 h5 3.266167601116D-02 h6 -2.642599090120D-03 h7 1.182307520821D-04 h8 -2.237623328108D-06 Max. rel. Error: .0906 % Mean rel. Error: .0450 % \end{verbatim}\end{small} \subsection{ Reaction 2.26B1 $e + Fe^+ \rightarrow e + Fe^{++} + e$ 2/06 update } Electron cooling rates for neutral and single charged Iron Particles $ \langle de*sigma*vrel \rangle(T_e) (eV*cm**3/s), Fe^+ \rightarrow Fe^{+*} $ \begin{small}\begin{verbatim} h0 -1.624809050332D+01 h1 4.421997781459D+00 h2 -2.249312140674D+00 h3 5.326087246569D-01 h4 -3.768433369019D-02 h5 -8.032685540054D-03 h6 1.913339126234D-03 h7 -1.516002249042D-04 h8 4.332622078891D-06 Max. rel. Error: .4042 % Mean rel. Error: .2088 % \end{verbatim}\end{small} \begin{figure} \label{2.26Bl} \epsfxsize=16truecm \epsffile{Amjuel_PS/fel.ps} \end{figure} \newpage \subsection{ Reaction 3.1.8L $p + H(1s) \rightarrow H(1s) + p $ } Langevin CX rate, for testing only. $E_p$ is the kinetic energy of the impacting ion in eV. The energy weighted rate for the Langevin approximation is 3/2 kT * 2e-8 \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: h0 -1.732206846000D+01 h1 1.000000000000D+00 h2 0.000000000000D+00 h3 0.000000000000D+00 h4 0.000000000000D+00 h5 0.000000000000D+00 h6 0.000000000000D+00 h7 0.000000000000D+00 h8 0.000000000000D+00 \end{verbatim}\end{small} \section{H.9 :Fits for $\langle\sigma \cdot v \cdot E_p \rangle (E_0,T_p) \ [cm^3/s \cdot eV]$} \subsection{ Reaction 3.1.8 $p + H(1s) \rightarrow H(1s) + p $ } $E_p$ is the kinetic energy of the impacting ion in eV. The energy-weighted rate coefficient is a function of ion temperature $T_p$ [eV] and of the impacting neutral particle kinetic energy $E_0$ [eV] \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -1.777579549728D+01 1.009523650881D-01 4.654228527844D-02 1 1.275231758810D+00 -9.644906009036D-02 -2.211669235384D-02 2 4.530160377165D-02 2.342045574729D-02 -9.203651373424D-03 3 -5.955369019980D-03 3.554165401021D-03 5.687922583665D-03 4 -1.979653552345D-03 -2.139061718958D-03 -5.015782273336D-05 5 1.387089441785D-04 2.267300682383D-04 -4.035280214497D-04 6 9.252160306969D-05 1.040699979357D-05 8.704096952722D-05 7 -1.432658980502D-05 -2.945710692553D-06 -7.300036168036D-06 8 5.659366058900D-07 1.274167039318D-07 2.222526255554D-07 E-Index: 3 4 5 T-Index: 0 1.086931313538D-02 -2.594201995447D-03 -7.731266223508D-04 1 8.467481122042D-03 1.412559491188D-03 -7.442507107710D-04 2 -4.737882712502D-03 1.276905220752D-03 2.370696675146D-04 3 -1.107407133685D-03 -5.709773444309D-04 1.803637598216D-04 4 6.785109655871D-04 -6.025307354437D-05 -5.642411701218D-05 5 -5.545614797192D-05 6.129382543768D-05 -3.599116584649D-06 6 -9.853811706993D-06 -1.141186867496D-05 2.733706713304D-06 7 1.708575489575D-06 8.872884700942D-07 -3.140831827282D-07 8 -6.988406373694D-08 -2.556421038443D-08 1.135791478659D-08 E-Index: 6 7 8 T-Index: 0 2.413613977749D-04 -2.132300538605D-05 6.057223635716D-07 1 9.518302025258D-05 -4.753012706978D-06 7.069997192010D-08 2 -1.000952289205D-04 1.059536089242D-05 -3.696859736968D-07 3 -1.512070888533D-05 5.360958997427D-08 2.773215541900D-08 4 1.500712819446D-05 -1.393253051164D-06 4.521246252095D-08 5 -1.937812763003D-06 3.059696948703D-07 -1.282436081613D-08 6 -9.308661633534D-08 -1.924954958807D-08 1.274653104848D-09 7 2.993136285588D-08 -4.094687301095D-10 -4.251053762140D-11 8 -1.386563064570D-09 5.641978567123D-11 -1.151564989100D-13 Max. rel. Error: 1.2514 % Mean rel. Error: 0.2865 % \end{verbatim}\end{small} \newpage This page is intentionally left blank \newpage \subsection{ Reaction 3.1.8L $p + H(1s) \rightarrow H(1s) + p $ } $E_p$ is the kinetic energy of the impacting ion in eV. The energy-weighted rate for the Langevin approximation is 3/2 kT * 2e-8 \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -1.732206846000D+01 0.000000000000D+00 0.000000000000D+00 1 1.000000000000D+00 0.000000000000D+00 0.000000000000D+00 2 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 3 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 4 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 5 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 6 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 7 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 8 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 E-Index: 3 4 5 T-Index: 0 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 1 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 2 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 3 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 4 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 5 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 6 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 7 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 8 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 E-Index: 6 7 8 T-Index: 0 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 1 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 2 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 3 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 4 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 5 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 6 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 7 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 8 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00 Max. rel. Error: 0.0000 % Mean rel. Error: 0.0000 % \end{verbatim}\end{small} \newpage This page is intentionally left blank \newpage \subsection{ Reaction 3.3.1 $ p + He(1s^21S) \rightarrow H + He^+(1s) $ } Proton energy weighted charge exchange rate coefficient, protons with ground state Helium He, $E_{th} \approx 11.2$ eV. Corresponding un-weighted rate coefficient is given also here in an earlier section and in HYHEL with same sub-section number. \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.445873460852D+01 8.326134682590D-01 1.933054122941D-01 1 7.061207340144D+00 -1.313817435577D+00 -2.022008463051D-02 2 -1.736559910607D+00 9.850170907730D-01 -2.150416408177D-01 3 2.831856629788D-01 -4.245131595514D-01 1.739383391445D-01 4 2.241285385641D-02 1.103647192643D-01 -6.088038032579D-02 5 -2.212724523621D-02 -1.746079083640D-02 1.145240838422D-02 6 4.425243772505D-03 1.637736454226D-03 -1.204202849751D-03 7 -3.781548873891D-04 -8.345178061307D-05 6.671405376586D-05 8 1.193024795969D-05 1.774873395657D-06 -1.517888839586D-06 E-Index: 3 4 5 T-Index: 0 6.873661138878D-02 -2.530594845507D-02 3.637744786711D-03 1 -1.061062949296D-01 4.412103967546D-02 -3.685824519445D-03 2 6.376880737273D-02 -1.785764179094D-02 1.574503264024D-03 3 -2.171235372363D-02 -3.103258502378D-04 -7.908060831688D-05 4 5.072440380901D-03 1.643836342594D-03 -1.585285238384D-04 5 -8.662593688148D-04 -3.914961081124D-04 5.595248036912D-05 6 1.004763175634D-04 3.863654089420D-05 -8.367160814608D-06 7 -6.737998131918D-06 -1.587918693338D-06 6.003371579626D-07 8 1.916686027968D-07 1.615498260138D-08 -1.693306893859D-08 E-Index: 6 7 8 T-Index: 0 -4.698314268303D-04 4.502855041540D-05 -1.724119064743D-06 1 -4.081552915490D-04 7.523889576611D-05 -3.020854867113D-06 2 1.755019472132D-04 -3.622077917093D-05 1.578825987882D-06 3 8.820311155289D-05 -1.096383895966D-05 4.077966484815D-07 4 -4.325767085415D-05 7.303630284565D-06 -3.055052941782D-07 5 3.995980258215D-06 -1.053387214627D-06 4.789068581038D-08 6 4.989305627062D-07 4.799823908148D-09 -9.771077724410D-10 7 -1.009348152873D-07 8.912440158402D-09 -3.117095091366D-10 8 4.438767986041D-09 -4.806081198001D-10 1.835893653264D-11 Max. rel. Error: 13.4603 % Mean rel. Error: 0.9308 % \end{verbatim}\end{small} \newpage This page is intentionally left blank \newpage \subsection{ Reaction 3.3.6a $ p + He^*(1s^12s^11S) \rightarrow H^*(2s) + He^+(1s) $ } Proton energy weighted charge exchange rate coefficient, protons with first meta-stable He*, $E_{th} \approx 0.57$ eV. Corresponding (un-weighted) rate coefficient is given here in an earlier section and in HYHEL with same sub-section number. \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.397668404788D+01 3.159485036283D-01 1.251349908668D-01 1 3.791127359443D+00 -3.761884787063D-01 -1.201611289430D-01 2 -3.031005464839D-01 1.547966958268D-01 3.418807730147D-02 3 -2.042285843152D-02 -1.849518757027D-02 -2.705500175969D-03 4 9.317257534521D-03 -3.497722978839D-03 5.266899471936D-04 5 -4.841929631711D-04 1.244615194159D-03 -3.264196261141D-04 6 -9.483126811734D-05 -1.399032118750D-04 6.356897513547D-05 7 1.241207591818D-05 6.987980280667D-06 -4.975196671014D-06 8 -4.191666003951D-07 -1.299861951387D-07 1.392550743313D-07 E-Index: 3 4 5 T-Index: 0 3.856067365269D-02 -2.026573130919D-03 -2.759136201694D-03 1 -6.229570032866D-03 7.539673693629D-03 3.228125296776D-05 2 -1.117399758747D-02 -3.402440317662D-03 1.301470355832D-03 3 4.346233632875D-03 2.577875598472D-04 -4.359935280851D-04 4 -6.346015739054D-04 1.053315422043D-04 3.920000120015D-05 5 6.551645356748D-05 -2.376485094163D-05 1.685178990397D-06 6 -8.200597026708D-06 1.844480677683D-06 -3.712741557353D-07 7 7.170567793961D-07 -5.326280408650D-08 9.229946485903D-09 8 -2.381772742595D-08 2.014368954375D-10 2.686050437848D-10 E-Index: 6 7 8 T-Index: 0 5.281724050161D-04 -3.697200097287D-05 9.237548925974D-07 1 -2.159762940362D-04 2.275443392926D-05 -7.099802232376D-07 2 -1.482835634810D-04 6.952989686416D-06 -1.085642522433D-07 3 7.949763771555D-05 -5.715813906994D-06 1.481611026493D-07 4 -1.214272931648D-05 1.128632380175D-06 -3.510270530142D-08 5 5.986765602098D-07 -9.526271005415D-08 3.781185514127D-09 6 4.147212027299D-09 4.109065328207D-09 -2.316799675035D-10 7 -6.505709803163D-11 -1.612579446392D-10 9.811627985408D-12 8 -4.990895417628D-11 5.743415083193D-12 -2.467665429406D-13 Max. rel. Error: 6.2499 % Mean rel. Error: 0.8870 % \end{verbatim}\end{small} \newpage This page is intentionally left blank \newpage \subsection{ Reaction 3.3.6b $ p + He^*(1s^12s^13S) \rightarrow H^*(2s) + He^+(1s)$ } Proton energy weighted charge exchange rate coefficient, protons with second meta-stable He*, $E_{th} \approx 1.37$ eV. Corresponding (un-weighted) rate coefficient is given here in an earlier section and in HYHEL with same sub-section number. \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.956696212252D+01 5.281567610030D-01 1.525645856454D-01 1 5.608996254071D+00 -5.554651091960D-01 -8.310107491980D-02 2 -5.586148730643D-01 2.869596240969D-01 2.693533782880D-02 3 8.445222522903D-02 -9.885450333344D-02 -2.375836603441D-02 4 -4.080969150629D-02 2.380017857884D-02 1.216452673035D-02 5 1.109225928721D-02 -3.788861207335D-03 -2.898997798061D-03 6 -1.454903843517D-03 3.686204124267D-04 3.488800425650D-04 7 9.246654975855D-05 -1.956645015230D-05 -2.070012209875D-05 8 -2.304179941047D-06 4.310780137920D-07 4.810780135493D-07 E-Index: 3 4 5 T-Index: 0 5.501159994270D-02 5.231877282834D-03 -5.104807314720D-03 1 -3.503708291156D-02 -6.194296661419D-03 8.545246673022D-03 2 -2.619680827152D-02 9.409111065614D-03 -3.292720454900D-03 3 3.066491792837D-02 -6.421108100188D-03 1.185509375312D-04 4 -1.125547411729D-02 2.175569508209D-03 9.073341073380D-05 5 2.024041838757D-03 -4.121003738472D-04 7.128259787760D-06 6 -1.907412735028D-04 4.489456337277D-05 -6.215149457584D-06 7 8.849836285624D-06 -2.639451182160D-06 7.576420403373D-07 8 -1.534752844870D-07 6.492509343847D-08 -2.852852143477D-08 E-Index: 6 7 8 T-Index: 0 6.537231707620D-04 -2.747946210980D-05 1.809150198692D-07 1 -1.763283177626D-03 1.440173210330D-04 -4.252159818280D-06 2 6.322499969920D-04 -5.569656379195D-05 1.811409365339D-06 3 9.910404393999D-05 -1.096951926860D-05 3.556184138250D-07 4 -7.195067291013D-05 7.772807797383D-06 -2.677198674596D-07 5 8.134485110505D-06 -1.024492516657D-06 3.813168247354D-08 6 4.630863375819D-07 -1.150736736272D-08 -2.200040624310D-10 7 -1.265796349526D-07 9.977170726720D-09 -2.923241327427D-10 8 5.638328877632D-09 -4.845499350959D-10 1.514129155630D-11 Max. rel. Error: 6.1811 % Mean rel. Error: 0.6136 % \end{verbatim}\end{small} \newpage This page is intentionally left blank \newpage \section{H.10 :Fits for $\langle\sigma \cdot v \cdot E_p \rangle (n_p,T_p) \ [cm^3/s \cdot eV]$} $E_p$ is either the kinetic energy (or the energy loss per event) of the impacting electron or ion, in eV, or the energy loss (energy cost), associated with a process or set of processes. In the latter case these energy-weighted rate coefficients are obtained from collisional radiative modelling. \newpage This page is intentionally left blank \newpage \subsection{ Reaction 2.1.5JH $ e + H \rightarrow H^+ + 2e $ } Electron energy loss weighted rate coefficient. Total: radiation plus potential energy cost. Data: Johnson, \cite{kn:Mahn} \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.508124023824D+01 1.734108135759D-02 -1.891777149512D-02 1 9.961634412423D+00 -1.573307884566D-02 1.843734255418D-02 2 -4.776180166264D+00 2.970917601727D-04 -3.807758859655D-03 3 1.630713043514D+00 3.457819922651D-03 -1.182846239993D-03 4 -3.862246458538D-01 -1.354707016609D-03 5.758335877954D-04 5 5.908348117252D-02 2.467671779140D-04 -9.707776439937D-05 6 -5.502149035570D-03 -2.550039601080D-05 9.186912710069D-06 7 2.825693139758D-04 1.479374192570D-06 -5.357992990165D-07 8 -6.126373636033D-06 -3.768914931663D-08 1.516539648383D-08 E-Index: 3 4 5 T-Index: 0 7.823415079914D-03 -1.631549805821D-03 1.886435723148D-04 1 -7.526506973636D-03 1.445482212534D-03 -1.430089553311D-04 2 2.108820285359D-03 -4.156648351099D-04 3.407098816806D-05 3 -1.066332982000D-05 2.942499095980D-05 -8.976235585729D-07 4 -6.053903755468D-05 -4.227285712967D-07 -2.352473868493D-09 5 7.784473195273D-06 7.205874145075D-07 -9.883252326876D-08 6 -5.442048934307D-07 -8.990161485463D-08 8.933475010389D-09 7 4.797758886682D-08 -1.637030558354D-09 5.735798106880D-10 8 -2.404105327023D-09 3.753206693445D-10 -6.002003170733D-11 E-Index: 6 7 8 T-Index: 0 -1.224700235983D-05 4.170427242828D-07 -5.775556894342D-09 1 7.221376553657D-06 -1.633748217561D-07 1.028215793306D-09 2 -8.300185166679D-07 -2.671730459566D-08 1.140062425575D-09 3 -3.006283377398D-07 2.400198464058D-08 -4.901297252541D-10 4 4.544140153285D-08 -2.854579885273D-09 3.868612101415D-11 5 2.577124843878D-09 -1.007675407273D-10 6.215200297376D-12 6 -1.937960153333D-10 1.664413123118D-11 -9.521242149750D-13 7 -6.978042599136D-11 1.836020981290D-12 1.884922171479D-14 8 5.011156979547D-12 -1.641995819473D-13 1.257296690473D-15 Max. rel. Error: .4678 % Mean rel. Error: .2498 % \end{verbatim}\end{small} \begin{figure} \label{2.1.5i} \epsfxsize=16truecm \epsffile{Amjuel_PS/hydli1_tr.ps} \end{figure} \newpage \subsection{ Reaction 2.1.5 $ e + H \rightarrow H^+ + 2e $ } Electron energy loss weighted rate coefficient. Data: Sawada/Fujimoto, \cite{kn:Sawada} (redone May 2016: extend Te range of fit validity from 0.1 -- 1e3 now to 0.1 -- 2e4 eV) \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.497580168306D+01 1.081653961822D-03 -7.358936044605D-04 1 1.004448839974D+01 -3.189474633369D-03 2.510128351932D-03 2 -4.867952931298D+00 -5.852267850690D-03 2.867458651322D-03 3 1.689422238067D+00 7.744372210287D-03 -3.087364236497D-03 4 -4.103532320100D-01 -3.622291213236D-03 1.327415215304D-03 5 6.469718387357D-02 8.268567898126D-04 -2.830939623802D-04 6 -6.215861314764D-03 -9.836595524255D-05 3.017296919092D-05 7 3.289809895460D-04 5.845697922558D-06 -1.479323780613D-06 8 -7.335808238917D-06 -1.367574486885D-07 2.423236476442D-08 E-Index: 3 4 5 T-Index: 0 4.122398646951D-04 -1.408153300988D-04 2.469730836220D-05 1 -7.707040988954D-04 1.031309578578D-04 -3.716939423005D-06 2 -8.328668093987D-04 2.056134355492D-04 -3.301570807523D-05 3 4.707676288420D-04 -5.508611815406D-05 7.305867762241D-06 4 -1.424078519508D-04 3.307339563081D-06 5.256679519499D-09 5 2.411848024960D-05 5.707984861100D-07 -1.016945693300D-07 6 -1.474253805845D-06 -2.397868837417D-07 1.518743025531D-08 7 -4.633029022577D-08 3.337390374041D-08 -1.770252084837D-09 8 5.733871119707D-09 -1.512777532459D-09 8.733801272834D-11 E-Index: 6 7 8 T-Index: 0 -2.212823709798D-06 9.648139704737D-08 -1.611904413846D-09 1 -4.249704742353D-07 4.164960852522D-08 -9.893423877739D-10 2 2.831739755462D-06 -1.164969298033D-07 1.785440278790D-09 3 -6.000115718138D-07 2.045211951761D-08 -1.790312871690D-10 4 7.597020291557D-10 1.799505288362D-09 -9.280890205774D-11 5 3.517154874443D-09 -4.453195673947D-10 2.002478264932D-11 6 4.149084521319D-10 -6.803200444549D-12 -1.151855939531D-12 7 -5.289806153651D-11 3.864394776250D-12 -8.694978774411D-15 8 7.196798841269D-13 -1.441033650378D-13 1.734769090475D-15 T1MIN = 0.10000D 00 EV T1MAX = 2.00000D 04 EV N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 0.922E+00 % Mean rel. Error: 0.471E+00 % \end{verbatim}\end{small} \begin{figure} \label{2.1.5iFU} \epsfxsize=16truecm \epsffile{Amjuel_PS/H10-2.1.5.eps} \end{figure} \newpage \subsection{ Reaction 2.1.5o $ e + H \rightarrow H^+ + 2e $ Ly-opaque} Ditto, all Lyman lines (and continuum) opaque \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.431395592098D+01 -2.395941007384D-01 2.591565194903D-01 1 1.113429718187D+01 1.849722545279D-01 -2.423728103974D-01 2 -6.654446687338D+00 2.195366491981D-02 6.179888393756D-02 3 2.747075059275D+00 -6.901300857989D-02 1.006521130909D-02 4 -7.372137934626D-01 2.943069908340D-02 -7.829953302392D-03 5 1.227074461193D-01 -6.057176837025D-03 1.694081601397D-03 6 -1.216484938923D-02 6.701189895777D-04 -1.793079853259D-04 7 6.566484532457D-04 -3.779995638455D-05 8.950721046575D-06 8 -1.483802107723D-05 8.441118380444D-07 -1.530047985372D-07 E-Index: 3 4 5 T-Index: 0 -1.087825788137D-01 2.304158174814D-02 -2.708007727528D-03 1 9.801393644159D-02 -1.946235514182D-02 2.079309382971D-03 2 -2.979923286006D-02 5.913142010781D-03 -5.549143094821D-04 3 1.702193123225D-03 -6.298136767386D-04 4.093195127037D-05 4 6.752425702279D-04 2.856788083851D-05 -7.732295592583D-07 5 -1.621646872661D-04 -2.526799196487D-06 2.543500809367D-07 6 1.506237912301D-05 4.384573257407D-07 -1.137888186554D-08 7 -4.568263582843D-07 -5.697388918232D-08 -1.072747527249D-09 8 -6.560997301392D-09 3.141908302488D-09 3.111434993423D-12 E-Index: 6 7 8 T-Index: 0 1.777247119352D-04 -6.080187141189D-06 8.438023009891D-08 1 -1.231134698172D-04 3.827948966411D-06 -4.895455818239D-08 2 2.684044174965D-05 -6.633266274667D-07 6.895128780616D-09 3 -4.598542858756D-09 -5.542757391998D-08 9.032937294372D-10 4 -3.124180764582D-07 1.188861911457D-08 1.649196327692D-11 5 1.826904076362D-08 4.273639168838D-10 -5.875558984747D-11 6 -4.163110915594D-09 3.345977887826D-11 5.495071058936D-12 7 6.106046869680D-10 -2.063138694762D-11 -9.709542597057D-16 8 -2.241669215814D-11 9.998773490453D-13 -9.539526341658D-15 Max. rel. Error: 2.4939 % Mean rel. Error: .6828 % \end{verbatim}\end{small} \begin{figure} \label{2.1.5io} \epsfxsize=16truecm \epsffile{Amjuel_PS/hydli1_op.ps} \end{figure} \newpage \subsection{ Reaction 2.1.8 $H^+ + e \rightarrow H(1s) $ } effective electron cooling rate due to rad.+three-b. recombination potential energy loss 13.6*(eff-rec.rate) still needs to be subtracted (may render the loss negative, i.e., turn it into a gain) Hence: the quantitity given here happens to be the radiation loss. June17: Fit range extended from 0.1--1e3 to 0.1--2e4 \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.592450349909D+01 1.222097271874D-02 4.278499401907D-05 1 -7.290670236493D-01 -1.540323930666D-02 -3.406093779190D-03 2 2.363925869096D-02 1.164453346305D-02 -5.845209334594D-03 3 3.645333930947D-03 -1.005820792983D-03 6.956352274249D-04 4 1.594184648757D-03 -1.582238007548D-05 4.073695619272D-04 5 -1.216668033378D-03 -3.503070140126D-04 1.043500296633D-04 6 2.376115895241D-04 1.172709777146D-04 -6.695182045674D-05 7 -1.930977636766D-05 -1.318401491304D-05 8.848025453481D-06 8 5.599257775146D-07 4.977823319311D-07 -3.615013823092D-07 E-Index: 3 4 5 T-Index: 0 1.943967743593D-03 -7.123474602102D-04 1.303523395892D-04 1 1.532243431817D-03 -4.658423772784D-04 5.972448753445D-05 2 2.854145868307D-03 -5.077485291132D-04 4.211106637742D-05 3 -9.305056373739D-04 2.584896294384D-04 -3.294643898894D-05 4 -9.379169243859D-05 1.490890502214D-06 2.245292872209D-06 5 9.536162767321D-06 -6.908681884097D-06 8.232019008169D-07 6 1.188184006210D-05 -4.381514364966D-07 -6.936267173079D-08 7 -2.072370711390D-06 2.055919993599D-07 -7.489632654212D-09 8 9.466989306497D-08 -1.146485227699D-08 6.772338917155D-10 E-Index: 6 7 8 T-Index: 0 -1.186560752561D-05 5.334455630031D-07 -9.349857887253D-09 1 -4.070843294052D-06 1.378709880644D-07 -1.818079729166D-09 2 -1.251436618314D-06 -1.626555745259D-08 1.073458810743D-09 3 2.112924018518D-06 -6.544682842175D-08 7.810293075700D-10 4 -3.150901014513D-07 1.631965635818D-08 -2.984093025695D-10 5 -2.905331051259D-08 -3.169038517749D-10 2.442765766167D-11 6 6.592249255001D-09 -1.778887958831D-10 1.160762106747D-12 7 -7.073797030749D-11 1.047087505147D-11 -1.877446271350D-13 8 -1.776496344763D-11 7.199195061382D-14 3.929300283002D-15 T1MIN = 0.10000D 00 EV T1MAX = 2.00000D 04 EV N2MIN = 1.00000D 08 1/CM3 N2MAX = 1.00000D 16 1/CM3 Max. rel. Error: 0.930E+01 % Mean rel. Error: 0.127E+01 % \end{verbatim}\end{small} \begin{figure} \label{2.1.8r} \epsfxsize=16truecm \epsffile{Amjuel_PS/H10-2.1.8.eps} \end{figure} \newpage \subsection{ Reaction 2.1.8o $H^+ + e \rightarrow H(1s) $ Ly-opaque } effective electron cooling rate due to rad.+three-b. recombination potential energy loss 13.6*(eff-rec.rate) still needs to be subtracted (may render the loss negative, i.e., turn it into a gain) Hence: the quantity given here happens to be the radiation loss. \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.626461971500D+01 -1.141522828006D-01 1.076393602102D-01 1 -8.898849653304D-02 -3.942292858703D-01 4.197250110873D-01 2 -4.795279065913D-01 -1.335489318623D-01 1.698162748512D-01 3 -6.457641001473D-02 4.613800494941D-02 -6.378456442460D-02 4 6.800392305050D-02 2.637589098726D-02 -2.927766641228D-02 5 -7.780596827160D-03 -1.696354616404D-03 4.101919602398D-03 6 -9.252420142124D-04 -2.153234057341D-03 1.724087525894D-03 7 2.115742192807D-04 3.847511359996D-04 -3.531396348434D-04 8 -9.909336050813D-06 -1.829769520002D-05 1.745121101762D-05 E-Index: 3 4 5 T-Index: 0 -3.951176865624D-02 7.434448907130D-03 -7.651735363726D-04 1 -1.819873891755D-01 3.954265794034D-02 -4.746673604459D-03 2 -7.777618558640D-02 1.791770402443D-02 -2.265419802670D-03 3 3.368756666920D-02 -8.588159967647D-03 1.161221464744D-03 4 1.215210455092D-02 -2.536449841814D-03 2.949052179931D-04 5 -2.853313172787D-03 8.331295381374D-04 -1.219354343653D-04 6 -3.889280715498D-04 1.445906496031D-05 5.400239087927D-06 7 1.117507761644D-04 -1.626382515941D-05 1.138105849294D-06 8 -5.935692251130D-06 9.750922276399D-07 -8.514634639125D-08 E-Index: 6 7 8 T-Index: 0 4.256550578560D-05 -1.183957210565D-06 1.267430439071D-08 1 3.160257175597D-04 -1.090132407225D-05 1.518762884136D-07 2 1.597834560300D-04 -5.867107114568D-06 8.703048627852D-08 3 -8.476482397035D-05 3.148378986370D-06 -4.661383263216D-08 4 -1.945865547958D-05 6.794359168371D-07 -9.714166652574D-09 5 9.388539733773D-06 -3.625759741848D-07 5.530677587059D-09 6 -7.463824586159D-07 3.657036916983D-08 -6.329837178101D-10 7 -3.277550512167D-08 -2.762994890889D-11 1.306756395427D-11 8 4.007910080852D-09 -9.447800370353D-11 8.488148236190D-13 Max. rel. Error: 26.2822 % Mean rel. Error: 8.6945 % \end{verbatim}\end{small} \begin{figure} \label{2.1.8ro} \epsfxsize=16truecm \epsffile{Amjuel_PS/hydlr1_op.ps} \end{figure} \newpage \subsection{ Reaction 2.2.h2c $H_2 + e \rightarrow ....$ } effective electron cooling rate due to destruction of H2 molecules by processes 2.2.5 or 2.2.9, i.e. by dissociation or ionisation. $\Delta E_d = 9.94$, $\Delta E_i = 15.386$ \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.511426358838D+01 -1.502968736502D-03 2.270301997818D-03 1 1.039650366780D+01 1.940526565095D-03 -2.039057105217D-03 2 -5.056418866002D+00 4.267610495700D-04 -1.570825376355D-03 3 1.698357023335D+00 -1.100217175513D-03 1.346702996596D-03 4 -3.946794266607D-01 8.530611978697D-04 -5.956794001881D-04 5 6.332951863565D-02 -3.363804010733D-04 1.935332922569D-04 6 -7.076439854566D-03 6.801240259521D-05 -3.813794805193D-05 7 5.117651399462D-04 -6.744466929271D-06 3.834955698487D-06 8 -1.768573967186D-05 2.610531177384D-07 -1.508866204608D-07 E-Index: 3 4 5 T-Index: 0 -1.160949145671D-03 2.711890444924D-04 -3.316751545455D-05 1 8.471089743180D-04 -1.668780150866D-04 1.846170371568D-05 2 1.011062331716D-03 -2.493635375898D-04 3.107778205672D-05 3 -6.015963727342D-04 1.254388145616D-04 -1.431788137516D-05 4 1.440206127855D-04 -1.821423270769D-05 1.364766339804D-06 5 -3.053105755056D-05 1.434719315650D-06 1.264447977870D-07 6 6.171515920637D-06 -4.045829346605D-07 -5.237650672670D-09 7 -7.117247208887D-07 7.283932745297D-08 -3.875678618801D-09 8 3.137300758374D-08 -3.990100914364D-09 3.015422105813D-10 E-Index: 6 7 8 T-Index: 0 2.179799509766D-06 -7.292508854487D-08 9.764136720820D-10 1 -1.200391601516D-06 4.255709533045D-08 -6.263044644580D-10 2 -2.068798871142D-06 7.024008304152D-08 -9.571647703521D-10 3 9.254739688370D-07 -3.161858685796D-08 4.410801074405D-10 4 -7.044718093836D-08 2.445238251993D-09 -3.975970296405D-11 5 -1.650023620224D-08 6.035147397334D-10 -6.735406816093D-12 6 2.105913693789D-09 -9.389056833568D-11 1.197541371030D-12 7 6.547129244936D-11 1.340983691609D-12 -3.151269189538D-14 8 -1.176278308629D-11 2.089055860523D-13 -1.505656589693D-15 Max. rel. Error: 3.4722 % Mean rel. Error: 1.4166 % \end{verbatim}\end{small} \begin{figure} \label{2.2.h2c} \epsfxsize=16truecm \epsffile{Amjuel_PS/H2-coolrate-225+229.eps} \end{figure} \newpage \subsection{ Reaction 2.2.h2r $H_2 + e \rightarrow ....$ } effective electron radiation energy loss rate due to destruction of H2 molecules by processes 2.2.5 or 2.2.9, i.e. by dissociation or ionisation \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.801822188516D+01 -2.680763935218D-02 4.076970248467D-02 1 1.226559489761D+01 -1.963731382190D-01 1.282479989566D-01 2 -5.867759617478D+00 8.536319354128D-02 -3.568022393739D-02 3 1.891664482986D+00 1.471792937991D-01 -9.271446717483D-02 4 -4.033980053975D-01 -1.394921763886D-01 7.381914918665D-02 5 5.439662377414D-02 4.818384180161D-02 -2.188105491841D-02 6 -4.642268879563D-03 -8.093950922937D-03 2.987412465436D-03 7 2.626009837514D-04 6.623097639192D-04 -1.742669318441D-04 8 -8.606720377928D-06 -2.105277432641D-05 2.632539922731D-06 E-Index: 3 4 5 T-Index: 0 -2.299699721311D-02 5.853248550552D-03 -7.648533513094D-04 1 -3.150018219862D-02 3.847305623421D-03 -2.332949388707D-04 2 4.210762118334D-03 -7.901166941528D-05 -2.122748674317D-05 3 2.257794051374D-02 -2.486055370273D-03 1.021925655299D-04 4 -1.526303663894D-02 1.475511672936D-03 -5.499022366195D-05 5 3.689194332467D-03 -2.674426267836D-04 4.688389683681D-06 6 -3.073444697161D-04 -7.067430960799D-06 3.032281232409D-06 7 -7.581041097732D-06 6.310703738513D-06 -7.164508757577D-07 8 1.619250275583D-06 -4.490216679338D-07 4.418606553487D-08 E-Index: 6 7 8 T-Index: 0 5.258892572564D-05 -1.807126279032D-06 2.441424496287D-08 1 5.066091926016D-06 9.700999841682D-08 -4.515881112268D-09 2 2.343578854939D-06 -1.149634211274D-07 2.218794688735D-09 3 2.171207268498D-06 -2.959885648343D-07 6.448680553698D-09 4 -1.169850372738D-06 1.491856181978D-07 -3.172311462398D-09 5 4.636734103570D-07 -2.759830094699D-08 4.590631115748D-10 6 -1.829914413027D-07 3.868936732678D-09 -1.492736071699D-11 7 3.248465119283D-08 -5.180769016510D-10 -6.701126858615D-13 8 -1.932812965191D-09 3.208399835617D-11 -1.703503159464D-14 Max. rel. Error: 9.7237 % Mean rel. Error: 2.8617 % \end{verbatim}\end{small} \begin{figure} \label{2.2.h2r} \epsfxsize=16truecm \epsffile{Amjuel_PS/H2-radrate-225+229.eps} \end{figure} \newpage \subsection{ Reaction 2.3.9a $e + He(1s^21S) \rightarrow He^+(1s) + 2e$ } Eth=24.588 eV effective electron cooling rate due to ionization of Helium atoms. Fujimoto Formulation II (only ground level transported, no meta-stables kept explicit), \cite{kn:Fujimoto}. \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.535258393674D+01 -3.428249311738D-02 6.378071832382D-02 1 1.981855871044D+01 4.854482688892D-02 -5.088928946831D-02 2 -9.334355651224D+00 -4.524206463148D-02 2.103002869692D-02 3 2.800314250410D+00 2.474350787980D-02 -6.012991773715D-03 4 -5.489088598705D-01 -7.339538872774D-03 7.783071302508D-04 5 6.902095610357D-02 1.234159378604D-03 2.989745411104D-05 6 -5.342940069130D-03 -1.223169549107D-04 -1.500790305823D-05 7 2.313175089975D-04 6.966436907981D-06 8.944962909810D-07 8 -4.279800193256D-06 -1.815466669910D-07 -2.282174576618D-09 E-Index: 3 4 5 T-Index: 0 -2.849818870377D-02 6.041903480645D-03 -6.864532165560D-04 1 1.732110218818D-02 -2.781419068092D-03 2.244804771683D-04 2 -4.463941003028D-03 2.900917070658D-04 2.482449118881D-05 3 8.918009845745D-04 -2.616249899141D-05 -6.885545577757D-06 4 -4.483274558979D-05 1.900991581685D-06 -9.747171692727D-07 5 -3.040906203340D-05 2.951386149372D-06 7.592185107575D-08 6 5.253922160283D-06 -4.468905893926D-07 7.483496971361D-09 7 -1.712024596447D-07 -9.782015167261D-09 2.499416349949D-09 8 -6.972920569943D-09 2.607191494540D-09 -2.870919514967D-10 E-Index: 6 7 8 T-Index: 0 4.251155616815D-05 -1.351759350582D-06 1.728801977101D-08 1 -8.875290574348D-06 1.399429819761D-07 -1.389778740510D-10 2 -4.278064413224D-06 2.040570181783D-07 -3.324224092217D-09 3 7.013616309712D-07 -2.570063437935D-08 3.573487194914D-10 4 1.349829568374D-07 -5.815812094637D-09 6.686532777575D-11 5 -1.805060230413D-08 3.156859219121D-10 1.071168697340D-11 6 -9.777558713428D-10 1.770619394125D-10 -6.050995244427D-12 7 4.731973382221D-11 -1.845161957843D-11 6.011070143230D-13 8 8.059675146168D-12 3.704316808942D-13 -1.713225271579D-14 Max. rel. Error: 1.8148 % Mean rel. Error: .1839 % \end{verbatim}\end{small} \begin{figure} \label{2.3.9aer} \epsfxsize=16truecm \epsffile{Amjuel_PS/heliaecr.ps} \end{figure} \newpage \subsection{ Reaction 2.3.13a $e+ He^+(1s) \rightarrow He(1s^21S)$ } Helium multi-step model, here recombination: radiative + threebody + dielectronic Fujimoto Formulation II (only ground level transported, no meta-stables kept explicit), \cite{kn:Fujimoto}. The quantity given here happens to be the radiation loss. The loss of potential energy still needs to be subtracted to make this a total electron energy loss (or gain) rate. \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.538377692766D+01 -4.826880987619D-02 6.796575967310D-02 1 2.472758419513D+00 1.668058989207D-01 -1.265192781981D-01 2 -8.864417999957D+00 -1.882326730037D-01 1.194028674310D-01 3 8.394970578944D+00 8.397993216045D-02 -5.796972813740D-02 4 -3.465864794112D+00 -1.572684180220D-02 1.398192327776D-02 5 7.479071085372D-01 5.997666028811D-04 -1.614053457119D-03 6 -8.863575102304D-02 1.901540166344D-04 6.941090299375D-05 7 5.484926807853D-03 -2.510359436743D-05 1.123735445147D-06 8 -1.388441945179D-04 9.141995596700D-07 -1.168915890330D-07 E-Index: 3 4 5 T-Index: 0 -2.401710021390D-02 4.130156138736D-03 -3.494803122018D-04 1 2.938171777028D-02 -2.216525055070D-03 -1.261523686946D-04 2 -2.382836629119D-02 1.134820469638D-03 1.782113978272D-04 3 1.158600348753D-02 -7.504743150582D-04 -2.602911694939D-05 4 -2.700181027443D-03 1.902304157269D-04 -1.534387905925D-06 5 2.620866439317D-04 -1.103039382799D-05 -4.215447554819D-07 6 -3.042043168371D-06 -1.677907209787D-06 2.153652742395D-07 7 -9.198494797723D-07 2.058851315121D-07 -1.866416375894D-08 8 3.485370731777D-08 -5.086412415216D-09 3.674153797642D-10 E-Index: 6 7 8 T-Index: 0 1.345025100540D-05 -1.323917127568D-07 -2.551716207606D-09 1 2.701401918133D-05 -1.370446267883D-06 2.313673787201D-08 2 -2.305554399898D-05 9.430294093180D-07 -1.305188423829D-08 3 4.568209602293D-06 -1.458110560501D-07 9.826599911934D-10 4 -1.032060079260D-07 -1.355858638619D-08 5.917279771473D-10 5 -9.926133276192D-09 4.148813674084D-09 -1.207867670158D-10 6 -6.354480058307D-09 -1.223103792568D-10 5.543057946730D-12 7 7.564835556537D-10 -1.622993472948D-11 2.428986170198D-13 8 -1.621809988343D-11 6.737654534264D-13 -1.678705755876D-14 Max. rel. Error: 22.6665 % Mean rel. Error: 8.4662 % \end{verbatim}\end{small} \begin{figure} \label{2.3.13aer} \epsfxsize=16truecm \epsffile{Amjuel_PS/helraecr.ps} \end{figure} \newpage \subsection{ Reaction 2.6A0 $e + C \rightarrow C^+ + 2e $ } electron cooling rate due to ionization of C atoms [eV * cm**3/s] ADAS 93 \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -1.541340319198D+01 -4.635323668693D+00 1.424306255525D+00 1 6.871565603800D+00 3.062312115608D-02 1.785653882692D-02 2 -2.581732757825D+00 -1.272125958091D-01 3.493561583728D-02 3 4.800945236897D-01 9.573076930006D-02 -2.511071760242D-02 4 -3.221877058224D-02 -1.391798645331D-02 2.175585061019D-03 5 -8.242753615795D-03 1.145594247121D-03 3.885428995621D-05 6 2.099340312561D-03 -1.276880024615D-04 -4.884605861642D-06 7 -1.795437092836D-04 1.389068259360D-05 -1.113237444693D-06 8 5.520442022231D-06 -6.375114106630D-07 9.859364572176D-08 E-Index: 3 4 5 T-Index: 0 -2.158652670331D-01 1.412329738807D-02 1.168676999154D-04 1 -1.094056812899D-02 3.136700005660D-03 -3.963442307288D-04 2 -5.370773139210D-03 2.974489768572D-04 -1.432652388384D-05 3 3.687719429910D-03 -2.848608239928D-04 1.690331087319D-05 4 -1.746771988767D-04 -3.294582308635D-06 8.485083720382D-07 5 -1.528532398519D-05 1.555056417236D-06 -5.074853324543D-08 6 6.205604777862D-08 1.558979315126D-07 -1.140737345155D-08 7 1.652357272442D-07 -1.003365245229D-08 -1.633709577156D-09 8 -1.163642679910D-08 2.003281042296D-10 1.350639090685D-10 E-Index: 6 7 8 T-Index: 0 -6.658345040546D-05 3.254244791032D-06 -5.053767538668D-08 1 2.266757015103D-05 -5.406980202349D-07 3.681457471642D-09 2 1.906448581780D-06 -9.658075171996D-08 7.628999658428D-10 3 -6.509994237871D-07 -1.483571537540D-08 1.479901251703D-09 4 -1.063260940363D-07 1.336948585246D-08 -5.357328879289D-10 5 2.810998774881D-09 -8.868420910603D-10 4.953950208308D-11 6 9.322775355772D-10 -5.119114288255D-11 -2.546806508137D-13 7 1.240247466159D-10 1.352672081064D-12 -1.036766300560D-13 8 -1.122860695875D-11 2.002505887771D-13 1.458669917591D-15 Max. rel. Error: 9.7643 % Mean rel. Error: 3.1877 % \end{verbatim}\end{small} \begin{figure} \label{2.6il} \epsfxsize=16truecm \epsffile{Amjuel_PS/carbil.ps} \end{figure} \newpage \subsection{ Reaction 2.7A0 $e + N \rightarrow N^+ + 2e $ } electron cooling rate due to ionization of N atoms [eV * cm**3/s] ADAS 96 \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.253812547614D+01 -6.608569288276D-01 1.150452384879D-01 1 5.432527437912D+00 1.539439865129D+00 -1.576693820511D-01 2 -2.952608997109D-01 -1.412585437109D+00 4.638775789522D-02 3 -8.226013960740D-01 6.717054943053D-01 2.187384074057D-02 4 3.729388695172D-01 -1.832836584927D-01 -1.722342009795D-02 5 -7.841898395520D-02 2.976002632760D-02 4.564235143138D-03 6 8.985696288257D-03 -2.839310501238D-03 -6.044432608775D-04 7 -5.395985855412D-04 1.468399332248D-04 4.023312734034D-05 8 1.328834197911D-05 -3.174449965134D-06 -1.072687574774D-06 E-Index: 3 4 5 T-Index: 0 -1.065634043574D-02 9.532285913431D-04 -1.346476910993D-04 1 5.813528015171D-03 -1.646122278862D-03 3.939136003165D-04 2 1.251511770456D-02 1.934102369820D-04 -2.591298980417D-04 3 -1.391948893870D-02 6.061371309834D-04 4.715854993637D-05 4 5.665942301636D-03 -2.864541076848D-04 -2.009919110756D-06 5 -1.191674192800D-03 5.671367249642D-05 1.560417026937D-07 6 1.394992142385D-04 -6.170732864889D-06 -5.745521323400D-08 7 -8.635747882439D-06 3.695648390668D-07 5.028838822894D-09 8 2.207714212398D-07 -9.661992346983D-09 -1.002410123923D-10 E-Index: 6 7 8 T-Index: 0 1.499025275503D-05 -8.381690183270D-07 1.754250184956D-08 1 -4.099253727990D-05 2.056031618879D-06 -4.072262920583D-08 2 2.795198852134D-05 -1.439391948855D-06 3.065144075600D-08 3 -5.768287114529D-06 3.294456589515D-07 -8.730420469452D-09 4 3.415790996484D-07 -2.777746715732D-08 1.367779235643D-09 5 1.791473635965D-09 7.602227311451D-10 -1.668997333521D-10 6 9.035743229573D-10 -4.011075190405D-11 1.670019578529D-11 7 -1.822072807905D-10 6.518277639583D-12 -1.040108515933D-12 8 4.463372771101D-12 -1.949905209490D-13 2.634684643675D-14 Max. rel. Error: 5.8662 % Mean rel. Error: 1.3550 % \end{verbatim}\end{small} \begin{figure} \label{2.7il} \epsfxsize=16truecm \epsffile{Amjuel_PS/nitil-erate.eps} \end{figure} \newpage \subsection{ Reaction 2.8A0 $e + O \rightarrow O^+ + 2e $ } electron cooling rate due to ionization of O atoms [eV * cm**3/s] ADAS 96 \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.445741605915D+01 -7.558170805452D-01 6.462171267483D-02 1 5.492606381344D+00 1.669520214597D+00 -1.021865903908D-01 2 9.943826013037D-01 -1.499918897355D+00 6.087399488466D-02 3 -1.654552652454D+00 7.182604764825D-01 -1.614322696382D-02 4 6.113756777865D-01 -2.013060379640D-01 1.632283021337D-03 5 -1.156778163561D-01 3.398915754215D-02 8.787006821195D-05 6 1.226872019465D-02 -3.396064383950D-03 -3.540766244850D-05 7 -6.927024005103D-04 1.846756585347D-04 3.021508483124D-06 8 1.622250023780D-05 -4.207838369666D-06 -8.903799103489D-08 E-Index: 3 4 5 T-Index: 0 1.750162767171D-02 -7.322414636615D-03 1.347646519764D-03 1 -2.873370694294D-02 8.462882768193D-03 -1.412980882660D-03 2 1.848835552799D-02 -2.365388843634D-03 2.826588118171D-04 3 -8.427594128571D-03 1.652841141310D-04 5.183935809798D-05 4 2.680245268321D-03 -2.704851290479D-05 -2.072676809016D-05 5 -5.202897127637D-04 1.692837429290D-05 1.540185566308D-06 6 5.734498698465D-05 -3.001759890924D-06 7.192469818350D-08 7 -3.294622184638D-06 2.062548801876D-07 -1.157818482174D-08 8 7.669410612531D-08 -4.861603869267D-09 2.925221400690D-10 E-Index: 6 7 8 T-Index: 0 -1.286672269176D-04 6.000293275220D-06 -1.078783359137D-07 1 1.379642813223D-04 -6.752421303830D-06 1.268943574449D-07 2 -3.651758284440D-05 2.307784252948D-06 -5.079380257776D-08 3 1.044710535961D-06 -3.994468803276D-07 1.234290357456D-08 4 3.081389976655D-07 8.140394138239D-08 -2.815585650608D-09 5 1.040513862277D-07 -1.905054927605D-08 5.310423435817D-10 6 -2.833458966155D-08 2.502214203633D-09 -5.916747741154D-11 7 2.098501461403D-09 -1.497495555462D-10 3.217115168440D-12 8 -4.734353103748D-11 3.144698339762D-12 -6.342196909047D-14 Max. rel. Error: 3.7053 % Mean rel. Error: 0.5707 % \end{verbatim}\end{small} \begin{figure} \label{2.8il} \epsfxsize=16truecm \epsffile{Amjuel_PS/oxyil-erate.eps} \end{figure} \newpage \subsection{ Reaction 2.3.6A0 $C^+ + e \rightarrow C $ } electron cooling rate due to recombination of C$^+$ ions [eV * cm**3/s], ADAS 96 One must subtract: 11.3 eV per recombination to turn ADAS radiation rate into electron cooling (or heating) rate. Hence: the quantity ``PRB" given here happens to be the radiation loss only. Note: these ADAS ``PRB" rates include Bremsstrahlung. \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.449331531577D+01 9.258971812737D+00 -4.304690527938D+00 1 -4.179856306879D+00 4.719723714161D+00 -1.109771079252D+00 2 2.311733850808D+00 -2.370285434332D+00 1.216699592702D+00 3 1.806779837905D+00 -1.398234905586D+00 8.251852305561D-02 4 -8.032014606781D-01 6.243519059852D-01 -7.917711523053D-02 5 1.301554943312D-01 -9.725337184215D-02 9.508579166285D-03 6 -1.242233736267D-02 8.700165808817D-03 -5.616784271834D-04 7 7.954435301193D-04 -5.273273516585D-04 4.271193045387D-05 8 -2.500391513086D-05 1.626059504628D-05 -2.107306577342D-06 E-Index: 3 4 5 T-Index: 0 1.092764777565D+00 -1.657866594525D-01 1.542303956967D-02 1 1.775353255679D-02 2.925284499345D-02 -4.933757846201D-03 2 -2.172778536056D-01 1.779079567056D-02 -5.919155623354D-04 3 6.930042877150D-03 -9.404827643211D-04 1.001550181383D-04 4 7.717002987717D-03 -8.219046168773D-04 3.450097852128D-05 5 -9.044019514499D-04 1.495651404294D-04 -9.330495889321D-06 6 4.344451591441D-05 -1.310415385953D-05 8.765092218798D-07 7 -3.990191176291D-06 7.319258744806D-07 -2.097979773124D-08 8 2.278134731858D-07 -1.867601250526D-08 -8.878768861855D-10 E-Index: 6 7 8 T-Index: 0 -8.596236746746D-04 2.630726640545D-05 -3.398545538061D-07 1 3.628156323586D-04 -1.299989445086D-05 1.856398634322D-07 2 -1.839176473763D-06 5.227710471502D-07 -7.972639217563D-09 3 -1.421063531104D-05 9.098399911722D-07 -1.924615837222D-08 4 3.127888270655D-06 -3.185873097827D-07 7.374750430973D-09 5 -3.945898698541D-07 5.543052440997D-08 -1.361067307243D-09 6 5.284131939957D-08 -6.565852326841D-09 1.587125861820D-10 7 -6.267687595428D-09 5.231170570451D-10 -1.155780084007D-11 8 2.974065900351D-10 -1.882199061890D-11 3.774990290039D-13 Max. rel. Error: 8.2940 % Mean rel. Error: 3.7511 % \end{verbatim}\end{small} \begin{figure} \label{2.3.6rl} \epsfxsize=16truecm \epsffile{Amjuel_PS/carbrl-erate.eps} \end{figure} \subsection{ Reaction 2.3.7A0 $N^+ + e \rightarrow N $ } electron cooling rate due to recombination of N$^+$ ions [eV * cm**3/s], ADAS 96 One must subtract: 14.53 eV per recombination to turn ADAS radiation rate into electron cooling (or heating) rate. Hence: the quantity ``PRB" given here happens to be the radiation loss only. Note: these ADAS ``PRB" rates include Bremsstrahlung. \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.586820731518D+01 -3.773123878982D-04 7.482871509909D-02 1 4.400357172984D-01 -5.955879689023D-02 -6.069655421640D-02 2 1.523969394400D+00 3.425371495869D-02 -8.101981223987D-02 3 -3.077040183629D-01 5.713803828212D-03 4.307965640960D-02 4 -2.499858560511D-01 -1.181574525071D-02 3.378336563136D-03 5 1.122891964175D-01 4.206198954046D-03 -4.429675538662D-03 6 -1.845412035984D-02 -6.674583671370D-04 8.097511152946D-04 7 1.383369072901D-03 5.032061800809D-05 -5.815584065023D-05 8 -3.962101000292D-05 -1.468219566959D-06 1.461427252466D-06 E-Index: 3 4 5 T-Index: 0 -4.804133327132D-02 1.306447013294D-02 -1.812654742590D-03 1 5.106007492864D-02 -1.546284626871D-02 2.268830444441D-03 2 4.279413046901D-02 -1.024270007475D-02 1.316026883921D-03 3 -3.115909800990D-02 8.767085102681D-03 -1.239304971154D-03 4 2.713999948320D-03 -1.295602004725D-03 2.196982388776D-04 5 1.151215043288D-03 -1.200389519219D-04 3.592098287396D-06 6 -2.493973858283D-04 3.804621927607D-05 -3.384244902180D-06 7 1.658217707026D-05 -2.328052761042D-06 1.932298218606D-07 8 -3.196107515802D-07 2.507602295919D-08 -5.676151311100D-11 E-Index: 6 7 8 T-Index: 0 1.354629644171D-04 -5.174213693006D-06 7.914218642264D-08 1 -1.751819021358D-04 6.833826024190D-06 -1.061582477502D-07 2 -9.341518771019D-05 3.450572575050D-06 -5.173974255663D-08 3 9.351800226170D-05 -3.596490667485D-06 5.541585525207D-08 4 -1.805778311706D-05 7.263438826071D-07 -1.148112128372D-08 5 2.332387839470D-07 -1.879365909923D-08 3.676966892592D-10 6 1.870011605909D-07 -6.064415580300D-09 8.687600130338D-11 7 -1.049655308155D-08 3.552860851546D-10 -5.454408362195D-12 8 -8.202530145299D-11 3.479987632860D-12 -4.036153078945D-14 Max. rel. Error: 32.2303 % Mean rel. Error: 12.2391 % \end{verbatim}\end{small} \begin{figure} \label{2.3.7rl} \epsfxsize=16truecm \epsffile{Amjuel_PS/nitrl-erate.eps} \end{figure} \newpage \subsection{ Reaction 2.3.8A0 $O^+ + e \rightarrow O $ } electron cooling rate due to recombination of O$^+$ ions [eV * cm**3/s], ADAS 96 One must subtract: 13.62 eV per recombination to turn ADAS radiation rate into electron cooling (or heating) rate. Hence: the quantity ``PRB" given here happens to be the radiation loss only. Note: these ADAS ``PRB" rates include Bremsstrahlung. \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.653313950168D+01 2.216925829689D-02 5.476125200862D-03 1 -6.354270172271D-02 -2.970370946175D-02 -2.924232567362D-03 2 1.136262534246D+00 -1.638321618233D-02 4.543680765812D-03 3 -1.281599573767D-01 3.819386824901D-03 3.005270657055D-04 4 -1.909197964757D-01 5.701759939452D-03 -1.426212735570D-03 5 7.244841497960D-02 -2.697317691499D-03 5.384553818515D-04 6 -1.085354529891D-02 4.751006113548D-04 -9.079081560679D-05 7 7.572289001622D-04 -3.780469918978D-05 7.402729380985D-06 8 -2.041631801536D-05 1.138361613897D-06 -2.361510545802D-07 E-Index: 3 4 5 T-Index: 0 -4.314967559213D-03 1.308676572081D-03 -1.736787698498D-04 1 1.081523218557D-03 -3.561991531376D-04 4.308167373509D-05 2 8.372086622214D-04 -3.337360481944D-04 3.545299576488D-05 3 -4.893123129767D-04 7.578633030575D-05 2.917876532730D-06 4 -3.128536602414D-05 7.234833821022D-05 -1.233696295835D-05 5 3.583912600700D-05 -2.670990378994D-05 2.932629504712D-06 6 -2.993913602201D-06 2.724569084701D-06 -9.569324831913D-08 7 -2.244802134509D-07 -2.933697608069D-08 -2.654846978216D-08 8 2.401245642186D-08 -5.331361909937D-09 1.859310874804D-09 E-Index: 6 7 8 T-Index: 0 1.143937144703D-05 -3.426119753220D-07 3.343988039951D-09 1 -2.436289695706D-06 4.547126890253D-08 2.943681279832D-10 2 -9.130986620243D-07 -5.056377574243D-08 2.244312734391D-09 3 -1.421649431925D-06 1.060528794829D-07 -2.467404974614D-09 4 9.066971436761D-07 -3.076963252506D-08 3.790588865731D-10 5 -7.287895559905D-08 -4.525321022016D-09 1.980047129074D-10 6 -2.908578180313D-08 2.796398755095D-09 -7.153988149004D-11 7 5.437629784614D-09 -3.630282613909D-10 8.162616568071D-12 8 -2.565417747456D-10 1.497599750014D-11 -3.151739443995D-13 Max. rel. Error: 29.6584 % Mean rel. Error: 9.6090 % \end{verbatim}\end{small} \begin{figure} \label{2.3.8rl} \epsfxsize=16truecm \epsffile{Amjuel_PS/oxyrl-erate.eps} \end{figure} \newpage \section{H.11: Other single polynomial fits} \subsection{ Reaction 2.2B0 $ He + e \rightarrow He^*, \ (T_e) \ [eV], $ } Electron cooling for neutral and single charged Helium Particles, divided by corresponding collision rates, i.e. the fit here is for the mean electron energy cost per collision [eV] \begin{small}\begin{verbatim} k0 1.151324376008D+01 k1 -4.473761205167D+00 k2 1.778986582799D+00 k3 -6.438551868755D-01 k4 1.608511765799D-01 k5 -2.421866396738D-02 k6 2.091573687632D-03 k7 -9.493936758931D-05 k8 1.736942898336D-06 \end{verbatim}\end{small} \subsection{ Reaction 2.4B0 $ Be + e \rightarrow Be^*, \ (T_e) \ [eV],$ } Electron cooling rates for neutral and single charged Beryllium Particles, divided by corresponding collision rates, i.e. the fit here is for the mean electron energy cost per collision [eV] \begin{small}\begin{verbatim} k0 1.100391045815D+01 k1 -5.081216135395D+00 k2 2.036662223616D+00 k3 -6.960133333130D-01 k4 1.785218452743D-01 k5 -2.998205644075D-02 k6 3.046320376267D-03 k7 -1.693432568467D-04 k8 3.950464677598D-06 \end{verbatim}\end{small} \subsection{ Reaction 2.5B0 $ B + e \rightarrow B^*, \ (T_e) \ [eV] $ } Electron cooling rates for neutral and single charged Boron Particles, divided by corresponding collision rates, i.e. the fit here is for the mean electron energy cost per collision [eV] \begin{small}\begin{verbatim} k0 7.978054620918D+00 k1 -2.341359084919D+00 k2 8.199491879599D-01 k3 -4.624629728853D-01 k4 1.778831014506D-01 k5 -3.767862190039D-02 k6 4.410579417779D-03 k7 -2.699007579966D-04 k8 6.760485583089D-06 \end{verbatim}\end{small} \begin{figure} \label{2.5ll} \epsfxsize=16truecm \epsffile{Amjuel_PS/HeBeB_il.ps} \end{figure} \newpage \subsection{ Reaction 2.6B0 $ C + e \rightarrow C^*, \ (T_e) \ [eV] $ } Electron cooling rates for neutral and single charged Carbon Particles, divided by corresponding collision rates, i.e. the fit here is for the mean electron energy cost per collision [eV]. Currently: constant, = ionisation potential of Carbon = 11.30 eV \begin{small}\begin{verbatim} k0 2.424802725729D+00 k1 0.000000000000D+00 k2 0.000000000000D+00 k3 0.000000000000D+00 k4 0.000000000000D+00 k5 0.000000000000D+00 k6 0.000000000000D+00 k7 0.000000000000D+00 k8 0.000000000000D+00 Max. rel. Error: .0000 % Mean rel. Error: .0000 % \end{verbatim}\end{small} \subsection{ Reaction 2.7B0 $ N + e \rightarrow N^*, \ (T_e) \ [eV] $ } Electron cooling rates for neutral Nitrogen particles, divided by corresponding collision rates, i.e. the fit here is for the mean electron energy cost per collision [eV]. Currently: constant, = ionisation potential of Nitrogen = 14.534 eV \begin{small}\begin{verbatim} k0 2.676490732000D+00 k1 0.000000000000D+00 k2 0.000000000000D+00 k3 0.000000000000D+00 k4 0.000000000000D+00 k5 0.000000000000D+00 k6 0.000000000000D+00 k7 0.000000000000D+00 k8 0.000000000000D+00 Max. rel. Error: .0000 % Mean rel. Error: .0000 % \end{verbatim}\end{small} \subsection{ Reaction 2.10B0 $ Ne + e \rightarrow Ne^*, \ (T_e) \ [eV] $ } Electron cooling rates for neutral and single charged Neon Particles, divided by corresponding collision rates, i.e. the fit here is for the mean electron energy cost per collision [eV] \begin{small}\begin{verbatim} k0 1.059049152999D+01 k1 -5.769454465431D+00 k2 2.125621468764D+00 k3 -6.517811286454D-01 k4 1.883422085531D-01 k5 -3.905034526242D-02 k6 4.823070375814D-03 k7 -3.148120306333D-04 k8 8.365625760942D-06 Max. rel. Error: .9028 % Mean rel. Error: .5524 % \end{verbatim}\end{small} \subsection{ Reaction 2.18B0 $ Ar + e \rightarrow Ar^*, \ (T_e) \ [eV] $ } Electron cooling rates for neutral and single charged Argon Particles, divided by corresponding collision rates, i.e. the fit here is for the mean electron energy cost per collision [eV] here use constant ionisation potential $Delta E_e = I_p = 15.7596$ eV. \begin{small}\begin{verbatim} k0 2.757449703000D+00 k1 0.000000000000D+00 k2 0.000000000000D+00 k3 0.000000000000D+00 k4 0.000000000000D+00 k5 0.000000000000D+00 k6 0.000000000000D+00 k7 0.000000000000D+00 k8 0.000000000000D+00 Max. rel. Error: .0000 % Mean rel. Error: .0000 % \end{verbatim}\end{small} \begin{figure} \label{2.18ll} \epsfxsize=16truecm \epsffile{Amjuel_PS/CNeAr_il.ps} \end{figure} \newpage \subsection{ Reaction 2.0b $ p + H_2(v=0) \rightarrow H_2^+ + ... $, Ratio \ $H_2^+/H_2$ } \textbf{gain }of $H_2^+$: production by CX (ion conversion, proton impact) on cold (0.1 eV) $H_2(0)$, vibr. ground state only. Only dependence on one temperature $T_p$. \\ \textbf{loss }of $H_2^+$: coll. rad. model for $H_2, H_2^+$, Sawada, Fujimoto, \cite{kn:Sawada}, electron impact dissociative recombination, excitation and ionization. Total loss: electron density independent.\\ Note: the contribution 2.0a to this ratio from electron impact processes leading to $H_2^+$ is electron density dependent, because the effective electron impact ionisation is density dependent. This contribution to the ratio is given in the next chapter under the ``double-polynomial fits''. \medskip \begin{small}\begin{verbatim} k0 -8.061954078771D+00 k1 2.475896585902D+00 k2 -2.933737852849D+00 k3 1.492083638260D+00 k4 -3.461597813263D-01 k5 3.266006392880D-02 k6 1.357009637322D-03 k7 -5.021441756376D-04 k8 2.737802193621D-05 Max. rel. Error: 1.3369 % Mean rel. Error: .8127 % \end{verbatim}\end{small} \subsection{ Reaction 2.0c $p + H_2(v) \rightarrow H_2^+ + ... $, Ratio \ $H_2^+/H_2$ } \textbf{gain }of $H_2^+$: coll. model for vibr. excitation, Greenland, Reiter, \cite{kn:Green}), and then: $H_2^+$ production by CX (ion conversion, proton impact) on these $H_2(v)$. The density dependence on vibrational distribution $P(v)$ of $H_2(v)$ vanishes for $n_e=n_p$. Only dependence on one temperature for $T_e=T_p$. \\ \textbf{loss }of $H_2^+$: coll. rad. model for $H_2, H_2^+$, Sawada, Fujimoto, \cite{kn:Sawada}, electron impact dissociative recombination, excitation and ionization. Total loss: electron density independent.\\ Assumptions: $E_{H2} = 0.1$ eV, $T_i = T_e$, vibrational distribution $P(v)$ in electr. ground state of $H_2$ with no coupling to B,C states, hence: also gain rate of $H_2^+$ due to this process is independent of $n_e$. B,C coupling to vibr. states is non-linear in density and would hence make this ratio density dependent. \begin{small}\begin{verbatim} k0 -5.281428900665D+00 k1 3.115995571855D+00 k2 -3.690629726865D+00 k3 1.448918180601D+00 k4 -3.928689243481D-01 k5 1.236809448625D-01 k6 -2.877121006548D-02 k7 3.391113110854D-03 k8 -1.521565312043D-04 Max. rel. Error: 9.3977 % Mean rel. Error: 5.6685 % \end{verbatim}\end{small} \begin{figure} \label{2.0a} \epsfxsize=16truecm \epsffile{Amjuel_PS/ratioH11_2ab.ps} \end{figure} \newpage \subsection{ Reaction 4.0a $ H_2 + H_2^+ \rightarrow H_3^+ + H$, Ratio \ $H_3^+/H_2$ } Fit for ln(RATIO), defined such that $n_{H_3^+}/n_{H_2}$ = RATIO $\times n_{H_2^+}/n_e$ Ratio of densities: $n_{H_3^+}/n_{H_2}$ = Ratio of production rate constant to destruction rate coefficient $\times n_{H_2^+}/n_e$. \\ Production of $H_3^+$ from $H_2(v)$: rate constant obtained from HYDHEL rate coefficient for $ H_2^+ + H_2(v) \rightarrow H_3^+ + H$ evaluated at $T_{H_2} = T_{H_2^+} = 0.1$ eV, $ \approx 1.160947956 e-9$. \\ Destruction of $H_3^+$: diss. recombination (DR) from HYDHEL, 2.2.15, vs. $T_e$. Used here: algebraic expression from original rate constant and fit of ln(DR rate coef.) for this ln(RATIO). \begin{small}\begin{verbatim} k0 -3.571300000000e+00 k1 4.050073042947e-01 k2 -1.018733477232e-08 k3 1.695586285687e-08 k4 -1.564311217508e-10 k5 -1.979725412288e-09 k6 4.395545994733e-10 k7 -3.584926377078e-11 k8 1.024189019465e-12 \end{verbatim}\end{small} \newpage \subsection{ Reaction 7.0a $ e + H_2(v) \rightarrow H^- + H$, Ratio \ $H^-/H_2$ from DA } Ratio of densities: $n_{H^-}/n_{H_2}$. \\ vibr. distribution $P(v)$ of $H_2(v)$: coll. model for vibr. excitation, Greenland, Reiter, \cite{kn:Green}\\ Vibrational distribution $H_2(v)$ evaluated at $E_{H_2} = 0.1 eV$, $T_p = T_e$ and $n_p = n_e$.\\ Production of $H^-$ from $H_2(v)$: Dissociative attachment on $H_2(v): e+H_2(v) \rightarrow H^- + H$ \\ Destruction of $H^-$: electron detachment, proton MN, with $E_{H^-}=0.1$ and $T_p = T_e$ and $n_p = n_e$. \begin{small}\begin{verbatim} k0 -6.001820741967D+00 k1 1.247273997745D+00 k2 -2.753387653632D+00 k3 2.274419556537D-01 k4 1.148400271668D-02 k5 8.614331916062D-02 k6 -3.482537437480D-02 k7 4.822974299102D-03 k8 -2.291190247346D-04 Max. rel. Error: 23.4821 % Mean rel. Error: 10.7677 % \end{verbatim}\end{small} \subsection{ Reaction 7.0b $ e + H_2(0) \rightarrow H^- + H$, Ratio \ $H^-/H_2$ from DA } same as 7.0a, but DA (diss. attachment) only from vibr. ground state Ratio of densities: $n_{H^-}/n_{H_2}$\\ Production of $H^-$ from $H_2(v=0)$: Dissociative attachment on $H_2(v=0): e+H_2(0) \rightarrow H^- + H$ \\ Destruction of $H^-$: electron detachment, proton MN, with $E_{H^-}=0.1$ and $T_p = T_e$ and $n_p = n_e$. \begin{small}\begin{verbatim} k0 -1.608434690479D+01 k1 2.105039374877D+00 k2 -2.553803267076D+00 k3 7.038135447597D-01 k4 -6.586584264400D-02 k5 -2.548302462129D-03 k6 2.922944743984D-04 k7 8.800611380131D-05 k8 -7.939105674896D-06 Max. rel. Error: 3.3989 % Mean rel. Error: 1.0220 % \end{verbatim}\end{small} \begin{figure} \label{7.0} \epsfxsize=16truecm \epsffile{Amjuel_PS/ratio7.ps} \end{figure} \newpage \section{H.12: Other double polynomial fits} \subsection{ Reaction 2.1.5 $H + e \leftrightarrow H^+ +2e$, Ratio $H^+/H(1)$ } This ratio provides the collisional radiative equilibrium ion density, for a given ground state atom density. In CR equilibrium this ratio is a function of $T_e$ and $n_e$. From $0 = n_1 \times \langle s_{ion} \rangle - n^+ \times \langle\alpha_{rec} \rangle$. Assumed: $n^+ = n_e$ \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.885296435411D+00 -5.697204983970D-02 7.332383617797D-02 1 1.505487187018D+01 4.633572829771D-04 -1.702732444633D-03 2 -6.749191912028D+00 1.050145613783D-03 -3.148776304951D-03 3 2.212221660002D+00 4.854461323593D-03 -2.452783916892D-03 4 -5.257981277508D-01 -3.179654723425D-03 1.767567981601D-03 5 8.824411449640D-02 9.193475524397D-04 -4.299802583958D-04 6 -9.799369577387D-03 -1.679454700153D-04 7.381643118061D-05 7 6.413937652029D-04 1.902440743752D-05 -9.875692439849D-06 8 -1.861114574375D-05 -9.394367819466D-07 5.893327001637D-07 E-Index: 3 4 5 T-Index: 0 -3.505183129037D-02 8.175768579910D-03 -1.025860190568D-03 1 1.882868187070D-03 -6.728098565933D-04 1.133241004935D-04 2 1.594704172137D-03 -3.246647453262D-04 3.184754694533D-05 3 4.064257852894D-04 -2.059459670150D-05 -2.358171220598D-06 4 -3.839001285389D-04 4.783673711689D-05 -3.378269018931D-06 5 6.248027250326D-05 -4.077787495573D-06 1.124935475483D-07 6 -7.865967145477D-06 -4.674862715791D-08 4.744742742259D-08 7 1.734207080274D-06 -1.760833256154D-07 1.551629723045D-08 8 -1.457328885095D-07 2.193301182972D-08 -2.248254389232D-09 E-Index: 6 7 8 T-Index: 0 7.041006112962D-05 -2.467291455100D-06 3.436102553376D-08 1 -9.735191629933D-06 4.053170686858D-07 -6.463282471161D-09 2 -1.387656614654D-06 1.600623293301D-08 2.722493472041D-10 3 3.488698891258D-07 -1.422059161908D-08 1.698254518458D-10 4 9.511636577030D-08 6.913540712148D-10 -5.483090178167D-11 5 1.140116701448D-08 -1.211498169926D-09 3.020216342872D-11 6 -4.127705769609D-09 2.185243304602D-10 -4.848384547542D-12 7 -9.432683181108D-10 2.682232500047D-11 -2.216051536502D-13 8 1.398963108397D-10 -4.493865381320D-12 5.590467018306D-14 Max. rel. Error: .9684 % Mean rel. Error: .4161 % \end{verbatim}\end{small} \begin{figure} \label{2.1.5_equil} \epsfxsize=16truecm \epsffile{Amjuel_PS/ratioH12_2.1.5.ps} \end{figure} \newpage \subsection{ Reaction 2.1.5a $H + e \rightarrow H^+ + 2e $, Ratio $H(3)/H(1)$ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.082877684472D+01 9.740982428834D-01 2.693447564427D-02 1 1.187030265272D+01 1.968338090648D-02 -2.495504765088D-02 2 -5.889482037865D+00 -8.737684945730D-03 9.951688266911D-03 3 2.017399399792D+00 -1.014609925009D-02 1.040081859210D-02 4 -5.303360302839D-01 3.297808176838D-03 -2.712205422397D-03 5 1.080451047951D-01 9.673290806118D-04 -1.096708705743D-03 6 -1.555010466762D-02 -5.167168286670D-04 4.637911190482D-04 7 1.327158680898D-03 7.389473703435D-05 -5.797555862425D-05 8 -4.872105203992D-05 -3.537584073064D-06 2.453443334473D-06 E-Index: 3 4 5 T-Index: 0 -9.004934091051D-03 1.222843687947D-03 -5.210804049741D-05 1 1.123130855030D-02 -2.651909936461D-03 3.534709147248D-04 2 -5.241271640755D-03 1.372483328336D-03 -1.917275090304D-04 3 -3.478025606446D-03 5.572774095384D-04 -4.848784231802D-05 4 8.454526208306D-04 -1.362168127545D-04 1.306146151315D-05 5 3.872258199271D-04 -6.353971343367D-05 5.417022322731D-06 6 -1.380893374707D-04 1.849429028886D-05 -1.166761555949D-06 7 1.440341699187D-05 -1.290902554237D-06 -4.889963932464D-09 8 -4.745956710582D-07 5.546604517157D-09 7.579547673173D-09 E-Index: 6 7 8 T-Index: 0 -2.739765256223D-06 2.927097984040D-07 -6.646459819509D-09 1 -2.632450715422D-05 9.987762315441D-07 -1.501421276021D-08 2 1.441627470961D-05 -5.481720522735D-07 8.264009775214D-09 3 2.416915703008D-06 -6.658457254421D-08 8.215818515744D-10 4 -7.772290534634D-07 2.655224800515D-08 -3.968977724198D-10 5 -2.470245979511D-07 5.722044899754D-09 -5.443566855045D-11 6 2.955124264492D-08 3.184408123607D-11 -8.216232831023D-12 7 7.390396686250D-09 -4.052521721349D-10 6.720841155202D-12 8 -8.635578634097D-10 3.738695038824D-11 -5.757075610089D-13 Max. rel. Error: 3.7804 % Mean rel. Error: 1.3368 % \end{verbatim}\end{small} \begin{figure} \label{2.1.5a} \epsfxsize=16truecm \epsffile{Amjuel_PS/hn3fu.ps} \end{figure} \newpage \subsection{ Reaction 2.1.5b $H + e \rightarrow H^+ + 2e$, Ratio $H(2)/H(1)$ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.888782240542D+01 9.694042304562D-01 4.613129045722D-02 1 9.909537514500D+00 -4.163537878599D-02 2.444011013342D-02 2 -4.942743781185D+00 1.230545313063D-02 -1.289174377763D-02 3 1.715668267417D+00 3.034149311755D-02 -1.837812030403D-02 4 -4.508004155190D-01 -1.136449435241D-02 7.857406065923D-03 5 9.042516000563D-02 -2.874540451423D-03 1.787805444265D-03 6 -1.280973933282D-02 1.947546784046D-03 -1.325209820376D-03 7 1.084341450206D-03 -3.175349945580D-04 2.227323600480D-04 8 -3.974359134401D-05 1.688199339120D-05 -1.209472946500D-05 E-Index: 3 4 5 T-Index: 0 -2.216757216719D-02 5.067711671376D-03 -6.212032986616D-04 1 -5.092551836572D-03 4.080645015829D-04 -5.739581031596D-06 2 4.174980751883D-03 -5.559754475561D-04 2.207616832672D-05 3 3.719122644080D-03 -2.039974521144D-04 -2.170634046629D-05 4 -1.818309410916D-03 1.348196284756D-04 7.621772971297D-06 5 -4.049163510078D-04 3.839701084642D-05 -1.182790529172D-06 6 3.200749637228D-04 -3.075854301471D-05 4.485031199179D-07 7 -5.559573928329D-05 5.656373947352D-06 -1.236115053324D-07 8 3.100021285561D-06 -3.323560174565D-07 9.896407186442D-09 E-Index: 6 7 8 T-Index: 0 4.172445968364D-05 -1.439572350231D-06 1.978486731178D-08 1 -6.441112682031D-07 1.766524953307D-08 4.500335193180D-11 2 1.604359947467D-06 -1.668549821257D-07 3.956288361818D-09 3 3.319046346231D-06 -1.530562339677D-07 2.467744887550D-09 4 -1.742105663717D-06 9.539025646066D-08 -1.764749848063D-09 5 -3.224230256996D-08 2.293257666191D-09 -2.626033062059D-11 6 1.187820950781D-07 -7.725204735890D-09 1.455730327605D-10 7 -1.829679294498D-08 1.312011360384D-09 -2.576831583186D-11 8 8.003219743811D-10 -6.578827971726D-11 1.343525928267D-12 Max. rel. Error: 5.0202 % Mean rel. Error: .9593 % \end{verbatim}\end{small} \begin{figure} \label{2.1.5b} \epsfxsize=16truecm \epsffile{Amjuel_PS/hn2fu.ps} \end{figure} \newpage \subsection{ Reaction 2.1.5c $H + e \rightarrow H^+ + 2e$, Ratio $H(4)/H(1)$ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.121459339796D+01 8.335828009713D-01 2.325042085123D-01 1 1.250950592132D+01 9.112878380113D-03 -5.491646502669D-02 2 -6.229984587067D+00 -1.938627422961D-02 1.621303063286D-02 3 2.142105600364D+00 3.084489232048D-02 -3.147946146487D-03 4 -5.615155300856D-01 -5.885518785970D-03 -1.131771898094D-03 5 1.127449459065D-01 -6.211271050025D-03 3.856805502108D-03 6 -1.590343046823D-02 2.950230045038D-03 -1.748272049931D-03 7 1.333705010633D-03 -4.583201098446D-04 2.858630200307D-04 8 -4.836027605927D-05 2.417569815070D-05 -1.585276481393D-05 E-Index: 3 4 5 T-Index: 0 -1.096388203376D-01 2.434624647621D-02 -2.848412091044D-03 1 2.972045500915D-02 -6.752777629102D-03 7.907482466413D-04 2 -6.819605362801D-03 1.639046907231D-03 -2.316409264833D-04 3 -4.981563534979D-03 1.797076203455D-03 -2.547644660956D-04 4 2.277414510956D-03 -7.295707497520D-04 1.047093315160D-04 5 -9.720154554360D-04 1.201895430371D-04 -7.956678504065D-06 6 3.838584264558D-04 -3.212460389716D-05 -8.181068284295D-08 7 -6.739012881651D-05 6.684315041032D-06 -1.703080933280D-07 8 4.013119711268D-06 -4.619672863742D-07 2.215787076654D-08 E-Index: 6 7 8 T-Index: 0 1.789669578362D-04 -5.712451213773D-06 7.267386885023D-08 1 -5.078726612521D-05 1.694110618282D-06 -2.296731891384D-08 2 1.859544292047D-05 -7.663932535000D-07 1.248233937322D-08 3 1.790413918002D-05 -6.225635876900D-07 8.589352663796D-09 4 -7.734966472367D-06 2.868598630187D-07 -4.235795995646D-09 5 2.942004754571D-07 -6.030861909870D-09 5.715848860621D-11 6 1.721805311242D-07 -9.730371684031D-09 1.730299677672D-10 7 -1.655594650506D-08 1.235894145239D-09 -2.408500349383D-11 8 2.731478375019D-11 -3.750344543532D-11 9.061707694269D-13 Max. rel. Error: 3.6808 % Mean rel. Error: 1.2901 % \end{verbatim}\end{small} \begin{figure} \label{2.1.5c} \epsfxsize=16truecm \epsffile{Amjuel_PS/hn4fu.ps} \end{figure} \newpage \subsection{ Reaction 2.1.5d $H + e \rightarrow H^+ + 2e$, Ratio $H(5)/H(1)$ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.126718125624D+01 9.282945460974D-01 1.070213380676D-01 1 1.281374709913D+01 3.573873112144D-02 -4.872701879146D-02 2 -6.380408105491D+00 -1.144110981890D-03 -4.680598150266D-05 3 2.191577061685D+00 -5.161589020256D-03 6.439656957369D-03 4 -5.751755938054D-01 1.676622419964D-03 -1.568501026478D-03 5 1.157406495600D-01 1.486290009897D-04 -1.404765081110D-04 6 -1.631671197369D-02 -2.016003370833D-04 1.639222741263D-04 7 1.362647208936D-03 3.901702147732D-05 -3.141140575728D-05 8 -4.908854946631D-05 -2.325049769834D-06 1.888930116590D-06 E-Index: 3 4 5 T-Index: 0 -5.984835557747D-02 1.574482420977D-02 -2.152803383431D-03 1 2.122340688681D-02 -4.335261058803D-03 4.511000731668D-04 2 4.899399906199D-04 -1.730051136321D-04 2.045111743029D-05 3 -2.595193985854D-03 5.083896758770D-04 -5.001475048416D-05 4 5.235042780927D-04 -8.901350181088D-05 8.437562876296D-06 5 1.953433357615D-05 3.171136646292D-06 -1.281135706652D-06 6 -3.782479181914D-05 2.829273502486D-06 1.645529677700D-07 7 7.810730453019D-06 -7.640509497691D-07 9.357372398314D-09 8 -4.970298877362D-07 5.607762235203D-08 -2.232480288100D-09 E-Index: 6 7 8 T-Index: 0 1.533450613139D-04 -5.416190220272D-06 7.503092506245D-08 1 -2.514757812007D-05 7.098607959133D-07 -7.948198678409D-09 2 -4.780097207035D-07 -3.664829135622D-08 1.435704784493D-09 3 2.378856833473D-06 -4.662729327187D-08 1.885707833825D-10 4 -4.722754735716D-07 1.525662957088D-08 -2.277373255316D-10 5 1.539182389681D-07 -7.795475709363D-09 1.408203935795D-10 6 -3.844013350899D-08 2.070018927471D-09 -3.568996816514D-11 7 3.398945819263D-09 -2.120439941817D-10 3.643140818164D-12 8 -6.095037813579D-11 6.718495301125D-12 -1.229967242093D-13 Max. rel. Error: 2.8664 % Mean rel. Error: 1.0041 % \end{verbatim}\end{small} \begin{figure} \label{2.1.5d} \epsfxsize=16truecm \epsffile{Amjuel_PS/hn5fu.ps} \end{figure} \newpage \subsection{ Reaction 2.1.5e $H + e \rightarrow H^+ + 2e$, Ratio $H(6)/H(1)$ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.118788806329D+01 1.051705868661D+00 -6.954764617920D-02 1 1.300365034969D+01 5.806024278787D-02 -7.054107872877D-02 2 -6.464611656902D+00 -3.350148712230D-02 3.809632279775D-02 3 2.198690942590D+00 -1.651116960139D-02 1.248202030331D-02 4 -5.762198964354D-01 8.782966049217D-03 -7.253814512300D-03 5 1.190459835777D-01 7.937734220940D-04 -3.032198147605D-04 6 -1.758172528529D-02 -8.425168421647D-04 4.935184501531D-04 7 1.540671110406D-03 1.322737632505D-04 -7.161027491097D-05 8 -5.782468318198D-05 -6.483373521666D-06 3.088146690349D-06 E-Index: 3 4 5 T-Index: 0 2.612329534702D-02 -3.911384137475D-03 1.474794675693D-04 1 3.209814487839D-02 -7.336538391803D-03 8.838327301328D-04 2 -1.663574690203D-02 3.667522832624D-03 -4.409479869479D-04 3 -3.600008781362D-03 5.273464947078D-04 -4.137511227236D-05 4 2.434417487959D-03 -4.385057360151D-04 4.589037396076D-05 5 -6.693627833492D-05 4.755833322780D-05 -8.654363224389D-06 6 -8.020637279277D-05 -2.254322145665D-06 1.858918078917D-06 7 9.120131097155D-06 1.138969748088D-06 -3.791832116704D-07 8 -1.704370060355D-07 -1.258928004543D-07 2.744344149529D-08 E-Index: 6 7 8 T-Index: 0 9.191757017392D-06 -7.898231632650D-07 1.514512376570D-08 1 -5.779085565904D-05 1.935287412436D-06 -2.603161887414D-08 2 2.975048782418D-05 -1.054940416948D-06 1.523660684271D-08 3 1.553774051571D-06 -1.704433673171D-08 -2.016881015852D-10 4 -2.785668187173D-06 9.065547432614D-08 -1.223436753078D-09 5 7.303664535216D-07 -2.952279140710D-08 4.597194098628D-10 6 -1.970736415814D-07 8.619751903229D-09 -1.383868509607D-10 7 3.596045684588D-08 -1.495930494169D-09 2.332244458469D-11 8 -2.357827363714D-09 9.371149524100D-11 -1.424213663602D-12 Max. rel. Error: 5.6136 % Mean rel. Error: 1.7770 % \end{verbatim}\end{small} \begin{figure} \label{2.1.5e} \epsfxsize=16truecm \epsffile{Amjuel_PS/hn6fu.ps} \end{figure} \newpage \subsection{ Reaction 2.1.5tot $ H + e \rightarrow H^+ + 2e$, Ratio $H(tot)/H(1)$ } total density (ground plus all excited states) in CR equilibrium with ground state \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 9.999989080920D-01 6.569869814870D-04 -6.526259178085D-04 1 -6.684079057216D-06 -1.624733380895D-03 1.517116722391D-03 2 2.553992642225D-05 9.833706477844D-04 -8.771533719662D-04 3 -2.462557791473D-05 -2.342847322381D-04 2.116654525863D-04 4 1.062360801108D-05 2.225391064535D-05 -2.995563308037D-05 5 -2.399855499712D-06 2.478808045973D-06 1.242643822457D-06 6 2.951154702233D-07 -7.469982004941D-07 1.518536644908D-07 7 -1.871893412626D-08 5.751651874704D-08 -1.380451507029D-08 8 4.796659338151D-10 -1.452959768161D-09 2.101916949778D-10 E-Index: 3 4 5 T-Index: 0 2.446820545529D-04 -4.633538453818D-05 4.889372584120D-06 1 -5.196975095555D-04 8.835186629866D-05 -8.286820244724D-06 2 2.694565448733D-04 -3.889200026191D-05 2.928290705068D-06 3 -5.533211626824D-05 5.123221852559D-06 -1.729804749149D-08 4 8.273895035263D-06 -6.797808694765D-07 -1.060219799928D-08 5 -5.874504858843D-07 4.859497595281D-08 1.114394044002D-09 6 7.883226202848D-09 -1.005021139591D-09 -2.177196303683D-10 7 -9.799681363679D-10 4.054138156358D-10 -2.970144566810D-11 8 1.213701692902D-10 -3.377976381012D-11 3.362497319640D-12 E-Index: 6 7 8 T-Index: 0 -2.917482144379D-07 9.209996969945D-09 -1.195587997940D-10 1 4.378814547750D-07 -1.223407550017D-08 1.405657502664D-10 2 -1.169351655337D-07 2.258524229896D-09 -1.460715455401D-11 3 -2.426972326758D-08 1.404805094637D-09 -2.540724522759D-11 4 3.476416204584D-09 -1.330157773056D-10 1.424915474012D-12 5 -8.129340876771D-11 -1.183776577049D-11 5.125710307402D-13 6 5.313468965034D-12 1.675867714679D-12 -6.770309443179D-14 7 1.619425683239D-12 -1.268121213878D-13 3.934356277466D-15 8 -1.798937732279D-13 6.521970562366D-15 -1.251030581090D-16 \end{verbatim}\end{small} \begin{figure} \label{2.1.5tot} \epsfxsize=16truecm \epsffile{Amjuel_PS/hydic.ps} \end{figure} \newpage \subsection{ Reaction 2.1.5de $ H + e \rightarrow H^+ + 2e$, \ $ \ [eV]$} \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 7.845107077886D+00 -4.158388629994D-02 2.060681712432D-02 1 -4.270502285463D+00 9.505957771815D-02 -7.673602080150D-02 2 1.726068286328D+00 -4.522519386379D-02 5.154287556942D-02 3 -3.652415321353D-01 -5.349008403944D-03 -1.089345117269D-02 4 3.713344797329D-02 9.550154852851D-03 -1.137782108759D-03 5 -1.816044037023D-04 -2.867587202499D-03 8.354453807701D-04 6 -3.430690631609D-04 3.909898872586D-04 -1.337503951808D-04 7 3.098356603724D-05 -2.559885625243D-05 9.077886701887D-06 8 -8.899184097510D-07 6.519466167972D-07 -2.268251226270D-07 E-Index: 3 4 5 T-Index: 0 -8.052322446345D-03 1.361616907232D-03 -1.426513742220D-04 1 2.563880114503D-02 -3.821401798942D-03 2.937551907788D-04 2 -1.720715317463D-02 2.290689977061D-03 -1.253606753443D-04 3 4.775945182204D-03 -6.467228312794D-04 2.975489992699D-05 4 -3.721823938539D-04 7.419831565375D-05 -3.809552723616D-06 5 -8.073915024648D-05 3.196729352202D-06 -4.577796946576D-08 6 1.863239051629D-05 -1.462457758789D-06 6.102229658187D-08 7 -1.331114942698D-06 1.094119960469D-07 -4.763060764998D-09 8 3.160102832021D-08 -2.366622776376D-09 9.028757163018D-11 E-Index: 6 7 8 T-Index: 0 9.199187026673D-06 -3.626126425744D-07 6.526649455096D-09 1 -1.081310544107D-05 1.291895685695D-07 1.068484717217D-09 2 -1.280245967862D-08 2.592986543781D-07 -7.113378488276D-09 3 8.057527653614D-07 -1.189385405932D-07 2.982171776258D-09 4 -9.060932716087D-08 1.580536007694D-08 -4.320760123314D-10 5 -5.069290362681D-10 -2.785729865499D-10 1.593762976817D-11 6 2.554338381631D-10 -9.890935002552D-11 1.770328452101D-12 7 -9.336950682103D-12 8.093464288205D-12 -1.767574119215D-13 8 1.044083905543D-12 -2.066392792622D-13 4.436324698144D-15 Max. rel. Error: .4629 % Mean rel. Error: .0970 % \end{verbatim}\end{small} \begin{figure} \label{2.1.5li2} \epsfxsize=16truecm \epsffile{Amjuel_PS/hydli2_tr.ps} \end{figure} \newpage \subsection{ Reaction 2.1.5o $ H + e \rightarrow H^+ + 2e $, \ $ \ [eV]$ Ly-opaque} Lyman opaque \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 4.257426092590D+00 -2.648139307081D-01 2.747475375517D-01 1 -1.580642905913D+00 1.856918325247D-01 -1.887867610999D-01 2 9.487720032428D-01 -4.334108248024D-02 4.027363438413D-02 3 -3.653667544231D-01 1.938361132039D-03 -1.064922255960D-03 4 9.142288235830D-02 6.321600657670D-04 -1.359591518986D-04 5 -1.446402551044D-02 -2.277509541327D-04 -1.939963902602D-05 6 1.384901599216D-03 4.074186530390D-05 1.262940841492D-06 7 -7.297260412218D-05 -3.278960026730D-06 5.700992619392D-08 8 1.620578859074D-06 9.263823594567D-08 1.592211120194D-09 E-Index: 3 4 5 T-Index: 0 -1.211356030412D-01 2.685695232533D-02 -3.317777605290D-03 1 8.363647099141D-02 -1.868059156820D-02 2.327504355627D-03 2 -1.875679395058D-02 4.434521459505D-03 -5.945647526149D-04 3 7.959030639825D-04 -2.528345636722D-04 5.007272230577D-05 4 5.074526064710D-06 -3.035134696595D-06 -2.203465100709D-06 5 2.365267620753D-05 -2.398473162099D-06 3.489675236875D-07 6 -3.631085495565D-06 4.137564902109D-07 -2.971694422141D-08 7 2.493062937307D-07 -3.179509396878D-08 1.585728061318D-09 8 -9.298947595442D-09 1.468230792208D-09 -9.887260958280D-11 E-Index: 6 7 8 T-Index: 0 2.278436663051D-04 -8.091967627921D-06 1.156866070535D-07 1 -1.605612738266D-04 5.703707563566D-06 -8.131849775947D-08 2 4.346897926519D-05 -1.605515516330D-06 2.346223121561D-08 3 -4.662162321782D-06 1.981562216998D-07 -3.155996422050D-09 4 3.653404338885D-07 -1.942106127435D-08 3.499018522662D-10 5 -3.942216779052D-08 2.001379932680D-09 -3.673145766979D-11 6 1.954467664699D-09 -8.738736712781D-11 1.665200022479D-12 7 -2.359672833575D-11 -4.475930371767D-13 7.240045137258D-15 8 2.798900106658D-12 -1.040603787711D-14 -5.219184133080D-16 Max. rel. Error: .4321 % Mean rel. Error: .0858 % \end{verbatim}\end{small} \begin{figure} \label{2.1.5li2o} \epsfxsize=16truecm \epsffile{Amjuel_PS/hydli2_op.ps} \end{figure} \newpage \subsection{ Reaction 2.1.8 $H^+ + e \leftrightarrow H(1s) $, Ratio $H(1)/H^+$ } This ratio provides the collisional radiative equilibrium ground state atom density, for a given ion density. From $0 = n_1 \times \langle s_{ion} \rangle - n^+ \times \langle\alpha_{rec} \rangle$. Assumed: $n^+ = n_e$. This is the inverse ratio of the ratio H$^+$/H given above. \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 3.884817920291D+00 5.748230037228D-02 -7.354743589465D-02 1 -1.505405435407D+01 -2.069666264052D-03 2.740273217181D-03 2 6.752413643513D+00 -2.852568692095D-03 2.645950103684D-03 3 -2.218947925718D+00 3.880371810496D-04 2.448954939235D-03 4 5.306456586404D-01 -1.106924750936D-03 -1.425570179604D-03 5 -8.996474445862D-02 8.001173589203D-04 1.442342394885D-04 6 1.012370581895D-02 -1.970308892236D-04 1.763054900761D-05 7 -6.725100993525D-04 2.003187510884D-05 -2.805603265326D-06 8 1.980680600260D-05 -7.148042140142D-07 5.062324995954D-08 E-Index: 3 4 5 T-Index: 0 3.514369843739D-02 -8.200095897737D-03 1.029247980732D-03 1 -2.232044284757D-03 7.372183809405D-04 -1.199006377953D-04 2 -1.418041310973D-03 3.361254031169D-04 -3.854655884633D-05 3 -6.306614528176D-04 2.629206773651D-05 6.811979362899D-06 4 5.100161790571D-04 -6.541482923176D-05 3.819981137349D-06 5 -6.628089424783D-05 7.250593421266D-06 -4.680128307062D-07 6 -2.918830286653D-06 1.005848267335D-06 -7.444889071158D-08 7 5.969286375471D-07 -1.181102409670D-07 3.398470038793D-09 8 3.373896520254D-09 -1.875159711383D-09 7.447934965772D-10 E-Index: 6 7 8 T-Index: 0 -7.065616546499D-05 2.476181590024D-06 -3.448732313124D-08 1 1.010186897559D-05 -4.156554445603D-07 6.576866918837D-09 2 2.077865905425D-06 -4.493493845615D-08 1.680184085191D-10 3 -8.395863513859D-07 3.306347645323D-08 -4.092185917718D-10 4 -9.078967708851D-08 7.126270754412D-10 -1.502691682691D-11 5 2.975843593936D-08 -1.562087549982D-09 3.533269604119D-11 6 -2.195532523309D-09 3.847295886912D-10 -1.006718276842D-11 7 8.756896081564D-10 -7.247037436751D-11 1.603229219763D-12 8 -9.983397630247D-11 5.334255622655D-12 -1.003858224247D-13 Max. rel. Error: .9699 % Mean rel. Error: .4163 % \end{verbatim}\end{small} \begin{figure} \label{2.1.8_equil} \epsfxsize=16truecm \epsffile{Amjuel_PS/ratioH12_2.1.8.ps} \end{figure} \newpage \subsection{ Reaction 2.1.8a $H^+ + e \rightarrow H(1s) $, Ratio $H(3)/H^+$ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.026567737773D+01 1.152583719426D+00 -1.626038509544D-01 1 -8.879460687468D-01 -5.351933360860D-02 4.426984905627D-02 2 -2.779342631813D-02 6.030457249067D-03 1.515441331512D-03 3 -1.196375890811D-02 -2.871588085187D-03 2.404285503458D-04 4 1.822980963695D-03 -1.575168978328D-06 8.405772103417D-04 5 -2.196477309909D-04 5.066260303625D-04 -5.971643097799D-04 6 3.323843511157D-05 -1.520492801515D-04 1.281232614617D-04 7 -1.697007294106D-06 1.825841763069D-05 -1.220563921933D-05 8 -5.916439943353D-08 -8.242186020597D-07 4.677827163183D-07 E-Index: 3 4 5 T-Index: 0 7.198684018769D-02 -1.490875604355D-02 1.619553420918D-03 1 -1.852578901204D-02 3.331452439870D-03 -2.948572788751D-04 2 -9.056841023031D-04 3.563549006757D-04 -5.590965690725D-05 3 -8.226476286514D-05 2.960920971970D-05 -8.086208258569D-06 4 -3.464740688021D-04 5.922304252082D-05 -4.850028146748D-06 5 2.105198711062D-04 -3.609362517850D-05 3.423756972171D-06 6 -3.517980076344D-05 4.427958188863D-06 -2.493221748446D-07 7 2.198069639127D-06 -6.705985847102D-09 -4.128988875743D-08 8 -4.300266775823D-08 -1.512563397687D-08 4.068624995447D-09 E-Index: 6 7 8 T-Index: 0 -9.269115359815D-05 2.618073045777D-06 -2.835709536455D-08 1 1.169406889954D-05 -1.253572620552D-07 -1.886947676134D-09 2 4.196575697004D-06 -1.482582457939D-07 1.946426380509D-09 3 9.143236603084D-07 -4.362855429636D-08 7.452885416070D-10 4 2.164045324446D-07 -6.474547723428D-09 1.156823417385D-10 5 -1.851415491252D-07 5.487390918519D-09 -7.088510716926D-11 6 4.694709505540D-10 5.338069108949D-10 -1.542307935794D-11 7 5.373013388538D-09 -2.844239825756D-10 5.516973870161D-12 8 -4.168331974260D-10 2.004403028395D-11 -3.695127505869D-13 Max. rel. Error: 4.5193 % Mean rel. Error: .9402 % \end{verbatim}\end{small} \begin{figure} \label{2.1.8ra} \epsfxsize=16truecm \epsffile{Amjuel_PS/hpn3fu.ps} \end{figure} \newpage \subsection{ Reaction 2.1.8b $H^+ + e \rightarrow H(1s) $, Ratio $H(2)/H^+$ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.115038577088D+01 9.264747680865D-01 1.116069825638D-01 1 -8.266322399304D-01 -5.055344435832D-03 -5.172879304080D-03 2 -1.958933034940D-02 1.996587961213D-02 -1.406505755991D-02 3 -1.098097104386D-02 -8.026613963832D-03 2.384792377395D-03 4 2.240953060530D-03 6.216308441596D-04 4.708126181720D-04 5 -4.287502766451D-04 1.030957503524D-03 -8.066658779253D-04 6 2.695143837765D-05 -3.813692505803D-04 2.807631048773D-04 7 4.431006229058D-06 4.875879498318D-05 -3.657593211279D-05 8 -4.836943342929D-07 -2.119652719791D-06 1.615837004793D-06 E-Index: 3 4 5 T-Index: 0 -4.999361806664D-02 1.110692800547D-02 -1.318266873039D-03 1 -2.471719625656D-04 2.512113939106D-04 -4.782708408420D-05 2 6.003957672996D-03 -1.118685805994D-03 1.071846833065D-04 3 2.913902175387D-04 -3.137930614752D-04 6.113629942161D-05 4 -3.710502524841D-04 1.004704612837D-04 -1.265344424602D-05 5 1.874529789965D-04 -9.988538268116D-06 -1.920784234786D-06 6 -6.603768771619D-05 4.665491245671D-06 3.297381117360D-07 7 9.282643997639D-06 -9.265752285496D-07 1.709073955313D-08 8 -4.302365964264D-07 5.056403909495D-08 -2.595051961188D-09 E-Index: 6 7 8 T-Index: 0 8.540286307962D-05 -2.815699854432D-06 3.675943603675D-08 1 3.802889409563D-06 -1.453090712874D-07 2.181183016555D-09 2 -5.066273468359D-06 9.656495668618D-08 -2.071395871695D-10 3 -5.318038556138D-06 2.186221742805D-07 -3.426977855059D-09 4 7.996838066338D-07 -2.418791195391D-08 2.661640394733D-10 5 3.024841319851D-07 -1.543862403318D-08 2.709969256279D-10 6 -6.616004144573D-08 3.369760494944D-09 -5.636580218277D-11 7 3.122103721669D-09 -1.967871537035D-10 3.230724672289D-12 8 3.213236793835D-11 1.140062879563D-12 -1.343611820864D-14 Max. rel. Error: 3.9289 % Mean rel. Error: .5704 % \end{verbatim}\end{small} \begin{figure} \label{2.1.8rb} \epsfxsize=16truecm \epsffile{Amjuel_PS/hpn2fu.ps} \end{figure} \newpage \subsection{ Reaction 2.1.8c $H^+ + e \rightarrow H(1s) $, Ratio $H(4)/H^+$ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.953191910521D+01 9.871472575458D-01 8.335595020148D-03 1 -9.556069945203D-01 -3.479296508982D-02 3.951762140637D-02 2 -3.712742175485D-02 3.782567517335D-02 -3.658223474024D-02 3 -9.582306874061D-03 -1.030473600466D-02 8.044191938471D-03 4 1.337505622469D-03 3.261828837170D-04 5.825308847532D-04 5 -2.564587290898D-04 1.167215404726D-04 -2.625484568114D-04 6 1.083049171042D-04 2.603250284906D-05 -2.172994325710D-05 7 -1.652237169896D-05 -8.358946327039D-06 9.583200142966D-06 8 7.926514417410D-07 5.226431312203D-07 -6.190692135710D-07 E-Index: 3 4 5 T-Index: 0 1.287791418429D-02 -6.337729479020D-03 1.170329931626D-03 1 -2.556830678726D-02 7.040128215489D-03 -9.992314993605D-04 2 1.632735440252D-02 -3.401365727621D-03 3.765651076870D-04 3 -3.131290915260D-03 5.532459754610D-04 -4.812308414974D-05 4 -3.168083167077D-04 7.594919813871D-05 -9.295628844487D-06 5 1.297679885878D-04 -2.681169439239D-05 2.486736935154D-06 6 2.967532719536D-06 -1.552348470032D-07 9.914557379237D-08 7 -3.107547721696D-06 5.261339241776D-07 -6.078003254539D-08 8 2.129711932150D-07 -3.682886859964D-08 3.943673329206D-09 E-Index: 6 7 8 T-Index: 0 -1.003471065764D-04 4.052095946656D-06 -6.254934022483D-08 1 7.419247879214D-05 -2.738645028702D-06 3.973261293345D-08 2 -2.252802392381D-05 6.849333710573D-07 -8.279262117799D-09 3 1.952561489849D-06 -2.606240633525D-08 -1.668491146428D-10 4 6.041299678217D-07 -1.989967163130D-08 2.616873567872D-10 5 -9.162513063487D-08 2.197291562634D-10 3.883962188438D-11 6 -1.959030711680D-08 1.270158481004D-09 -2.671947435341D-11 7 4.857708161457D-09 -2.162490178679D-10 3.822243417577D-12 8 -2.753763204013D-10 1.095025653423D-11 -1.798235585379D-13 Max. rel. Error: 3.8778 % Mean rel. Error: .7384 % \end{verbatim}\end{small} \begin{figure} \label{2.1.8rc} \epsfxsize=16truecm \epsffile{Amjuel_PS/hpn4fu.ps} \end{figure} \newpage \subsection{ Reaction 2.1.8d $H^+ + e \rightarrow H(1s) $, Ratio $H(5)/H^+$ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.896620907578D+01 8.263162726911D-01 2.453412310701D-01 1 -1.020472386996D+00 6.774681712067D-02 -9.359887389995D-02 2 -3.909076727301D-02 9.233229043428D-03 -6.811898776723D-03 3 -8.108346091837D-03 -1.114009915066D-02 7.784902980212D-03 4 1.019109955231D-03 2.143186124447D-03 -7.445628503896D-04 5 -3.832012105835D-04 7.665209835422D-04 -6.615105657343D-04 6 2.074862770456D-04 -4.323660314654D-04 3.084220743425D-04 7 -3.467034971602D-05 7.046871983203D-05 -5.074193286238D-05 8 1.826483263765D-06 -3.843166437506D-06 2.864841439776D-06 E-Index: 3 4 5 T-Index: 0 -1.095918159657D-01 2.352340764192D-02 -2.606799746665D-03 1 3.777179622766D-02 -7.435824927042D-03 7.370730125395D-04 2 5.541316826680D-03 -1.652672599440D-03 2.451627952732D-04 3 -3.103060845765D-03 6.334549501483D-04 -7.027215944854D-05 4 -4.194692950067D-06 5.637881977255D-05 -1.207354069047D-05 5 2.344290799663D-04 -4.452581583360D-05 4.741482394533D-06 6 -8.589872787033D-05 1.127548136764D-05 -6.664466414066D-07 7 1.398275288859D-05 -1.748270612401D-06 8.910652633496D-08 8 -8.177688767346D-07 1.076944846317D-07 -6.310685093478D-09 E-Index: 6 7 8 T-Index: 0 1.550006217168D-04 -4.720230271207D-06 5.795820807765D-08 1 -3.773216809044D-05 9.378701533392D-07 -8.638031636714D-09 2 -1.885289195306D-05 7.183528697382D-07 -1.073414499710D-08 3 4.215222394060D-06 -1.276305499861D-07 1.520731912855D-09 4 1.096969913038D-06 -4.657703480617D-08 7.564520027104D-10 5 -2.779296405890D-07 8.321497480007D-09 -9.899754662843D-11 6 6.572553261299D-09 8.982707823537D-10 -2.633081356088D-11 7 6.037786936012D-10 -2.111950717307D-10 5.235642212608D-12 8 6.366831945852D-11 8.080764312523D-12 -2.351015375046D-13 Max. rel. Error: 5.3024 % Mean rel. Error: .9480 % \end{verbatim}\end{small} \begin{figure} \label{2.1.8rd} \epsfxsize=16truecm \epsffile{Amjuel_PS/hpn5fu.ps} \end{figure} \newpage \subsection{ Reaction 2.1.8e $H^+ + e \rightarrow H(1s) $, Ratio $H(6)/H^+$ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.853134339900D+01 1.025762058140D+00 4.820359378086D-02 1 -1.057384296999D+00 -1.367338116022D-02 -3.351784927664D-02 2 -4.357129898325D-02 -7.394478242994D-03 2.206668060201D-02 3 -1.022068439636D-02 8.205900215515D-03 -9.593969669623D-03 4 2.240869860862D-03 -2.398078272359D-03 2.119411722051D-03 5 -2.845620700011D-04 1.159424639874D-04 -6.688436690039D-05 6 1.056461895367D-04 6.774788436258D-05 -6.199652445552D-05 7 -1.924352018053D-05 -1.263343934006D-05 1.111364886603D-05 8 1.083397517395D-06 6.663341827792D-07 -5.889621084106D-07 E-Index: 3 4 5 T-Index: 0 -3.882358720615D-02 1.237087286269D-02 -1.764105210919D-03 1 2.391618457883D-02 -7.152556397423D-03 9.907047976258D-04 2 -1.040668635206D-02 2.383766498799D-03 -2.822620365202D-04 3 3.186917464795D-03 -4.976528642770D-04 3.877389269379D-05 4 -5.566686572310D-04 5.664600566222D-05 -5.658026509008D-07 5 2.276886525280D-06 2.992207488831D-06 -6.105459843829D-07 6 1.913273349345D-05 -2.523727510933D-06 1.167652225992D-07 7 -3.255526057721D-06 4.051238507748D-07 -1.532222680198D-08 8 1.737855470748D-07 -2.223530055553D-08 9.525747219138D-10 E-Index: 6 7 8 T-Index: 0 1.262454385864D-04 -4.469205240312D-06 6.250167666694D-08 1 -6.978776837879D-05 2.446946729997D-06 -3.400752053390D-08 2 1.791903200774D-05 -5.823791297469D-07 7.631403828079D-09 3 -1.446134439476D-06 1.918944143993D-08 6.658988931422D-11 4 -2.818155986041D-07 1.813752401935D-08 -3.433445792332D-10 5 5.203793299428D-08 -2.092865649431D-09 3.247676557005D-11 6 2.465131736062D-09 -3.635425072620D-10 8.132197656808D-12 7 -8.118597627154D-10 7.842131310409D-11 -1.656179057643D-12 8 3.184540505918D-11 -3.747826185419D-12 8.214908508402D-14 Max. rel. Error: 2.9379 % Mean rel. Error: .6634 % \end{verbatim}\end{small} \begin{figure} \label{2.1.8re} \epsfxsize=16truecm \epsffile{Amjuel_PS/hpn6fu.ps} \end{figure} \newpage \subsection{ Reaction 2.1.8tot $H^+ + e \rightarrow H(1s) $, Ratio $H(tot)/H^+$ } \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.235624329253D+01 9.763145521833D-01 1.918330680061D-02 1 -1.439934055420D+00 -2.519401923047D-02 3.585508737762D-03 2 1.060215606120D-03 -1.118872464044D-03 1.720136583820D-03 3 2.244412354881D-03 -6.704475990451D-04 -6.699472886502D-04 4 5.982736693346D-05 1.208170153071D-06 1.246488800870D-04 5 -8.466861405156D-05 3.561208397089D-05 -1.494745309621D-05 6 1.175099184836D-05 -4.822515840160D-06 7.839022932286D-07 7 -7.023031296681D-07 2.948938110645D-07 -5.225388371277D-08 8 1.609249642095D-08 -8.845142466159D-09 3.899049823853D-09 E-Index: 3 4 5 T-Index: 0 -4.691259242713D-03 6.288351029702D-04 -5.107818695069D-05 1 -3.606855133841D-04 2.098139498792D-05 4.491184999788D-07 2 -5.631447161500D-04 1.107941690049D-04 -1.324767192387D-05 3 3.084892726230D-04 -6.392879662268D-05 7.279340567526D-06 4 -4.311535218313D-05 7.637892784584D-06 -7.417970337062D-07 5 6.008386349890D-07 3.291652198945D-07 -7.214543918759D-08 6 3.310641902198D-07 -9.636153557710D-08 1.224666378778D-08 7 -4.418889088947D-09 -5.755172852233D-10 2.933776480728D-10 8 -1.417759796908D-09 4.224902609944D-10 -6.257737712706D-11 E-Index: 6 7 8 T-Index: 0 2.511251181976D-06 -6.877740736899D-08 8.022672312302D-10 1 -1.748905208728D-07 1.096079038665D-08 -2.309525766240D-10 2 9.284121363830D-07 -3.520965065456D-08 5.652221180618D-10 3 -4.730061277373D-07 1.650428248605D-08 -2.440356698087D-10 4 4.087003980074D-08 -1.104737352197D-09 9.985107172732D-12 5 6.581760780626D-09 -3.342177330708D-10 7.477370951765D-12 6 -9.009824883694D-10 4.485057352449D-11 -1.092334989093D-12 7 -2.513282999634D-11 7.402108547860D-14 3.356083702441D-14 8 4.562227755580D-12 -1.394585520243D-13 9.622937037320D-16 Max. rel. Error: 3.0878 % Mean rel. Error: 0.2211 % \end{verbatim}\end{small} \begin{figure} \label{2.1.8rtot} \epsfxsize=16truecm \epsffile{Amjuel_PS/hydrc.ps} \end{figure} \newpage \subsection{ Reaction 2.1.8de $H^+ + e \rightarrow H(1s) $, \ $ + 13.6 \ [eV] $ } electron energy loss (radiative) due to one effective recombination. 13.6 eV (ionization potential) has to be subtracted, which may render the total electron loss negative, i.e., make it a gain. June17: Fit range extended from 0.1--1e3 to 0.1--2e4 \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 2.665899500132D+00 6.909524133474D-03 -1.016251787345D-02 1 3.234097857001D-02 -1.342936828253D-03 2.649709301973D-03 2 1.839736371673D-02 -4.543287906774D-04 4.049474254061D-04 3 1.721979500535D-02 -2.420941858648D-04 1.070964671190D-04 4 -1.634188788045D-06 1.272188632742D-04 -9.608788872527D-05 5 -1.354019822678D-03 5.547796579740D-06 1.885659127034D-06 6 3.103952150736D-04 -7.717377610260D-06 4.450028524311D-06 7 -2.813815821385D-05 1.049652451777D-06 -6.757200946909D-07 8 9.248132243469D-07 -4.314339279524D-08 2.916075421796D-08 E-Index: 3 4 5 T-Index: 0 4.785952485138D-03 -1.111528620197D-03 1.389338869715D-04 1 -1.417016315380D-03 3.507678014757D-04 -4.569145026078D-05 2 -9.053523602330D-05 1.610290448013D-06 2.067872533338D-06 3 -9.886490927616D-06 -1.137795705868D-06 2.009074194306D-07 4 2.503871421337D-05 -2.776557044750D-06 8.202377087937D-08 5 -1.899847063838D-06 3.608820989932D-07 -1.820175080726D-08 6 -8.590535929797D-07 6.494073446907D-08 -1.005495853368D-09 7 1.536224332903D-07 -1.526291610537D-08 5.443143280155D-10 8 -7.087510165394D-09 7.772501731042D-10 -3.490536063716D-11 E-Index: 6 7 8 T-Index: 0 -9.560728735427D-06 3.390700499449D-07 -4.846257262550D-09 1 3.245267105321D-06 -1.188371670550D-07 1.758631015908D-09 2 -2.955908411210D-07 1.631510169903D-08 -3.250767238535D-10 3 -5.336134881504D-09 -2.995961467613D-10 1.244053679153D-11 4 8.526944203010D-09 -7.591463931965D-10 1.735202334766D-11 5 -1.160792778179D-09 1.375444359851D-10 -3.427633513798D-12 6 -7.157425528109D-11 1.695155282725D-12 2.341575042551D-14 7 1.259157231611D-11 -1.469505460319D-12 3.084731172193D-14 8 -1.453313559078D-13 6.474896531735D-14 -1.572212991946D-15 Max. rel. Error: 0.331E+01 % Mean rel. Error: 0.927E+00 % \end{verbatim}\end{small} \begin{figure} \label{2.1.8lr2} \epsfxsize=16truecm \epsffile{Amjuel_PS/H12-2.1.8.eps} \end{figure} \newpage \subsection{ Reaction 2.1.8o $H^+ + e \rightarrow H(1s) $, \ $ + 13.6 \ [eV] $ Ly-opaque } electron energy loss (radiative) due to one effective recombination event. 13.6 eV (ionization potential) has to be subtracted, which may render the total electron loss negative, i.e., make it a gain. \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 3.332760890904D+00 2.276467542533D-02 -3.375104085272D-02 1 2.095607992432D+00 2.149640996135D-01 -2.163109435324D-01 2 -7.718235594111D-03 5.342318925152D-02 -3.826264614382D-02 3 -2.796028848568D-01 -5.076194843679D-02 4.211090303923D-02 4 4.114054656028D-02 1.167368824693D-03 -2.634010977122D-03 5 1.379031566337D-02 4.766103150116D-03 -3.140405264654D-03 6 -4.442827387044D-03 -1.168245938217D-03 8.103728635753D-04 7 4.466408723499D-04 1.067947114632D-04 -7.426869611152D-05 8 -1.550852684757D-05 -3.448224819513D-06 2.365214591310D-06 E-Index: 3 4 5 T-Index: 0 1.533294583406D-02 -2.993999791570D-03 2.625217527284D-04 1 8.513801946679D-02 -1.708115211759D-02 1.908032465874D-03 2 9.848556553690D-03 -1.198540836499D-03 7.289210776603D-05 3 -1.343364231895D-02 2.197734625605D-03 -2.020807399429D-04 4 1.540828008778D-03 -3.888233553638D-04 5.009886243915D-05 5 6.669070177773D-04 -4.301617499659D-05 -3.131696299090D-06 6 -1.953437642437D-04 1.957310765780D-05 -4.682020227901D-07 7 1.819420479360D-05 -1.913117253436D-06 6.213331827001D-08 8 -5.704392451980D-07 5.826373961407D-08 -1.634950425947D-09 E-Index: 6 7 8 T-Index: 0 -7.802660138687D-06 -1.578343346285D-07 8.885318650802D-09 1 -1.191827223971D-04 3.886108418638D-06 -5.149798003444D-08 2 -1.886829891317D-06 -4.065327740691D-09 7.815045054601D-10 3 1.049475835680D-05 -2.854931151940D-07 3.138820449657D-09 4 -3.454361952343D-06 1.217245343098D-07 -1.725312803637D-09 5 5.905901174405D-07 -3.001019530996D-08 5.223614921536D-10 6 -5.627862273723D-08 4.147493653191D-09 -8.140380486253D-11 7 3.646425627446D-09 -3.215059278414D-10 6.559359042393D-12 8 -1.392555515521D-10 1.101965822929D-11 -2.192243607759D-13 Max. rel. Error: 17.4151 % Mean rel. Error: 7.1827 % \end{verbatim}\end{small} \begin{figure} \label{2.1.8lr2o} \epsfxsize=16truecm \epsffile{Amjuel_PS/hydlr2_op.ps} \end{figure} \newpage \subsection{ Reaction 2.2a $e + He \rightarrow He^* $ Ratio $He(6)/He(1)$ } $3^1S$ state reduced population coefficients, formulation II, Coupling to groundstate, \cite{kn:Fujimoto}. For 728 nm line: $\rightarrow 2^1P$, A(6,4)=1.810629e7, dE=1.7023 eV \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -4.311315252344D+01 1.068788324945D+00 4.607816591604D-01 1 2.227727400968D+01 2.533246784559D-02 -4.171642913247D-01 2 -1.092526995496D+01 -3.147570844629D-02 1.875310957896D-01 3 3.455212456083D+00 -1.389486107084D-02 -4.063899942293D-02 4 -7.374015718678D-01 2.242933213868D-02 -2.420756303296D-03 5 1.038623596715D-01 -8.572063066145D-03 3.324173037175D-03 6 -9.192956530427D-03 1.455904553910D-03 -6.673595425546D-04 7 4.616742167799D-04 -1.160328883781D-04 5.534829062629D-05 8 -1.001260661416D-05 3.542757576830D-06 -1.685458944344D-06 E-Index: 3 4 5 T-Index: 0 -2.288516993884D-01 4.934442752394D-02 -5.604584821093D-03 1 1.615799989993D-01 -2.658923546753D-02 2.208439837134D-03 2 -6.250400889583D-02 7.917685175679D-03 -4.072650465024D-04 3 1.516486061778D-02 -1.624326286753D-03 3.323367272941D-05 4 -1.576970797070D-03 2.296103941475D-04 -2.793441980969D-06 5 -2.351628215299D-04 -3.805995868992D-06 -3.856178638492D-07 6 7.622121272510D-05 -2.414972618793D-06 3.145956146766D-08 7 -6.623209681071D-06 1.396329196910D-07 1.644463329342D-08 8 1.880631768107D-07 2.036496093646D-09 -1.449219917820D-09 E-Index: 6 7 8 T-Index: 0 3.438226618132D-04 -1.077128821245D-05 1.352276198706D-07 1 -9.431672141577D-05 1.862180588113D-06 -1.132114188246D-08 2 4.546258048294D-06 2.365213157088D-07 -4.976268161753D-09 3 2.722186667141D-06 -9.017760018097D-08 -4.904178184171D-10 4 -4.152461824776D-07 -6.241223808031D-09 8.068574923944D-10 5 6.209519268505D-08 1.441911748739D-09 -1.316978098635D-10 6 -3.356847387494D-09 -3.697594587912D-11 7.240088197508D-12 7 -9.792067155585D-10 2.164943531687D-11 -2.800778214544D-13 8 8.944524915556D-11 -2.169200058693D-12 1.817590942107D-14 Max. rel. Error: 4.7466 % Mean rel. Error: 1.8012 % \end{verbatim}\end{small} \begin{figure} \label{2.2a} \epsfxsize=16truecm \epsffile{Amjuel_PS/he2.2a.ps} \end{figure} \newpage \subsection{ Reaction 2.2b $e + He \rightarrow He^* $ Ratio $He(7)/He(1)$ } $3^3S$ state, reduced population coefficients, formulation II, Coupling to groundstate, \cite{kn:Fujimoto}. For 706 nm line: $\rightarrow 2^3P$, A(7,5)=2.76441e7, dE =1.75437 eV \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -4.007960997971D+01 9.034446644096D-01 1.165111771540D-01 1 2.144863586125D+01 1.947485468069D-01 -1.301067140494D-01 2 -1.062424949389D+01 -2.036865355513D-01 1.502619709740D-01 3 3.274440069862D+00 6.002917850635D-02 -4.500559725551D-02 4 -6.910270587692D-01 -5.778030255527D-03 6.133919377226D-03 5 9.696455049644D-02 -3.615838261304D-04 -5.591761507584D-04 6 -8.558419026409D-03 1.372863071237D-04 3.079519906206D-05 7 4.299591264600D-04 -1.352177886718D-05 1.363347413015D-06 8 -9.396794815079D-06 5.081568411364D-07 -1.918622684719D-07 E-Index: 3 4 5 T-Index: 0 -2.597504506357D-02 1.439511190742D-04 5.735113536484D-04 1 -1.134174339750D-03 8.934529257747D-03 -1.672264590109D-03 2 -2.435598894352D-02 2.959994394968D-04 2.087336754163D-04 3 5.473014417323D-03 9.912931702266D-05 -3.121815866488D-05 4 -1.569913055752D-04 -1.068830646003D-04 5.591339866244D-06 5 3.468442843104D-05 -7.773486473364D-06 2.269135973852D-06 6 -1.109174473451D-05 3.766577588319D-06 -4.517137662136D-07 7 1.823956910222D-07 -1.482530106434D-07 6.084462068041D-09 8 4.597529153937D-08 -7.085546973595D-09 1.411547564036D-09 E-Index: 6 7 8 T-Index: 0 -7.136082319245D-05 3.362863636423D-06 -5.629721496083D-08 1 1.290346463406D-04 -4.579314176342D-06 6.164974848265D-08 2 -1.619346650396D-05 3.859684910385D-07 -1.226364851070D-09 3 -4.970042343218D-07 1.575739269032D-07 -4.434371121129D-09 4 4.546393179958D-07 -4.580471294432D-08 1.080771415075D-09 5 -1.879528911353D-07 6.906966394218D-09 -1.112570278287D-10 6 1.591625909374D-08 3.622976767180D-11 -6.002477025919D-12 7 1.509097136492D-09 -1.196127739728D-10 2.320887234439D-12 8 -1.631586971717D-10 7.893728865910D-12 -1.311109499334D-13 Max. rel. Error: 5.3070 % Mean rel. Error: 1.9605 % \end{verbatim}\end{small} \begin{figure} \label{2.2b} \epsfxsize=16truecm \epsffile{Amjuel_PS/he2.2b.ps} \end{figure} \newpage \subsection{ Reaction 2.2c $e + He \rightarrow He^* $ Ratio $He(8)/He(1)$ } $3^1P$ state, reduced population coefficients, formulation II, Coupling to groundstate, \cite{kn:Fujimoto}. For 501 nm line: $\rightarrow 2^1S$, A(8,2)=1.35143E7, dE = 2.47126 eV \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -4.653397136053D+01 1.061565404274D+00 1.538213466570D-01 1 2.341040126523D+01 -2.338924405778D-01 -1.620037152343D-01 2 -1.139498311209D+01 3.614149800761D-01 1.852266870603D-02 3 3.614773239756D+00 -2.470591133234D-01 1.639517537700D-02 4 -7.802147409864D-01 9.652798837959D-02 -1.139696161330D-02 5 1.129731936040D-01 -2.211800736270D-02 3.415302206693D-03 6 -1.046003037564D-02 2.894859026350D-03 -5.216830627677D-04 7 5.566146923182D-04 -1.990551598260D-04 3.914361279505D-05 8 -1.287797826551D-05 5.559558313857D-06 -1.141508901494D-06 E-Index: 3 4 5 T-Index: 0 -4.960776358631D-02 3.721007453372D-03 4.129592286060D-04 1 7.079138649586D-02 -1.107648995898D-02 7.955218807596D-04 2 -2.002227448100D-02 2.516435028232D-03 -8.077169032818D-05 3 4.996213760875D-03 -6.235419082909D-04 5.622895177211D-06 4 -8.188564258666D-04 1.489938947126D-04 -1.639651945413D-06 5 5.788680997946D-06 -1.848630429871D-05 -2.817393417179D-07 6 1.476821784698D-05 1.555280785423D-06 2.630583281095D-08 7 -1.461225058243D-06 -1.566386546423D-07 1.078484737480D-08 8 3.755714180141D-08 8.635247245624D-09 -9.744421400623D-10 E-Index: 6 7 8 T-Index: 0 -7.595441650236D-05 3.938916077091D-06 -6.904203416831D-08 1 -2.492979564442D-05 1.479965187751D-07 5.129381943121D-09 2 -3.279337614319D-06 2.317424648906D-07 -3.212001663062D-09 3 1.149833159917D-06 -1.744164295894D-09 -1.271403337443D-09 4 -1.099736125961D-07 -1.622513539030D-08 7.323542946653D-10 5 6.181107684745D-08 1.189086401587D-09 -1.030873863310D-10 6 -8.335949262711D-09 5.417107113342D-11 6.544932959532D-12 7 -2.073967263488D-10 1.158671282787D-11 -4.346356593657D-13 8 4.965186141757D-11 -1.582356159149D-12 2.463828951285D-14 Max. rel. Error: 4.4334 % Mean rel. Error: 1.0452 % \end{verbatim}\end{small} \begin{figure} \label{2.2c} \epsfxsize=16truecm \epsffile{Amjuel_PS/he2.2c.ps} \end{figure} \newpage \subsection{ Reaction 2.2d $e + He \rightarrow He^* $ Ratio $He(10)/He(1)$ } $3^1D$ state, reduced population coefficients, formulation II, Coupling to groundstate, \cite{kn:Fujimoto}. For 667 nm line: $\rightarrow 2^1P$, A(10,4)=6.27547e7, dE = 1.8561 eV \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -4.387462178720D+01 1.297729348975D+00 2.171426368859D-01 1 2.231897245990D+01 -7.254021696102D-02 -2.818676964157D-01 2 -1.103840904811D+01 8.933431516828D-03 1.084333935229D-01 3 3.439678364969D+00 8.110861039861D-03 -1.419780536561D-02 4 -7.194379330234D-01 -7.617376918719D-03 -7.804052035737D-04 5 9.977541313333D-02 2.492457513616D-03 4.151471795535D-04 6 -8.744899237837D-03 -3.818311009548D-04 -5.656979814142D-05 7 4.364458313084D-04 2.772577703683D-05 4.646402252581D-06 8 -9.420938125153D-06 -7.681794402039D-07 -1.810036079763D-07 E-Index: 3 4 5 T-Index: 0 -1.227267686184D-01 2.684569500768D-02 -3.084104019669D-03 1 1.283426585873D-01 -2.558157078407D-02 2.736593361910D-03 2 -4.640225933795D-02 8.670127027232D-03 -8.320926095332D-04 3 6.159942757994D-03 -1.210673774922D-03 1.034347467373D-04 4 2.605016526459D-04 3.287984864674D-05 -4.952370009630D-06 5 -1.787934297272D-04 7.093030346467D-06 1.042617033617D-06 6 2.864168088776D-05 -1.737189312029D-06 -1.314488727944D-07 7 -2.630470520737D-06 2.699291231064D-07 -6.034998122757D-09 8 1.046366140500D-07 -1.472124741829D-08 9.766999701447D-10 E-Index: 6 7 8 T-Index: 0 1.927330419368D-04 -6.192457335223D-06 8.013020564099D-08 1 -1.625900542113D-04 5.035250553353D-06 -6.326313962119D-08 2 4.258487531484D-05 -1.078934966891D-06 1.012644792468D-08 3 -3.461954139324D-06 -8.569915050105D-09 2.035476745628D-09 4 -6.887941807259D-08 2.782454606073D-08 -8.823571239501D-10 5 -7.282533905038D-08 -7.826443302463D-10 9.734519877427D-11 6 1.515466306533D-08 -2.609983592228D-10 -5.766562927060D-12 7 -2.777752615430D-10 -1.005417881311D-12 5.711155616810D-13 8 -4.089947705610D-11 1.537624472911D-12 -3.487131096914D-14 Max. rel. Error: 4.2913 % Mean rel. Error: 1.0561 % \end{verbatim}\end{small} \begin{figure} \label{2.2d} \epsfxsize=16truecm \epsffile{Amjuel_PS/he2.2d.ps} \end{figure} \newpage \subsection{ Reaction 2.2e $e + He \rightarrow He^* $ Ratio $He(16)/He(1)$ } $4^1D$ state, reduced population coefficients, formulation II, Coupling to groundstate, \cite{kn:Fujimoto} . For 492 nm line: $\rightarrow 2^1P$, A(16,4)=1.95062E7, dE = 2.5183 eV \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -4.471883009004D+01 1.379902734939D+00 -1.588304426869D-02 1 2.301803742916D+01 -4.112391837175D-01 4.020010647943D-02 2 -1.142290678089D+01 2.325073124471D-01 -2.363867774084D-02 3 3.584520289665D+00 -9.292301814148D-02 1.399795303239D-02 4 -7.588759927163D-01 2.769660867165D-02 -5.996411152428D-03 5 1.071981413506D-01 -5.846876265058D-03 1.730779175387D-03 6 -9.623807639587D-03 7.555908490695D-04 -2.665737696024D-04 7 4.938446976776D-04 -5.141246970493D-05 1.928578993317D-05 8 -1.097930969158D-05 1.395884806885D-06 -5.127774120276D-07 E-Index: 3 4 5 T-Index: 0 1.102005327143D-03 -2.776453047428D-03 5.951669267394D-04 1 -7.083881196314D-03 3.184653460498D-03 -5.939046552980D-04 2 2.183867697930D-04 -5.291800815389D-04 1.705675041358D-04 3 1.229903491947D-04 -5.697630240547D-05 -2.236164784844D-05 4 4.993998679121D-05 7.400566057679D-05 -3.844211220285D-06 5 -1.193787781320D-04 -6.321252008286D-06 5.997152437237D-07 6 2.840484021461D-05 -8.190964593875D-07 3.074212731682D-08 7 -2.172661190110D-06 5.852557117498D-08 9.693636966803D-10 8 4.622655761109D-08 2.165754381744D-09 -5.193903473398D-10 E-Index: 6 7 8 T-Index: 0 -5.438344417754D-05 2.323368482605D-06 -3.790056253508D-08 1 4.958874975704D-05 -1.935263751082D-06 2.888456240999D-08 2 -1.624226089828D-05 6.305375766051D-07 -8.706585722074D-09 3 2.531455667103D-06 -7.702409620971D-08 4.463396284857D-10 4 5.210309715124D-08 -6.836232292167D-09 2.958879358471D-10 5 -1.506763120215D-08 1.252708957129D-09 -4.685561440635D-11 6 -3.582721370055D-09 8.034963393881D-11 9.950344146148D-13 7 7.970509295800D-12 -1.219308703370D-12 -3.005051437224D-14 8 3.149843951988D-11 -9.361514367135D-13 1.191949633363D-14 Max. rel. Error: 3.6319 % Mean rel. Error: 1.2457 % \end{verbatim}\end{small} \begin{figure} \label{2.2e} \epsfxsize=16truecm \epsffile{Amjuel_PS/he2.2e.ps} \end{figure} \newpage \subsection{ Reaction 2.3.2a $e + He^+ \rightarrow He^* $ Ratio $He(6)/He^+$ } $3^1S$ state reduced population coefficients, formulation II, Coupling to He$^+$, \cite{kn:Fujimoto}. For 728 nm line: $\rightarrow 2^1P$, A(6,4)=1.810629e7, dE=1.7023 eV \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.216150314541D+01 1.017126728848D+00 2.503192212525D-01 1 2.472997234218D+00 -6.604244815764D-01 4.447853197254D-01 2 -7.273641530992D+00 6.512267559345D-01 -3.697133484751D-01 3 6.312899128558D+00 -3.221127513661D-01 1.407336611903D-01 4 -2.475271968793D+00 9.628490082958D-02 -3.860831119148D-02 5 5.141511842314D-01 -1.679217364205D-02 6.622911077550D-03 6 -5.911906094824D-02 1.521368851222D-03 -4.758101424176D-04 7 3.565096703678D-03 -5.540747253127D-05 -4.988643158537D-06 8 -8.814835329708D-05 1.000054107875D-07 1.442316009145D-06 E-Index: 3 4 5 T-Index: 0 -1.573779795630D-01 4.193259536500D-02 -5.714327145825D-03 1 -1.373512721569D-01 2.642773580772D-02 -3.333243832771D-03 2 8.180617352023D-02 -1.194178092608D-02 1.504343740838D-03 3 -1.575910145395D-02 -4.261270008957D-04 1.160434934873D-04 4 4.321891266732D-03 1.535428208875D-04 -5.462458572233D-05 5 -1.141504489899D-03 1.088062290891D-04 -6.933905317108D-06 6 9.243986342244D-05 -1.491809640805D-05 1.546659340673D-06 7 4.349712967453D-06 -5.545082995129D-07 3.861187877207D-08 8 -5.722874156419D-07 9.632513971858D-08 -9.509739163118D-09 E-Index: 6 7 8 T-Index: 0 4.136519317417D-04 -1.509799360230D-05 2.184621419674D-07 1 2.515045346534D-04 -1.007775905926D-05 1.635743918463D-07 2 -1.333316361152D-04 6.445989555292D-06 -1.234698479875D-07 3 2.714541315649D-06 -8.940705316636D-07 2.952675110887D-08 4 2.756655915997D-06 6.165051309359D-08 -5.082966020137D-09 5 3.178875894924D-07 -2.390667896507D-08 8.828419978172D-10 6 -7.331886684615D-08 2.614867580638D-09 -7.330106832639D-11 7 -4.023931989434D-09 1.812490590825D-10 -1.428342946112D-12 8 6.381564120008D-10 -2.352182090998D-11 3.197916618777D-13 Max. rel. Error: 23.9646 % Mean rel. Error: 6.2722 % \end{verbatim}\end{small} \begin{figure} \label{2.3.2a} \epsfxsize=16truecm \epsffile{Amjuel_PS/he2.3.2a.ps} \end{figure} \newpage \subsection{ Reaction 2.3.2b $e + He^+ \rightarrow He^* $ Ratio $He(7)/He^+$ } $3^3S$ state, reduced population coefficients, formulation II, Coupling to He$^+$, \cite{kn:Fujimoto}. For 706 nm line: $\rightarrow 2^3P$, A(7,5)=2.76441e7, dE =1.75437 eV \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.021804030158D+01 1.130848334651D+00 -1.073740464502D-01 1 3.523368969674D+00 -5.478378025513D-01 6.458417120865D-01 2 -8.974598355857D+00 3.778216418622D-01 -5.081928217917D-01 3 7.635897546212D+00 -9.147403628179D-02 1.662078021034D-01 4 -3.000303742731D+00 -9.002194876928D-03 -1.863105119205D-02 5 6.285699508085D-01 9.416908796340D-03 -3.038866915586D-03 6 -7.304205616620D-02 -1.989766581715D-03 1.144474905838D-03 7 4.453488758391D-03 1.821308292697D-04 -1.240908829743D-04 8 -1.113155471497D-04 -6.266781207601D-06 4.673905317880D-06 E-Index: 3 4 5 T-Index: 0 4.970170535549D-02 -1.165239967844D-02 1.510313083106D-03 1 -2.735061111112D-01 5.462012224337D-02 -5.869531956065D-03 2 2.064807405621D-01 -3.532912576039D-02 3.081608767454D-03 3 -7.412844397846D-02 1.064378821100D-02 -5.813109620435D-04 4 1.464638881441D-02 -1.982598876641D-03 5.279445200867D-05 5 -1.322561156054D-03 2.390586823075D-04 -8.306640146040D-06 6 -3.560089264490D-05 -1.201538636649D-05 1.411823544331D-06 7 1.602474940002D-05 -6.171115568805D-07 -8.146917989801D-08 8 -8.353650874253D-07 6.599657419719D-08 2.416556483484D-10 E-Index: 6 7 8 T-Index: 0 -1.081306838597D-04 3.980420063002D-06 -5.865611960494D-08 1 3.455835282567D-04 -1.051504918041D-05 1.297001161406D-07 2 -1.414786677129D-04 3.275747814089D-06 -3.119868249308D-08 3 1.147245647095D-06 8.409794703428D-07 -1.823740755654D-08 4 6.867272943685D-06 -4.730788976909D-07 8.026049328029D-09 5 -7.306589669632D-07 5.266691013685D-08 -8.117214675526D-10 6 -6.030271577709D-08 1.815641913753D-09 -4.671055888097D-11 7 1.133396885188D-08 -5.820505536000D-10 1.163064737956D-11 8 -3.847614776613D-10 2.391347375446D-11 -4.850942377843D-13 Max. rel. Error: 23.6466 % Mean rel. Error: 6.3388 % \end{verbatim}\end{small} \begin{figure} \label{2.3.2b} \epsfxsize=16truecm \epsffile{Amjuel_PS/he2.3.2b.ps} \end{figure} \newpage \subsection{ Reaction 2.3.2c $e + He^+ \rightarrow He^* $ Ratio $He(8)/He^+$ } $3^1P$ state, reduced population coefficients, formulation II, Coupling to He$^+$, \cite{kn:Fujimoto}. For 501 nm line: $\rightarrow 2^1S$, A(8,2)=1.35143E7 dE = 2.47126 eV \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.445572948968D+01 1.137519254060D+00 -1.204158609891D-01 1 2.775136339237D+00 -4.487673567858D-01 4.037515904078D-01 2 -9.482806590562D+00 5.618314205781D-01 -3.914168608519D-01 3 8.753415720243D+00 -3.569019076961D-01 1.753910146247D-01 4 -3.577960912550D+00 1.343719586718D-01 -5.423186626416D-02 5 7.706325166736D-01 -2.952144452037D-02 1.111018961085D-02 6 -9.158735526626D-02 3.628637458935D-03 -1.291959720425D-03 7 5.693572104634D-03 -2.288531778507D-04 7.302736513118D-05 8 -1.447822452674D-04 5.723900429738D-06 -1.455648868887D-06 E-Index: 3 4 5 T-Index: 0 5.518321955152D-02 -1.275404675701D-02 1.567946643590D-03 1 -1.505032740194D-01 3.105545096940D-02 -3.891527004898D-03 2 1.175987658408D-01 -2.021206967023D-02 2.440969566947D-03 3 -3.667084372893D-02 2.854422446911D-03 -1.660305334064D-04 4 9.559862125182D-03 -9.162545378146D-05 -8.032611295151D-05 5 -2.147001210922D-03 7.977007897719D-05 8.625984135551D-06 6 2.735972256964D-04 -1.938645862420D-05 6.853343303742D-07 7 -1.532878284339D-05 1.233959442253D-06 -9.081746795921D-08 8 2.445107599088D-07 -1.001706708366D-08 1.073020722799D-09 E-Index: 6 7 8 T-Index: 0 -1.004500270631D-04 3.178038428972D-06 -3.936121532969D-08 1 2.854040739913D-04 -1.113667661675D-05 1.772401326973D-07 2 -1.919209138406D-04 8.352922848971D-06 -1.483995437185D-07 3 1.763502677889D-05 -1.312005258433D-06 3.373289875724D-08 4 5.629040165925D-06 -5.258717216470D-08 -3.151242886886D-09 5 -7.699661573237D-07 7.542813546822D-09 5.034382828487D-10 6 -3.749930108264D-08 3.406483389911D-09 -1.104413275874D-10 7 7.612336214085D-09 -4.287524304739D-10 9.944501803630D-12 8 -1.818784682827D-10 1.208359092107D-11 -2.808344024957D-13 Max. rel. Error: 25.0250 % Mean rel. Error: 6.9230 % \end{verbatim}\end{small} \begin{figure} \label{2.3.2c} \epsfxsize=16truecm \epsffile{Amjuel_PS/he2.3.2c.ps} \end{figure} \newpage \subsection{ Reaction 2.3.2d $e + He^+ \rightarrow He^* $ Ratio $He(10)/He^+$ } $3^1D$ state, reduced population coefficients, formulation II, Coupling to He$^+$, \cite{kn:Fujimoto}. For 667 nm line: $\rightarrow 2^1P$, A(10,4)=6.27547e7, dE = 1.8561 eV \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.192508131204D+01 7.730604480077D-01 3.913705333191D-01 1 2.828623875238D+00 3.043166975331D-01 -5.394294436435D-01 2 -1.094286352161D+01 4.449752413106D-01 5.999182478623D-02 3 1.052099366893D+01 -7.603297466416D-01 3.020794746641D-01 4 -4.404840999690D+00 3.789883977105D-01 -1.864822739530D-01 5 9.659859829733D-01 -8.886124374969D-02 4.574019828906D-02 6 -1.164625241195D-01 1.078353226216D-02 -5.432191040269D-03 7 7.324584132923D-03 -6.529437247704D-04 3.049402440492D-04 8 -1.880391228394D-04 1.553160134143D-05 -6.266500198751D-06 E-Index: 3 4 5 T-Index: 0 -1.895103722167D-01 4.458135648534D-02 -5.670836879252D-03 1 3.196979542189D-01 -7.857255265840D-02 9.520006805526D-03 2 -2.102789422795D-01 6.659906282329D-02 -8.539428018247D-03 3 1.669978165448D-02 -2.112215942331D-02 3.118385995004D-03 4 2.327397267002D-02 1.834729531187D-03 -4.527735068892D-04 5 -7.557858145939D-03 1.796130918335D-04 2.396527075095D-05 6 8.888503829029D-04 -2.025043121277D-05 -2.255417061932D-06 7 -3.985563239078D-05 -2.090429714735D-06 4.928756876729D-07 8 3.268393543240D-07 2.036815496667D-07 -2.933925056569D-08 E-Index: 6 7 8 T-Index: 0 3.963745460112D-04 -1.424905218920D-05 2.052965619067D-07 1 -6.049392469505D-04 1.923558499837D-05 -2.397863109992D-07 2 5.302906384868D-04 -1.548203816799D-05 1.630918993190D-07 3 -1.871228014319D-04 4.525444542407D-06 -2.484052167901D-08 4 2.215031871253D-05 -3.969555753912D-09 -1.502410481834D-08 5 5.050715387567D-07 -1.944403098333D-07 6.132124950693D-09 6 -1.681357574652D-07 2.937982495017D-08 -8.509572249650D-10 7 -8.155554263527D-09 -1.366419067606D-09 4.898820258533D-11 8 1.198416940460D-09 5.339525486382D-12 -9.014052780522D-13 Max. rel. Error: 28.7561 % Mean rel. Error: 8.5118 % \end{verbatim}\end{small} \begin{figure} \label{2.3.2d} \epsfxsize=16truecm \epsffile{Amjuel_PS/he2.3.2d.ps} \end{figure} \newpage \subsection{ Reaction 2.3.2e $e + He^+ \rightarrow He^* $ Ratio $He(16)/He^+$ } $4^1D$ state, reduced population coefficients, formulation II, Coupling to He$^+$, \cite{kn:Fujimoto}. For 492 nm line: $\rightarrow 2^1P$, A(16,4)=1.95062E7, dE = 2.5183 eV \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.188482573905D+01 8.610245311120D-01 -7.871637904226D-02 1 9.933879030912D-01 2.266459651326D+00 -9.472857315400D-01 2 -7.486546162203D+00 -3.150308486050D+00 1.212822565689D+00 3 7.834652212756D+00 1.901758352641D+00 -6.605089155304D-01 4 -3.347990149324D+00 -6.248586863904D-01 2.007495980841D-01 5 7.366886873864D-01 1.190475683473D-01 -3.602551009154D-02 6 -8.864057763980D-02 -1.309846016686D-02 3.760565403015D-03 7 5.555256683180D-03 7.711297791954D-04 -2.099326142463D-04 8 -1.421052566331D-04 -1.878580877217D-05 4.822799528233D-06 E-Index: 3 4 5 T-Index: 0 1.007691814520D-01 -3.094881651282D-02 4.360394656253D-03 1 1.590010861827D-01 -1.031249533204D-02 -2.061971584679D-04 2 -2.039503541069D-01 1.940627970159D-02 -1.269842997337D-03 3 9.150327990878D-02 -6.639386857171D-03 3.547850561263D-04 4 -2.342313204830D-02 1.172376176842D-03 -2.311168366669D-05 5 3.768569485892D-03 -1.588304810091D-04 -2.066241218916D-07 6 -3.706654458246D-04 1.841194915725D-05 -4.050823848900D-07 7 1.996960560623D-05 -1.358423173826D-06 7.836592920988D-08 8 -4.433571946131D-07 4.149590065641D-08 -3.556757547808D-09 E-Index: 6 7 8 T-Index: 0 -3.145292638212D-04 1.131115258763D-05 -1.610863865001D-07 1 6.454814129154D-05 -3.308023119594D-06 5.784207966726D-08 2 6.690737638410D-05 -2.294961757856D-06 3.201017904975D-08 3 -2.521266112731D-05 1.253726502750D-06 -2.225943158869D-08 4 3.096507943757D-06 -2.590646481613D-07 5.452184158491D-09 5 -2.280634231739D-07 3.149850598031D-08 -6.947518389720D-10 6 3.729749615530D-08 -2.770965878183D-09 4.800254654826D-11 7 -4.762215328192D-09 1.745304400761D-10 -1.658813624438D-12 8 2.026923384162D-10 -5.318966772198D-12 2.100743151512D-14 Max. rel. Error: 37.7911 % Mean rel. Error: 6.9227 % \end{verbatim}\end{small} \begin{figure} \label{2.3.2e} \epsfxsize=16truecm \epsffile{Amjuel_PS/he2.3.2e.ps} \end{figure} \newpage \subsection{ Reaction 2.3.9a $He(1s^21S) + e \rightarrow He^+(1s) + 2e $ \ $ \ [eV] $ } electron energy loss (radiative plus potential) due to one effective ionization. \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 6.833598031940D+00 -2.581591750171D-01 3.002724552043D-01 1 -3.963803034848D+00 1.083742817806D-01 -2.185819272140D-01 2 2.340984418775D+00 7.960301860904D-02 -2.380541593246D-02 3 -8.720605342433D-01 -2.187065734893D-02 4.335409780587D-02 4 2.151914370389D-01 -2.025747886335D-02 -6.222418098960D-03 5 -3.480057305671D-02 1.039843241545D-02 -1.466657569917D-03 6 3.519085971631D-03 -1.896269271396D-03 4.723390036919D-04 7 -2.005331697724D-04 1.550021181454D-04 -4.460430898110D-05 8 4.890032176597D-06 -4.783948237900D-06 1.434239402361D-06 E-Index: 3 4 5 T-Index: 0 -1.562968002089D-01 3.804132257792D-02 -4.819950771068D-03 1 1.380891687214D-01 -3.493851885048D-02 4.336864850281D-03 2 -2.233168326792D-02 8.567898287243D-03 -1.135198845537D-03 3 -9.017359555794D-03 4.146449794934D-04 2.229593440360D-05 4 2.872369142740D-03 -3.563116903860D-04 2.183046296448D-05 5 -1.004362351325D-04 2.650562392977D-05 -1.006835018389D-06 6 -4.170965146914D-05 1.520955505512D-06 -1.199396957406D-07 7 4.727045263171D-06 -1.341691381461D-07 -9.067558155258D-09 8 -1.408579120961D-07 -2.631952383725D-09 1.504095408373D-09 E-Index: 6 7 8 T-Index: 0 3.251351974739D-04 -1.108119967409D-05 1.502088801630D-07 1 -2.788751037407D-04 8.919934156922D-06 -1.121476666732D-07 2 6.881062206346D-05 -1.901589536293D-06 1.850790588779D-08 3 -1.237210702996D-06 -5.350049703101D-08 2.614670721314D-09 4 -8.649474896814D-07 2.477033243810D-08 -3.749285231265D-10 5 -7.916173274377D-08 7.346267688694D-09 -1.619067607087D-10 6 2.102619442307D-08 -1.402551865343D-09 3.013612509314D-11 7 2.537560484891D-10 3.296713149429D-11 -1.211004021082D-12 8 -1.050110011758D-10 2.672317014529D-12 -1.734344850181D-14 Max. rel. Error: 4.8670 % Mean rel. Error: .4586 % \end{verbatim}\end{small} \begin{figure} \label{2.3.9aec} \epsfxsize=16truecm \epsffile{Amjuel_PS/heliaecc.ps} \end{figure} \newpage \subsection{ Reaction 2.3.13a $e + He^+(1s) \rightarrow He(1s^21S)+ hv $ \ $+24.58 \ [eV]$ } electron energy loss (radiative plus potential) due to one effective recombination. 24.586 eV (ionization potential) has to be subtracted, which may render the total electron loss negative, i.e., make it a gain. \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 3.433913136981D+00 -4.838690601594D-03 -3.012005651151D-03 1 3.571941963713D-01 1.366702629693D-01 4.305394970015D-03 2 -1.878217847962D+00 -2.687159886881D-01 3.681576112685D-02 3 2.424802386624D+00 1.668555927113D-01 -1.489289566691D-02 4 -1.167489860199D+00 -3.968312198499D-02 -5.806242392586D-03 5 2.785216165202D-01 2.794413323851D-03 3.748295131357D-03 6 -3.549870765089D-02 3.061971808105D-04 -6.964994225616D-04 7 2.325006625009D-03 -5.536285155093D-05 5.514149047897D-05 8 -6.167011906326D-05 2.237779310326D-06 -1.602672918010D-06 E-Index: 3 4 5 T-Index: 0 4.897530083159D-03 -1.501012076471D-03 1.946127138348D-04 1 -2.542692753033D-02 8.618718418466D-03 -1.155324896611D-03 2 4.404690243381D-03 -4.417465105562D-03 6.541649981092D-04 3 5.027112091534D-03 2.212796313573D-04 -6.372305615527D-05 4 -1.157260624154D-03 9.661422893980D-05 -7.830966474304D-06 5 -7.990778489925D-05 -5.166337856831D-06 5.389604603452D-07 6 3.596656976635D-05 1.433564986542D-07 1.512821193564D-08 7 -2.512892127544D-06 -2.280106015151D-07 1.957605446858D-08 8 3.299538986852D-08 1.871390766422D-08 -1.821480547627D-09 E-Index: 6 7 8 T-Index: 0 -1.279526998241D-05 4.198553031308D-07 -5.453125267641D-09 1 7.588474563611D-05 -2.435602148969D-06 3.048074124737D-08 2 -4.062514764122D-05 1.126080643711D-06 -1.084879079455D-08 3 1.646788579650D-06 1.017675408347D-07 -3.909525540561D-09 4 1.221818458812D-06 -7.525537630546D-08 1.491574341448D-09 5 -5.819508932994D-08 1.849145077320D-09 -1.280524821596D-12 6 -1.800399945032D-08 1.587416635024D-09 -3.976884843047D-11 7 1.171329251871D-09 -1.635594061798D-10 4.324427772952D-12 8 1.868229185881D-11 4.166329792374D-12 -1.347143462455D-13 Max. rel. Error: 22.5154 % Mean rel. Error: 7.8340 % \end{verbatim}\end{small} \begin{figure} \label{2.3.13aec} \epsfxsize=16truecm \epsffile{Amjuel_PS/helraecc.ps} \end{figure} \newpage \subsection{ Reaction 2.6A0 $C + e \rightarrow C^+ + 2e $ \ $ [eV] $ } electron energy loss (radiative+potential) due to one effective ionization. \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 9.498032398433D+00 -1.819265937462D+00 5.796344005492D-01 1 -2.316370818977D+00 -1.912413251967D+00 5.639266856065D-01 2 2.320704120275D+00 7.593550209141D-01 -2.384731751044D-01 3 -1.423469978730D+00 -3.888330744867D-02 1.868782289925D-02 4 4.441710451586D-01 -1.408402765701D-02 4.609271425672D-04 5 -8.198134345687D-02 3.816981348123D-03 -1.201041388569D-04 6 9.025343419623D-03 -5.956250281350D-04 3.460685141518D-05 7 -5.421408064934D-04 5.242557410997D-05 -5.660290060134D-06 8 1.358691589766D-05 -1.845719396806D-06 2.798854323430D-07 E-Index: 3 4 5 T-Index: 0 -9.876225428908D-02 7.923470670427D-03 -1.889758400029D-04 1 -7.502544061825D-02 4.301133626753D-03 1.263821297128D-04 2 3.513874434013D-02 -2.722831770062D-03 5.261936992701D-05 3 -2.516467231041D-03 1.815314237493D-04 -3.776094914794D-07 4 -5.595871698878D-05 1.172374862061D-05 -1.427876732685D-06 5 -9.049612725058D-06 -2.823320281538D-07 1.856100050999D-07 6 8.873065193751D-07 -1.786247323757D-07 6.579947427433D-09 7 2.934330556330D-07 5.202583801575D-09 -2.631835360203D-09 8 -2.439978518785D-08 7.004344333195D-10 1.000272415897D-10 E-Index: 6 7 8 T-Index: 0 -1.022904037358D-05 5.840788152953D-07 -6.375736799139D-09 1 -3.427310072061D-05 1.885339856267D-06 -3.505352276047D-08 2 6.880039401864D-06 -4.536973415974D-07 7.687829752307D-09 3 -3.936336799962D-07 -1.180564243948D-08 1.277731900255D-09 4 -4.740152838620D-08 1.512393664320D-08 -5.903109943091D-10 5 -1.544365666000D-09 -1.278608019932D-09 6.083549010546D-11 6 2.900458497992D-11 4.157695298962D-12 -1.518435981756D-12 7 1.539892599330D-10 -6.042934507312D-13 -4.298624172985D-14 8 -9.023325396014D-12 1.668395598922D-13 7.457156257137D-16 Max. rel. Error: 10.0848 % Mean rel. Error: 3.3383 % \end{verbatim}\end{small} \begin{figure} \label{2.3.6il1} \epsfxsize=16truecm \epsffile{Amjuel_PS/carbil1.ps} \end{figure} \newpage \subsection{ Reaction 2.3.6A0 $C^+ + e \rightarrow C $ \ $ +11.3 \ [eV] $ } electron energy loss (radiative) due to one effective recombination. For the total electron energy loss, 11.3 eV (potential) have to be subtracted, which may render the loss negative, i.e., make it a gain. \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 6.453628189480D+00 -3.411959121202D+00 1.027601643412D+00 1 5.566257359499D+00 -2.827487978046D+00 1.323581114195D+00 2 7.023144782419D-02 -8.719987617388D-01 2.676321249963D-01 3 -1.612434026349D-01 1.081834795086D-01 -7.116653339183D-02 4 6.539562167664D-02 4.139385617180D-02 2.769162614331D-03 5 -2.206442445551D-02 -7.840262448517D-03 -9.995675347671D-04 6 2.871920422343D-03 8.502276174927D-04 1.251507934880D-04 7 -1.549156846628D-04 -6.373587175654D-05 -3.129721638855D-06 8 3.278924523113D-06 1.670923171850D-06 8.554676549572D-08 E-Index: 3 4 5 T-Index: 0 -1.501284760092D-01 9.016194688684D-03 2.238571380263D-04 1 -3.322262917492D-01 4.865809696737D-02 -4.343709230425D-03 2 -2.643011608926D-02 5.658846165674D-04 1.413672739471D-04 3 7.688215878015D-03 -5.493080299892D-04 3.497209232351D-05 4 5.691532547205D-04 -1.149074252290D-04 4.807423173738D-06 5 5.044633066348D-05 4.715897395507D-06 -9.154583868877D-08 6 -1.234952236991D-05 -9.240109636586D-08 4.248634746180D-08 7 3.335538428637D-07 2.604300994523D-08 -3.070635332640D-09 8 -3.205409357745D-08 4.814828405950D-09 -5.332849014591D-10 E-Index: 6 7 8 T-Index: 0 -5.983556406852D-05 2.938264102004D-06 -4.865346084259D-08 1 2.324145347640D-04 -6.832076246100D-06 8.466507036184D-08 2 -1.468227303594D-05 5.744169024370D-07 -8.237111069147D-09 3 -2.064808887243D-06 7.798853036278D-08 -1.206248775248D-09 4 2.193418042952D-07 -1.995457258897D-08 3.575861953373D-10 5 -4.818418728971D-08 2.776256710020D-09 -3.694099060448D-11 6 -2.045420857293D-10 -3.406586578331D-11 -7.204537382726D-13 7 1.097056113387D-11 2.734596577436D-12 2.335553372556D-14 8 3.762885118005D-11 -1.334245563205D-12 1.722914980319D-14 Max. rel. Error: 9.9451 % Mean rel. Error: 4.6015 % \end{verbatim}\end{small} \begin{figure} \label{2.3.6lr1} \epsfxsize=16truecm \epsffile{Amjuel_PS/carbrl-de.eps} \end{figure} \newpage \subsection{ Reaction 2.2.5a $ H_2 + e \rightarrow ...+ H(3) $, \ Ratio $H(3)/H_2 $ } Multi-step hydrogenic population coefficients Data: K. Sawada, T.Fujimoto \cite{kn:Sawada} Ratio of population coefficients: p(3)/nH2 \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.843232308973D+01 9.866136797620D-01 -7.630767164474D-04 1 1.763737135501D+01 -7.268396239737D-02 1.044914850159D-01 2 -9.102596461463D+00 6.283138055344D-02 -7.375751509571D-02 3 3.044087169667D+00 -4.582914429668D-02 4.001305352976D-02 4 -6.799512263137D-01 2.529525369912D-02 -1.619747297605D-02 5 1.021208740284D-01 -9.089155747301D-03 4.651977381511D-03 6 -1.027903716284D-02 1.911308645888D-03 -8.844096702821D-04 7 6.460492607832D-04 -2.089424506198D-04 9.480996308587D-05 8 -1.923319726365D-05 9.093882674319D-06 -4.196010732530D-06 E-Index: 3 4 5 T-Index: 0 8.463761770878D-03 -3.668738045523D-03 6.470552634326D-04 1 -5.045692652261D-02 1.145016084229D-02 -1.370891627120D-03 2 2.874156352094D-02 -5.093075324948D-03 4.483604397328D-04 3 -1.247549414985D-02 1.733717971265D-03 -1.065732952139D-04 4 3.883454673035D-03 -4.379243673277D-04 2.751938724811D-05 5 -7.719439518973D-04 4.105848834550D-05 -9.791293810522D-07 6 1.045477116614D-04 4.536233386087D-06 -1.259893630895D-06 7 -9.553834264468D-06 -1.115019494878D-06 2.363713809533D-07 8 4.237208860211D-07 5.589085089129D-08 -1.252796449945D-08 E-Index: 6 7 8 T-Index: 0 -5.551234542034D-05 2.284493199758D-06 -3.621267376539D-08 1 8.882007338293D-05 -2.941321182498D-06 3.890740158619D-08 2 -1.885697574083D-05 2.852269978935D-07 8.496957677236D-10 3 1.618515118726D-06 9.254848831070D-08 -2.858249742968D-09 4 -1.329060444185D-06 5.670350444090D-08 -1.228700843631D-09 5 2.901690837726D-07 -2.818973160122D-08 7.385401732551D-10 6 2.538253614744D-08 3.282804098763D-09 -1.212274570019D-10 7 -1.107068687207D-08 -5.725981536387D-12 7.272031033863D-12 8 7.329111895115D-10 -1.221514806869D-11 -8.661756397302D-14 Max. rel. Error: 3.0327 % Mean rel. Error: 1.0280 % \end{verbatim}\end{small} \begin{figure} \label{2.2.5a} \epsfxsize=16truecm \epsffile{Amjuel_PS/h2n3fu.ps} \end{figure} \newpage \subsection{ Reaction 2.2.5b $H_2 + e \rightarrow ...+ H(2) $ , \ Ratio $H(2)/H_2 $ } Ratio of population coefficients: p(2)/nH2 Multi-step hydrogenic population coefficients Data: K. Sawada, T.Fujimoto \cite{kn:Sawada} \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.709244791220D+01 9.687241476053D-01 3.742262659150D-02 1 1.669985823625D+01 -1.746089790847D-02 2.153832458702D-02 2 -8.309237048353D+00 3.381127410703D-02 -3.556201387754D-02 3 2.657739315672D+00 -8.512812279243D-03 1.196655088860D-02 4 -6.132396646504D-01 -2.552858621025D-03 1.194454859764D-04 5 1.101743243476D-01 1.097984176326D-03 -4.977907148307D-04 6 -1.475653262109D-02 -4.324624980123D-05 -1.194492163554D-07 7 1.224129849314D-03 -1.978420677869D-05 1.695927041869D-05 8 -4.446691780917D-05 1.813978843455D-06 -1.455738811700D-06 E-Index: 3 4 5 T-Index: 0 -1.651081799644D-02 3.565764257714D-03 -4.174591391487D-04 1 -1.090577226038D-02 2.794096310833D-03 -3.908538558075D-04 2 1.407590381030D-02 -2.699474372936D-03 2.742035615058D-04 3 -5.055672344660D-03 9.440106236031D-04 -8.615580226180D-05 4 3.664276773773D-04 -1.108403409912D-04 1.373091515639D-05 5 1.084866241578D-04 -9.612225065207D-06 -3.739409418091D-07 6 -5.135563052511D-06 1.895456383045D-06 -1.588469158937D-07 7 -3.814928055218D-06 2.731245678489D-07 1.634952517283D-09 8 3.749880009743D-07 -3.989523167029D-08 1.603033939474D-09 E-Index: 6 7 8 T-Index: 0 2.688883877617D-05 -8.884834785320D-07 1.159228215260D-08 1 2.999154465824D-05 -1.175608698972D-06 1.820253115424D-08 2 -1.469100393011D-05 3.734482260499D-07 -3.177600597413D-09 3 3.725098060685D-06 -5.918174922608D-08 -6.433645161998D-11 4 -9.325142355108D-07 3.763485456338D-08 -7.145755570016D-10 5 1.704997971383D-07 -1.376296741989D-08 3.514893200953D-10 6 -1.145517528846D-08 1.898641500278D-09 -5.838483361781D-11 7 1.312392622432D-10 -1.035003695410D-10 4.030531144035D-12 8 -2.253655572832D-11 2.072693141970D-12 -9.944952208106D-14 Max. rel. Error: 1.9631 % Mean rel. Error: 0.6656 % \end{verbatim}\end{small} \begin{figure} \label{2.2.5b} \epsfxsize=16truecm \epsffile{Amjuel_PS/h2n2fu.ps} \end{figure} \newpage \subsection{ Reaction 2.2.5c $H_2 + e \rightarrow ...+ H(4) $ , \ Ratio $H(4)/H_2 $ } Ratio of population coefficients: p(4)/nH2 Multi-step hydrogenic population coefficients Data: K. Sawada, T.Fujimoto \cite{kn:Sawada} \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.912344526943D+01 9.262202059006D-01 9.389410302438D-02 1 1.756197573185D+01 -4.343762540494D-02 6.126434071800D-02 2 -8.886628104138D+00 2.119621111180D-02 -2.656188467734D-02 3 3.057910637954D+00 -1.535881342701D-03 2.932875657740D-03 4 -7.835206514361D-01 -1.389945765942D-03 1.255399530700D-03 5 1.580308696978D-01 1.928352522209D-04 -3.543899525036D-04 6 -2.353640097896D-02 4.031200319945D-05 2.846252498973D-05 7 2.128743508257D-03 -8.795964786784D-06 -1.512497781432D-06 8 -8.285077032772D-05 4.111725894460D-07 1.270837350725D-07 E-Index: 3 4 5 T-Index: 0 -4.264954883585D-02 9.104064233267D-03 -9.991876289465D-04 1 -3.242966270346D-02 8.357146835162D-03 -1.147734080465D-03 2 1.227590202063D-02 -2.719431170815D-03 3.144838167343D-04 3 -1.186497869383D-03 1.497138310345D-04 3.644078028099D-06 4 -5.552975953317D-04 1.352074320357D-04 -1.821378482602D-05 5 1.750515375163D-04 -3.621530587129D-05 3.319095280981D-06 6 -2.248136922616D-05 4.496488473333D-06 -2.595976205911D-07 7 2.265470434041D-06 -4.927085512215D-07 3.240824081247D-08 8 -1.404975048998D-07 3.246838389464D-08 -2.985897409147D-09 E-Index: 6 7 8 T-Index: 0 5.646131117170D-05 -1.541734784320D-06 1.563548973536D-08 1 8.491836730798D-05 -3.177470024031D-06 4.698887012882D-08 2 -1.909003815732D-05 5.644098554224D-07 -6.240476308631D-09 3 -2.108751238830D-06 1.449614494660D-07 -3.025489423066D-09 4 1.329682209766D-06 -4.835654939859D-08 6.736536866134D-10 5 -1.024702456679D-07 -1.838064127165D-09 1.096804376213D-10 6 -1.383903232721D-08 1.811451752221D-09 -4.443051906110D-11 7 8.783996080897D-10 -1.570045781133D-10 3.895723973541D-12 8 9.149043474391D-11 1.200102594315D-12 -7.103779862531D-14 Max. rel. Error: 5.8311 % Mean rel. Error: 2.4005 % \end{verbatim}\end{small} \begin{figure} \label{2.2.5c} \epsfxsize=16truecm \epsffile{Amjuel_PS/h2n4fu.ps} \end{figure} \newpage \subsection{ Reaction 2.2.5d $H_2 + e \rightarrow ...+ H(5) $ , \ Ratio $H(5)/H_2 $ } Ratio of population coefficients: p(5)/nH2 Multi-step hydrogenic population coefficients Data: K. Sawada, T.Fujimoto \cite{kn:Sawada} \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.951411187905D+01 9.845720830236D-01 2.965188823982D-02 1 1.754222947805D+01 8.247738158426D-03 -1.272102756074D-02 2 -8.876801014058D+00 4.901299958077D-03 -5.280618932755D-03 3 3.072154572289D+00 -1.530726569770D-03 2.607605517865D-03 4 -7.853999520176D-01 -2.345612983161D-03 2.701173976139D-03 5 1.567509317981D-01 8.814896942982D-04 -1.049815583642D-03 6 -2.318325485784D-02 -7.993944555387D-05 7.600898233240D-05 7 2.098355270569D-03 -3.387024520670D-06 9.244162752622D-06 8 -8.207983816964D-05 5.528578997147D-07 -1.019716004446D-06 E-Index: 3 4 5 T-Index: 0 -1.988697872409D-02 5.937630704750D-03 -8.791623431456D-04 1 5.501038151489D-03 -8.566607598092D-04 2.183252927157D-05 2 2.314980071502D-03 -5.478894140036D-04 7.109825032007D-05 3 -1.396561346251D-03 3.325686900420D-04 -3.809967071864D-05 4 -1.125294104660D-03 2.296369788655D-04 -2.539533631356D-05 5 4.447398821903D-04 -9.021186699180D-05 9.582338741375D-06 6 -2.411443826400D-05 2.990412729672D-06 -5.900509921306D-08 7 -5.982892783306D-06 1.671607281419D-06 -2.370199152045D-07 8 5.706608511575D-07 -1.455207707019D-07 1.922725997681D-08 E-Index: 6 7 8 T-Index: 0 6.453161013676D-05 -2.282669216724D-06 3.113968814246D-08 1 5.326208461631D-06 -4.221360253600D-07 8.838098533169D-09 2 -4.628672509606D-06 1.314409444715D-07 -1.108256720247D-09 3 1.973863091768D-06 -3.710162944512D-08 2.441617394808D-11 4 1.549890921198D-06 -4.822256530984D-08 5.795655841101D-10 5 -5.224195972980D-07 1.313051592940D-08 -1.087986680607D-10 6 -2.099205652655D-08 1.716078063896D-09 -3.742956025175D-11 7 1.822822435371D-08 -7.148600246211D-10 1.095760653021D-11 8 -1.375709745925D-09 5.028096539680D-11 -7.253832666784D-13 Max. rel. Error: 5.8770 % Mean rel. Error: 2.4838 % \end{verbatim}\end{small} \begin{figure} \label{2.2.5d} \epsfxsize=16truecm \epsffile{Amjuel_PS/h2n5fu.ps} \end{figure} \newpage \subsection{ Reaction 2.2.5e $H_2 + e \rightarrow ...+ H(6) $ , \ Ratio $H(6)/H_2 $ } Ratio of population coefficients: p(6)/nH2 Multi-step hydrogenic population coefficients Data: K. Sawada, T.Fujimoto \cite{kn:Sawada} \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.976375830432D+01 1.080938475473D+00 -1.041552669840D-01 1 1.755396272137D+01 1.997928889454D-02 -1.798710059345D-02 2 -8.859630135249D+00 -2.504982400656D-02 2.543100868921D-02 3 3.076066110143D+00 -7.835891215709D-03 3.545212479895D-03 4 -7.843523260590D-01 5.646209832689D-03 -3.561003903809D-03 5 1.561553501837D-01 7.187156275750D-04 -5.963069173321D-04 6 -2.332414342207D-02 -7.250674775397D-04 5.042502000331D-04 7 2.152674655984D-03 1.218456761872D-04 -8.096427977714D-05 8 -8.602048471984D-05 -6.415059271451D-06 4.107777281787D-06 E-Index: 3 4 5 T-Index: 0 4.597090039926D-02 -9.342295727179D-03 9.308478102486D-04 1 7.525111338364D-03 -1.729122256079D-03 1.982524112989D-04 2 -1.066061134667D-02 2.308937441320D-03 -2.749941500007D-04 3 -3.509536109581D-05 -2.051879002933D-04 4.063170393346D-05 4 8.140229792921D-04 -8.180427544392D-05 3.613298743897D-06 5 1.757400200541D-04 -2.144818777523D-05 7.661627732789D-07 6 -1.279018270105D-04 1.377362109836D-05 -4.685940627108D-07 7 1.925404378767D-05 -1.822283216087D-06 2.708967643411D-08 8 -9.154258157002D-07 7.217533878534D-08 1.433836277468D-09 E-Index: 6 7 8 T-Index: 0 -4.990551313939D-05 1.412124656401D-06 -1.686977249955D-08 1 -1.100090823914D-05 2.783571526155D-07 -2.545786068789D-09 2 1.844047875979D-05 -6.611108809876D-07 9.857959406283D-09 3 -3.580865956702D-06 1.526795464151D-07 -2.489702863615D-09 4 -5.514937069176D-08 1.282783100756D-09 -7.929654586724D-11 5 7.413860626664D-08 -7.230260739451D-09 1.670076436316D-10 6 -2.752310640534D-08 2.519485275718D-09 -5.096968024103D-11 7 6.897900227166D-09 -4.409727389145D-10 7.792707281870D-12 8 -5.340626613072D-10 2.786970513377D-11 -4.532087311135D-13 Max. rel. Error: 7.8110 % Mean rel. Error: 3.3876 % \end{verbatim}\end{small} \begin{figure} \label{2.2.5e} \epsfxsize=16truecm \epsffile{Amjuel_PS/h2n6fu.ps} \end{figure} \newpage \subsection{ Reaction 2.2.5fl $H_2 + e \rightarrow ...+ H_2(N=3,Triplet)$} Normalized emissivity: $H2(N=3, Triplet)/H_2/n_e*2/9* 2E7 $ Fulcher emissivity, $cm^3/s$. relative 2/9: statistical weight of upper d (Pi) triplet state amongst all N=3 triplet states. 2E7: approx. Fulcher Aik coeff for $N=3: d \rightarrow N=2: a$ transition in triplet system. Multi-step hydrogenic molecule population coefficients Data: K.Sawada, T.Fujimoto \cite{kn:Sawada} \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.504557850421D+01 9.344698340987D-02 -1.262393982454D-01 1 1.265185253675D+01 3.464589180343D-01 -1.897206206043D-01 2 -5.915984508527D+00 -4.770835779343D-01 2.383409770393D-01 3 1.567639302331D+00 3.390100280427D-01 -1.091189901772D-01 4 -2.590628281288D-01 -1.393257670314D-01 3.068867791726D-02 5 2.135659024123D-02 3.392916031088D-02 -5.998734336944D-03 6 2.067218294860D-04 -4.798473917584D-03 7.772903414015D-04 7 -1.751915106668D-04 3.619887562438D-04 -5.646895975370D-05 8 9.203730354946D-06 -1.119572886551D-05 1.591317926643D-06 E-Index: 3 4 5 T-Index: 0 5.877352224633D-02 -1.302261116596D-02 1.540680462958D-03 1 5.862703454732D-02 -1.095188520145D-02 1.183240573644D-03 2 -6.570429435087D-02 1.114775452853D-02 -1.070181983249D-03 3 1.814682024195D-02 -2.295511323493D-03 1.728358529303D-04 4 -1.552484350393D-03 1.648565252382D-05 -2.120282511290D-06 5 -1.441720545043D-04 3.491712665534D-05 3.814455169266D-06 6 5.391904676009D-05 -6.544745167097D-06 -9.545517784441D-07 7 -7.783493080968D-06 1.329842208929D-06 -2.466307689654D-08 8 4.941214511748D-07 -1.119035840584D-07 1.039673602122D-08 E-Index: 6 7 8 T-Index: 0 -1.002500011070D-04 3.343404484895D-06 -4.450494173734D-08 1 -7.027920699731D-05 2.111151704919D-06 -2.487468982378D-08 2 5.325609368599D-05 -1.188266988002D-06 7.422508082261D-09 3 -3.839135008823D-06 -1.858093262988D-07 7.490073429227D-09 4 -7.719566036043D-07 9.893554038792D-08 -2.773366208727D-09 5 -4.033028965823D-07 4.648379959066D-09 2.007004276332D-10 6 1.065338439445D-07 -2.602264223322D-09 -2.414058704987D-12 7 -9.313819595092D-10 -9.979867907432D-11 5.230579069087D-12 8 -7.005564197388D-10 3.183343414621D-11 -6.155115004501D-13 Max. rel. Error: 2.1244 % Mean rel. Error: .5558 % \end{verbatim}\end{small} \begin{figure} \label{2.2.5fl} \epsfxsize=16truecm \epsffile{Amjuel_PS/h2fulch.ps} \end{figure} \newpage \subsection{ Reaction 2.2.5fu $H_2 + e \rightarrow ...+ H_2(N=3,Triplet, d-state)$} redone March 18, fit range 0.1 to 1e4 eV. Ratio $H_2(N=3, Triplet)/H_2*2/9 $, 2/9 stat. weight to reduce N=3 state to d-state upper Fulcher population coefficient. Triplet d-state, A$_{Fulch} \approx $ 2.43E7 (priv. com. D.W.) for radiative d-triplet to a-triplet transitions. Multi-step hydrogenic molecule population coefficients Data: K.Sawada, T.Fujimoto \cite{kn:Sawada} \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.354489060165D+01 1.468103242439D+00 -4.646307499703D-01 1 1.277739086685D+01 3.336987615778D-01 -2.662110674962D-01 2 -6.100361344044D+00 -1.199272310765D+00 7.903343009701D-01 3 1.668734740401D+00 7.492770342809D-01 -3.449602217244D-01 4 -2.995198269449D-01 -2.252050456671D-01 5.136460634062D-02 5 3.362068612317D-02 4.204168766681D-02 -2.887256470209D-03 6 -2.119643421070D-03 -5.136593278645D-03 3.021224427790D-04 7 5.764101894151D-05 3.665248081377D-04 -5.591909814617D-05 8 -7.556159315810D-08 -1.116271612850D-05 3.029453078051D-06 E-Index: 3 4 5 T-Index: 0 1.917594272036D-01 -3.914204712405D-02 4.405136273290D-03 1 8.977043337317D-02 -1.465813195424D-02 1.295941582003D-03 2 -2.277339349300D-01 3.517830118856D-02 -3.086638209564D-03 3 7.427634680932D-02 -9.056373914556D-03 6.168596878350D-04 4 -8.289600947012D-04 -9.842202184975D-04 1.569147488627D-04 5 -1.991926819207D-03 4.475984672915D-04 -4.330338627262D-05 6 1.465996491981D-04 -1.802283714021D-05 -6.406153919161D-09 7 1.108868720206D-05 -3.651785291583D-06 5.709622791954D-07 8 -1.032756417661D-06 2.547765262252D-07 -3.281099947589D-08 E-Index: 6 7 8 T-Index: 0 -2.784827610173D-04 9.205781819517D-06 -1.234563971007D-07 1 -6.294510247871D-05 1.558832548058D-06 -1.505796810383D-08 2 1.508616892274D-04 -3.741483445376D-06 3.548369121880D-08 3 -1.858979358827D-05 -1.756205740430D-08 8.600099983333D-09 4 -1.263963013577D-05 5.424603147976D-07 -9.427049641092D-09 5 2.594991460544D-06 -9.710865279198D-08 1.635299658521D-09 6 5.807832346907D-08 -1.194710140642D-09 -2.074052769889D-11 7 -4.002665073483D-08 1.260114477597D-09 -1.421785470367D-11 8 2.142746257616D-09 -6.776734606365D-11 8.207577984364D-13 Max. rel. Error: 0.145E+02 % Mean rel. Error: 0.381E+01 % \end{verbatim}\end{small} \begin{figure} \label{2.2.5fu} \epsfxsize=16truecm \epsffile{Amjuel_PS/h2fu.eps} \end{figure} \newpage \subsection{ Reaction 2.2.5we $H_2 + e \rightarrow ...+ H_2(N=2,Singlet \ C)$} Ratio $H_2(N=2, Singlet \ C-state)/H_2 $ upper Werner band population coefficient. Singlet C-state, A$_{Werner} \approx $ 1.04E9 (priv. com. D.W.) Multi-step hydrogenic molecule population coefficients Data: K.Sawada, T.Fujimoto \cite{kn:Sawada} \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.593649328832D+01 8.308979586264D-01 1.868771272352D-01 1 1.358996226939D+01 1.144733915906D-01 -7.166182521067D-02 2 -5.734471422048D+00 -2.150843448759D-02 -3.824097076465D-02 3 1.467418653563D+00 -2.501578958293D-03 2.923616954773D-02 4 -2.188119913056D-01 1.995231637494D-03 -6.640370721872D-03 5 1.406297652325D-02 -6.783126412988D-04 7.510665534693D-04 6 5.561129014609D-04 1.351258986187D-04 -5.745270250733D-05 7 -1.327036442082D-04 -1.315685619246D-05 3.749140942633D-06 8 5.386791451187D-06 4.829742920546D-07 -1.381191058408D-07 E-Index: 3 4 5 T-Index: 0 -8.319521746811D-02 1.822290028150D-02 -2.139848284025D-03 1 3.561940208530D-02 -8.730170894414D-03 1.111181710062D-03 2 8.090632884354D-03 -3.760749351686D-04 -8.428342936127D-05 3 -7.006055255923D-03 9.723873035654D-04 -6.790200414082D-05 4 9.388209633191D-04 -1.188419004204D-04 8.205572285784D-06 5 4.252484681099D-05 -1.045078968002D-05 1.071348879998D-06 6 -1.359995374888D-05 1.767498689737D-06 -1.033888505778D-07 7 4.214609548524D-07 4.105679338979D-08 -1.391632590311D-08 8 1.760472357584D-08 -8.302282439471D-09 1.229878733295D-09 E-Index: 6 7 8 T-Index: 0 1.363166907638D-04 -4.410389531348D-06 5.649304185589D-08 1 -7.568165245508D-05 2.610898259323D-06 -3.590058481557D-08 2 1.332628938065D-05 -7.119317923666D-07 1.326801124893D-08 3 1.270541815502D-06 6.913679414367D-08 -2.456304218566D-09 4 -4.661860601440D-08 -1.560880825875D-08 4.036797301220D-10 5 -8.639208387211D-08 3.008291257423D-09 -2.251160398320D-11 6 2.681223177046D-09 1.999325699443D-10 -1.047788129925D-11 7 1.395885069414D-09 -8.052768706091D-11 1.889487362615D-12 8 -9.665361477916D-11 4.462593169355D-12 -8.850565688461D-14 Max. rel. Error: 0.115E+02 % Mean rel. Error: 0.299E+01 % \end{verbatim}\end{small} \begin{figure} \label{2.2.5we} \epsfxsize=16truecm \epsffile{Amjuel_PS/h2we.eps} \end{figure} \newpage \subsection{ Reaction 2.2.5ly $H_2 + e \rightarrow ...+ H_2(N=2,Singlet \ B)$} Ratio $H_2(N=2, Singlet \ B-state)/H_2 $ upper Lyman band population coefficient. Singlet B-state, A$_{Lyman} \approx $0.84E9 (priv. com. D.W.) Multi-step hydrogenic molecule population coefficients Data: K.Sawada, T.Fujimoto \cite{kn:Sawada} \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.397850573163D+01 1.006056939133D+00 -1.202042794510D-02 1 1.196167467450D+01 1.019392480038D-01 -3.246741602640D-02 2 -5.552980751071D+00 -2.182674613256D-01 1.310622385883D-01 3 1.710517188280D+00 1.056574565611D-01 -7.126216596227D-02 4 -3.699083854427D-01 -8.996140369756D-03 8.169425385102D-03 5 5.450770431960D-02 -5.497328775049D-03 3.109194223938D-03 6 -5.114378920377D-03 1.574026731653D-03 -9.964122308190D-04 7 2.718181436155D-04 -1.570909362877D-04 1.033573137707D-04 8 -6.182952661054D-06 5.533588242821D-06 -3.725344805031D-06 E-Index: 3 4 5 T-Index: 0 4.355523162462D-03 -6.382190527349D-04 3.974915237112D-05 1 3.508265857386D-04 1.382009361884D-03 -2.488403752281D-04 2 -3.383652044906D-02 4.052689315875D-03 -2.098203509930D-04 3 2.137531087390D-02 -2.874452928505D-03 1.560319164372D-04 4 -3.936780405633D-03 6.865779069553D-04 -4.267656587715D-05 5 -3.226247705626D-04 -2.485199148367D-05 4.187303245886D-06 6 1.949593539968D-04 -1.432573062806D-05 2.716870257549D-07 7 -2.279031922723D-05 2.122592718556D-06 -7.778350690825D-08 8 8.693803378144D-07 -8.875683289762D-08 3.853513064998D-09 E-Index: 6 7 8 T-Index: 0 -4.817941325124D-07 -4.818422950101D-08 1.400297189617D-09 1 1.880067470651D-05 -6.625349071032D-07 8.813516831326D-09 2 1.142439741442D-06 2.743493930710D-07 -7.006934630012D-09 3 4.392236473310D-07 -3.371829185419D-07 8.645219519537D-09 4 -3.428952578243D-07 1.270631026599D-07 -3.377504202843D-09 5 2.905622963853D-08 -1.867759838623D-08 5.575839817605D-10 6 -7.981727857836D-10 9.983567417040D-10 -3.988647877134D-11 7 3.870317660182D-10 8.064843019666D-12 7.746226928676D-13 8 -3.436981127862D-11 -1.627459347813D-12 2.106967385582D-14 Max. rel. Error: 0.922E+01 % Mean rel. Error: 0.210E+01 % \end{verbatim}\end{small} \begin{figure} \label{2.2.5ly} \epsfxsize=16truecm \epsffile{Amjuel_PS/h2ly.eps} \end{figure} \newpage \subsection{ Reaction 2.2.14a $ H_2^+ + e \rightarrow ...+ H(3) $, \ Ratio $H(3)/H_2^+ $ } Multi-step hydrogenic population coefficients Data: K. Sawada, T.Fujimoto \cite{kn:Sawada} Ratio of population coefficients: p(3)/nH2+ \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -1.722688127458D+01 1.153283206758D+00 -1.683858517653D-01 1 -6.130457183836D-01 1.914093897035D-01 -2.119334228080D-01 2 -3.288796872020D-02 -2.400733485492D-02 2.404651735462D-02 3 1.011296840186D-02 -1.550958978732D-02 1.584315646622D-02 4 1.661600971350D-02 4.557160690820D-03 -3.973908011295D-03 5 -1.332921799914D-03 1.037539779315D-05 6.731975412111D-05 6 -1.279967875089D-03 -2.589228947175D-04 1.486622411070D-04 7 2.677167178361D-04 5.420325237257D-05 -3.368818743134D-05 8 -1.506445178315D-05 -3.499465420549D-06 2.352582612122D-06 E-Index: 3 4 5 T-Index: 0 6.918918524329D-02 -1.429478386078D-02 1.613571468557D-03 1 9.109177794808D-02 -2.007505252911D-02 2.472425643895D-03 2 -9.020252068955D-03 1.671217936164D-03 -1.647723170945D-04 3 -6.589011823707D-03 1.468052024984D-03 -1.881996632423D-04 4 1.324545590207D-03 -2.271138929258D-04 2.197082919209D-05 5 -2.225087720532D-05 -3.948031909877D-06 2.183242092156D-06 6 -2.359201102735D-05 5.994534813816D-07 8.163420117561D-08 7 5.871647174879D-06 -7.017526293806D-08 -7.321361270638D-08 8 -4.869333174029D-07 2.666937131278D-08 2.907495025800D-09 E-Index: 6 7 8 T-Index: 0 -9.996182392999D-05 3.143558308195D-06 -3.894902873796D-08 1 -1.710731264281D-04 6.171658058460D-06 -8.994609018799D-08 2 8.489265493722D-06 -2.013488013000D-07 1.438802569384D-09 3 1.372284113113D-05 -5.221176658885D-07 7.993094218338D-09 4 -1.193452426271D-06 3.308071890623D-08 -3.519685687680D-10 5 -2.896287982222D-07 1.562000946898D-08 -3.009928452053D-10 6 1.559281307950D-09 -6.451643409471D-10 1.995316529751D-11 7 7.478573101616D-09 -2.883419180345D-10 3.944931881913D-12 8 -4.438182202186D-10 2.053419620687D-11 -3.291110119780D-13 Max. rel. Error: 3.5492 % Mean rel. Error: 1.1008 % \end{verbatim}\end{small} \begin{figure} \label{2.2.14a} \epsfxsize=16truecm \epsffile{Amjuel_PS/h2pn3fu.ps} \end{figure} \newpage \subsection{ Reaction 2.2.14b $ H_2^+ + e \rightarrow ...+ H(2) $, \ Ratio $H(2)/H_2^+ $ } Multi-step hydrogenic population coefficients Data: K. Sawada, T.Fujimoto \cite{kn:Sawada} Ratio of population coefficients: p(2)/nH2+ \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -1.893340627587D+01 9.384468043754D-01 6.845844295054D-02 1 -6.928605971087D-01 -8.026687490301D-02 9.467107255600D-02 2 -2.281426599901D-02 2.469204550924D-02 -2.484665906437D-02 3 7.477602038370D-02 2.032608947899D-02 -2.519725182225D-02 4 1.800864421577D-02 -6.090658281624D-03 7.017163446504D-03 5 -7.998916722808D-03 -9.279887714293D-05 2.698897287206D-04 6 -3.810034520682D-04 -2.106056251267D-05 -1.953567231400D-05 7 2.854892030780D-04 4.128701336617D-05 -4.250413339334D-05 8 -2.071857549683D-05 -4.001420432076D-06 4.379705502021D-06 E-Index: 3 4 5 T-Index: 0 -3.000866490557D-02 6.301221120024D-03 -7.121426054946D-04 1 -4.166524495938D-02 8.977392904028D-03 -1.051153710461D-03 2 9.033528728860D-03 -1.517598590401D-03 1.263880354474D-04 3 1.162950470259D-02 -2.606098938264D-03 3.140565339454D-04 4 -3.000019054211D-03 6.218383225871D-04 -6.912762960613D-05 5 -2.042942399126D-04 6.121533276155D-05 -8.909019790621D-06 6 3.395544918660D-05 -1.198646949905D-05 1.803522408198D-06 7 1.505473503739D-05 -2.586687292054D-06 2.484264221846D-07 8 -1.726884062383D-06 3.360010725821D-07 -3.628922644305D-08 E-Index: 6 7 8 T-Index: 0 4.370331341973D-05 -1.366214208274D-06 1.690062454965D-08 1 6.808364131429D-05 -2.298331729242D-06 3.151517460256D-08 2 -4.822206870495D-06 5.000680158777D-08 8.129482308185D-10 3 -2.070880988429D-05 7.034167608369D-07 -9.610489042355D-09 4 4.193160605355D-06 -1.303566995266D-07 1.616380399841D-09 5 6.656671628061D-07 -2.464877011413D-08 3.582951420528D-10 6 -1.317043941884D-07 4.601629603901D-09 -6.103803830641D-11 7 -1.416917248903D-08 4.608792938645D-10 -6.675661118338D-12 8 2.234037377054D-09 -7.375120969117D-11 1.017886320572D-12 Max. rel. Error: 10.9817 % Mean rel. Error: 4.1166 % \end{verbatim}\end{small} \begin{figure} \label{2.2.14b} \epsfxsize=16truecm \epsffile{Amjuel_PS/h2pn2fu.ps} \end{figure} \newpage \subsection{ Reaction 2.2.14c $ H_2^+ + e \rightarrow ...+ H(4) $, \ Ratio $H(4)/H_2^+ $ } Multi-step hydrogenic population coefficients Data: K. Sawada, T.Fujimoto \cite{kn:Sawada} Ratio of population coefficients: p(4)/nH2+ \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -1.676331978580D+01 9.080085441987D-01 1.147906180602D-01 1 -6.109051309024D-01 -8.294588654086D-03 1.632432484919D-02 2 -2.909737666296D-02 5.624264669551D-03 -1.197286367681D-02 3 7.623264778786D-03 -9.078213947581D-04 5.223194421632D-03 4 1.521423403054D-02 1.676511919497D-03 -2.501873457928D-03 5 -9.030920815279D-04 -1.632212690782D-03 1.351745824791D-03 6 -1.243913874997D-03 5.018902795712D-04 -3.645436069304D-04 7 2.498705414219D-04 -6.291439776017D-05 4.327516333116D-05 8 -1.382134054195D-05 2.822461526917D-06 -1.872083205062D-06 E-Index: 3 4 5 T-Index: 0 -5.270106237531D-02 1.127860512722D-02 -1.245143403573D-03 1 -1.096202696457D-02 3.286907157227D-03 -4.917565920190D-04 2 7.584360997821D-03 -2.062094702685D-03 2.791821975336D-04 3 -3.449375282404D-03 8.838838532938D-04 -1.095438324110D-04 4 1.102143471476D-03 -2.160129746705D-04 2.129894386269D-05 5 -3.962453758917D-04 5.313919176171D-05 -3.533864379468D-06 6 9.622258500169D-05 -1.184926396450D-05 7.911742891778D-07 7 -1.107791453066D-05 1.379188891744D-06 -1.041402141388D-07 8 4.704345845794D-07 -5.961078067778D-08 4.961931789364D-09 E-Index: 6 7 8 T-Index: 0 7.175810811923D-05 -2.069167769109D-06 2.363328371263D-08 1 3.752753236914D-05 -1.408607567442D-06 2.070687771858D-08 2 -1.963835974805D-05 6.884652898708D-07 -9.525997813634D-09 3 7.004585234319D-06 -2.213148187150D-07 2.720461054725D-09 4 -1.080619499451D-06 2.598412251320D-08 -2.157639142592D-10 5 1.153292411062D-07 -1.686998701330D-09 9.600285735482D-12 6 -3.457481362906D-08 1.132144357690D-09 -1.987071178818D-11 7 5.897518730021D-09 -2.354087236528D-10 4.278831126984D-12 8 -3.227509261038D-10 1.380778939747D-11 -2.522987941747D-13 Max. rel. Error: 3.2596 % Mean rel. Error: 1.2619 % \end{verbatim}\end{small} \begin{figure} \label{2.2.14c} \epsfxsize=16truecm \epsffile{Amjuel_PS/h2pn4fu.ps} \end{figure} \newpage \subsection{ Reaction 2.2.14d $ H_2^+ + e \rightarrow ...+ H(5) $ , \ Ratio $H(5)/H_2^+ $ } Multi-step hydrogenic population coefficients Data: K. Sawada, T.Fujimoto \cite{kn:Sawada} Ratio of population coefficients: p(5)/nH2+ \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -1.644185145736D+01 1.012436644382D+00 6.786438608987D-03 1 -6.098791364927D-01 5.430488667435D-02 -7.847894120730D-02 2 -2.950068702716D-02 -3.373771077709D-02 3.289895028745D-02 3 6.754065058068D-03 7.451626213157D-03 -3.969682127389D-03 4 1.537038416857D-02 4.118426250990D-03 -4.555083248726D-03 5 -9.947711516605D-04 -1.833979398896D-03 1.801381990375D-03 6 -1.192700661337D-03 3.791226761015D-05 -3.145634625643D-05 7 2.404465554223D-04 5.021181230894D-05 -5.066197038660D-05 8 -1.326828264262D-05 -4.564492434807D-06 4.606059092522D-06 E-Index: 3 4 5 T-Index: 0 -1.636359203529D-02 6.460968901937D-03 -1.074723144885D-03 1 3.737579519968D-02 -8.178265373295D-03 9.193848105982D-04 2 -1.134088065312D-02 1.754362025677D-03 -1.242294410730D-04 3 1.576874933190D-04 2.391978264795D-04 -5.252636585235D-05 4 1.826529292073D-03 -3.545645854345D-04 3.657837147066D-05 5 -6.662982315176D-04 1.215614803183D-04 -1.209604459175D-05 6 1.450525549912D-05 -3.710641046768D-06 5.511118540490D-07 7 1.829155353709D-05 -3.170388065293D-06 2.866743369560D-07 8 -1.697317371127D-06 3.048871380215D-07 -2.932146588732D-08 E-Index: 6 7 8 T-Index: 0 8.419235123864D-05 -3.153526630862D-06 4.581163952178D-08 1 -5.560014479351D-05 1.725272054044D-06 -2.159304879239D-08 2 3.243207880260D-06 3.071703458548D-08 -2.031512439383D-09 3 4.543948082974D-06 -1.784049810861D-07 2.642282279507D-09 4 -2.037354098418D-06 5.743682572167D-08 -6.369815462623D-10 5 6.745084225490D-07 -1.997093162477D-08 2.459303044047D-10 6 -4.734113162030D-08 2.110906778108D-09 -3.702822546028D-11 7 -1.322386162924D-08 2.686441115973D-10 -1.341741119398D-12 8 1.518492393831D-09 -3.921390964093D-11 3.853896510803D-13 Max. rel. Error: 3.3950 % Mean rel. Error: 1.2048 % \end{verbatim}\end{small} \begin{figure} \label{2.2.14d} \epsfxsize=16truecm \epsffile{Amjuel_PS/h2pn5fu.ps} \end{figure} \newpage \subsection{ Reaction 2.2.14e $ H_2^+ + e \rightarrow ...+ H(6) $, \ Ratio $H(6)/H_2^+ $ } Multi-step hydrogenic population coefficients Data: K. Sawada, T.Fujimoto \cite{kn:Sawada} Ratio of population coefficients: p(6)/nH2+ \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -1.622999065239D+01 1.114789960848D+00 -1.520045539695D-01 1 -6.128088795544D-01 4.799590905456D-02 -6.226002600050D-02 2 -2.843662556626D-02 -2.981491981788D-02 3.771158615252D-02 3 9.040540246117D-03 -5.376296672908D-03 2.724387350634D-03 4 1.488157339780D-02 4.117070101509D-03 -3.845342947354D-03 5 -1.100892809269D-03 6.973802180775D-05 2.700981820011D-04 6 -1.154443469425D-03 -2.746343562656D-04 1.329065248252D-04 7 2.372720363390D-04 4.450995037612D-05 -2.399096395388D-05 8 -1.321939690927D-05 -2.168171198227D-06 1.138090912890D-06 E-Index: 3 4 5 T-Index: 0 6.454947459361D-02 -1.251452482400D-02 1.176116823129D-03 1 3.120222040133D-02 -7.656737664171D-03 9.697768241674D-04 2 -1.714743824449D-02 3.730164832607D-03 -4.245864266326D-04 3 -7.284121072944D-04 1.754857033177D-04 -2.833588922766D-05 4 1.501531035131D-03 -3.095442801682D-04 3.552383842276D-05 5 -1.870097557763D-04 4.709088535767D-05 -5.863892714562D-06 6 -1.824639804367D-05 -6.062961769823D-07 4.017509350696D-07 7 4.371493229928D-06 -2.114447008583D-07 -3.261214899093D-08 8 -1.889513057698D-07 3.153827435466D-09 2.672896065823D-09 E-Index: 6 7 8 T-Index: 0 -5.801776455917D-05 1.436236089573D-06 -1.386191157402D-08 1 -6.554993759673D-05 2.252572465958D-06 -3.097271363753D-08 2 2.617269803427D-05 -8.313443339779D-07 1.069290183120D-08 3 2.404364824295D-06 -9.739423966586D-08 1.496981935094D-09 4 -2.266688480662D-06 7.510316070422D-08 -1.007253682698D-09 5 3.929720894592D-07 -1.368756170273D-08 1.948330325484D-10 6 -4.284044640046D-08 1.967059565426D-09 -3.388443373389D-11 7 5.152899170025D-09 -2.667100015865D-10 4.835046441176D-12 8 -3.370174839133D-10 1.633061281105D-11 -2.854661230035D-13 Max. rel. Error: 3.0278 % Mean rel. Error: 1.1252 % \end{verbatim}\end{small} \begin{figure} \label{2.2.14e} \epsfxsize=16truecm \epsffile{Amjuel_PS/h2pn6fu.ps} \end{figure} \newpage \subsection{ Reaction 2.2.15a $ H_3^+ + e \rightarrow ...+ H(3) $, \ Ratio $H(3)/H_3^+ $ } Multi-step hydrogenic population coefficients Data: K. Sawada, T.Fujimoto, \cite{kn:Sawada} and R. Janev et al., 1987 Production of initial $H(n=2)$ from $H_3^+$ via $1/3.5 \times \langle Hydhel~ 2.2.15\rangle$, then CR redistribution in H Ratio of population coefficients: p(3)/nH3+ \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.601119233903D+01 2.194488055582D+00 -2.490229101640D-01 1 1.652206692785D+00 -1.271092194312D-01 1.058603034484D-01 2 -8.700785019712D-01 -2.161600166796D-02 6.271502055705D-02 3 2.662217617059D-01 4.349904766090D-02 -3.964570429934D-02 4 -7.742301294851D-02 -1.588421393163D-02 6.518330779752D-03 5 1.931368710773D-02 -8.106962079405D-04 1.708355185624D-03 6 -3.409295405632D-03 1.740482076055D-03 -1.205558081593D-03 7 3.453367238152D-04 -3.495754916386D-04 2.280918882182D-04 8 -1.456129857393D-05 2.117574196146D-05 -1.399865611289D-05 E-Index: 3 4 5 T-Index: 0 1.132911350765D-01 -2.495101533471D-02 2.958065372132D-03 1 -3.391043609190D-02 5.252542828036D-03 -4.133003716081D-04 2 -3.563092105078D-02 8.658671254321D-03 -1.084373448947D-03 3 1.425402485426D-02 -2.606626099566D-03 2.640179631726D-04 4 2.942975651757D-05 -3.820356368930D-04 7.370218634646D-05 5 -9.096498355642D-04 2.144809623279D-04 -2.630207934234D-05 6 3.241732853912D-04 -4.279559204346D-05 2.895227184007D-06 7 -5.583861278880D-05 6.224370200950D-06 -2.797277959239D-07 8 3.502116490766D-06 -4.075936276354D-07 2.091741957019D-08 E-Index: 6 7 8 T-Index: 0 -1.921033371324D-04 6.398969176227D-06 -8.555066878081D-08 1 1.550419246049D-05 -2.077147754254D-07 -6.217681464656D-10 2 7.328429963825D-05 -2.541071707141D-06 3.547229620058D-08 3 -1.498023460658D-05 4.469952296008D-07 -5.466006320221D-09 4 -6.089548777788D-06 2.375890801408D-07 -3.584223895612D-09 5 1.746057261430D-06 -5.958058472873D-08 8.192333835651D-10 6 -9.061691336736D-08 6.391542243791D-10 1.652477882971D-11 7 -2.150518066178D-09 5.692555261125D-10 -1.288476392288D-11 8 -1.494056033386D-10 -2.437016814580D-11 6.330132340750D-13 Max. rel. Error: 14.3433 % Mean rel. Error: 2.2859 % \end{verbatim}\end{small} \begin{figure} \label{2.2.15a} \epsfxsize=16truecm \epsffile{Amjuel_PS/h3pn3fu.ps} \end{figure} \newpage \subsection{ Reaction 2.2.15b $ H_3^+ + e \rightarrow ...+ H(2) $, \ Ratio $H(2)/H_3^+ $ } Multi-step hydrogenic population coefficients Data: K. Sawada, T.Fujimoto, \cite{kn:Sawada} and R. Janev et al 1987 Production of initial $H(n=2)$ from $H_3^+$ via $1/3.5 \times \langle Hydhel~ 2.2.15\rangle$, then CR redistribution in H Ratio of population coefficients: p(2)/nH3+ \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -1.980337179098D+01 9.999289774464D-01 3.393626221267D-03 1 -4.071476496934D-01 2.924762633195D-02 -2.851786085227D-02 2 5.495688975883D-04 -1.023099678564D-02 1.171745245738D-02 3 7.151298543821D-04 -1.106236848753D-02 1.167194822465D-02 4 -1.082581109495D-04 2.080154145037D-03 -2.381045517182D-03 5 -5.784697350796D-05 8.818867850337D-04 -9.290488913510D-04 6 7.828814939830D-06 -1.410356074545D-04 1.579270228374D-04 7 1.289405712476D-06 -1.803694888454D-05 1.839342236091D-05 8 -1.757435874999D-07 2.740075492523D-06 -2.922976584923D-06 E-Index: 3 4 5 T-Index: 0 -2.831872924647D-03 8.844257796365D-04 -1.335820142114D-04 1 9.798033707980D-03 -1.513369733986D-03 1.052372400307D-04 2 -5.063164235821D-03 1.105581200627D-03 -1.355736418332D-04 3 -4.519763859219D-03 8.509755038057D-04 -8.608757693484D-05 4 1.016230997894D-03 -2.163134055907D-04 2.552512545027D-05 5 3.594734574380D-04 -6.760036792740D-05 6.820693101367D-06 6 -6.562061294501D-05 1.349897286883D-05 -1.527216042839D-06 7 -6.838474731524D-06 1.216126202961D-06 -1.128282531105D-07 8 1.149792069313D-06 -2.210992439606D-07 2.299563923333D-08 E-Index: 6 7 8 T-Index: 0 1.039688098878D-05 -3.967254803956D-07 5.751612166377D-09 1 -2.022407714950D-06 -9.533644334113D-08 3.425386624889D-09 2 9.500661752185D-06 -3.550036000270D-07 5.446553318204D-09 3 4.757811195092D-06 -1.348973665777D-07 1.542565685557D-09 4 -1.703589672933D-06 6.030500436147D-08 -8.781256295629D-10 5 -3.748567528049D-07 1.051005276609D-08 -1.176476798245D-10 6 9.704016493388D-08 -3.256173927393D-09 4.497431785523D-11 7 5.418531608876D-09 -1.198313236434D-10 8.246578075788D-13 8 -1.317209482279D-09 3.905293970215D-11 -4.696677196057D-13 Max. rel. Error: 10.2841 % Mean rel. Error: 0.8237 % \end{verbatim}\end{small} \begin{figure} \label{2.2.15b} \epsfxsize=16truecm \epsffile{Amjuel_PS/h3pn2fu.ps} \end{figure} \newpage \subsection{ Reaction 2.2.15c $ H_3^+ + e \rightarrow ...+ H(4) $, \ Ratio $H(4)/H_3^+ $ } Multi-step hydrogenic population coefficients Data: K. Sawada, T.Fujimoto, \cite{kn:Sawada} and R. Janev et al 1987 Production of initial $H(n=2)$ from $H_3^+$ via $1/3.5 \times \langle Hydhel~ 2.2.15\rangle$, then CR redistribution in H Ratio of population coefficients: p(4)/nH3+ \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.699168687840D+01 2.001554576899D+00 2.962673017164D-03 1 2.327818682219D+00 -6.477623277677D-03 1.302747597894D-02 2 -1.222503946813D+00 1.123694153535D-02 -1.836859736247D-02 3 3.759451408212D-01 -6.964877949667D-03 8.967141291539D-03 4 -1.057717328620D-01 1.811746894110D-03 -1.588506334985D-03 5 2.564558082290D-02 -1.557448494435D-04 -1.318163984811D-04 6 -4.362034354566D-03 1.336313932390D-05 5.677385912381D-05 7 4.213673231999D-04 -5.353070791744D-06 -1.630395162429D-06 8 -1.690754255016D-05 5.204418811823D-07 -2.764507346651D-07 E-Index: 3 4 5 T-Index: 0 -3.049473442883D-03 8.934957580265D-04 -1.187680147766D-04 1 -7.302167340628D-03 1.743088872108D-03 -2.033314551240D-04 2 7.937475042441D-03 -1.495920915105D-03 1.335789358832D-04 3 -3.759736445513D-03 7.328783639342D-04 -7.467260815755D-05 4 7.588920331506D-04 -1.913322099599D-04 2.691316713419D-05 5 6.936970796563D-05 -9.160519294976D-06 -1.145889879420D-07 6 -4.339223919979D-05 1.175796204569D-05 -1.577537099191D-06 7 4.425066124877D-06 -1.614546001621D-06 2.599419206670D-07 8 -9.831082955550D-08 6.376842626606D-08 -1.222812849688D-08 E-Index: 6 7 8 T-Index: 0 7.833656739024D-06 -2.831734234040D-07 4.376125518706D-09 1 1.154895519966D-05 -3.074042636582D-07 2.967824771774D-09 2 -5.103130444119D-06 3.555541061620D-08 1.457153306360D-09 3 4.119385753462D-06 -1.159886623812D-07 1.308198318452D-09 4 -2.112133421406D-06 8.508133152131D-08 -1.360850938372D-09 5 1.014287149029D-07 -6.777611535609D-09 1.373041841284D-10 6 1.137461746810D-07 -4.208250772675D-09 6.264373124745D-11 7 -2.137126396561D-08 8.696995094294D-10 -1.384296355974D-11 8 1.098305710577D-09 -4.703325555132D-11 7.717446791356D-13 Max. rel. Error: 9.0711 % Mean rel. Error: 1.5148 % \end{verbatim}\end{small} \begin{figure} \label{2.2.15c} \epsfxsize=16truecm \epsffile{Amjuel_PS/h3pn4fu.ps} \end{figure} \newpage \subsection{ Reaction 2.2.15d $ H_3^+ + e \rightarrow ...+ H(5) $, \ Ratio $H(5)/H_3^+ $ } Multi-step hydrogenic population coefficients Data: K. Sawada, T.Fujimoto, \cite{kn:Sawada} and Janev et al. 1987 Production of initial $H(n=2)$ from $H_3^+$ via $1/3.5 \times \langle Hydhel~ 2.2.15\rangle$, then CR redistribution in H Ratio of population coefficients: p(5)/nH3+ \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.726636544624D+01 2.133976447955D+00 -1.437643407818D-01 1 2.607984145369D+00 3.736342257132D-02 -5.206732236717D-02 2 -1.372459802644D+00 -1.168450793414D-02 1.039452553074D-02 3 4.381136968184D-01 -1.599858338454D-03 5.567058463253D-03 4 -1.232102950459D-01 7.200465026127D-04 -1.555111093198D-03 5 2.788050336665D-02 -7.778193777532D-04 5.986504728580D-04 6 -4.325272890946D-03 4.366753618704D-04 -3.489782061433D-04 7 3.870202141408D-04 -8.396034178185D-05 7.283739797379D-05 8 -1.472534680030D-05 5.195720673557D-06 -4.730954375662D-06 E-Index: 3 4 5 T-Index: 0 5.266218557769D-02 -8.735567392297D-03 6.919538677059D-04 1 2.575215280557D-02 -6.008209560283D-03 7.323649110173D-04 2 -3.335259288099D-03 5.070348402932D-04 -4.437286309383D-05 3 -3.908320707976D-03 1.078790219266D-03 -1.445807390811D-04 4 1.013385566510D-03 -2.751391890149D-04 3.756629725211D-05 5 -1.609098607097D-04 2.001630094507D-05 -1.302966127214D-06 6 9.381316606795D-05 -1.092384086404D-05 4.836506460925D-07 7 -2.247960619374D-05 3.327027913749D-06 -2.544047801913D-07 8 1.570234172126D-06 -2.565871792243D-07 2.263302154308D-08 E-Index: 6 7 8 T-Index: 0 -2.537313706204D-05 2.755002502292D-07 3.064689208500D-09 1 -4.894113742491D-05 1.689063212815D-06 -2.350820776172D-08 2 2.940248173139D-06 -1.320244963238D-07 2.543920290364D-09 3 1.004638359166D-05 -3.485706886049D-07 4.792765609299D-09 4 -2.744526032933D-06 1.021810292434D-07 -1.520931726158D-09 5 5.431702781882D-08 -1.711017659423D-09 2.880788636234D-11 6 6.484042961226D-09 -1.162802787754D-09 2.568800325791D-11 7 9.642946338642D-09 -1.417047906131D-10 -7.123549343893D-14 8 -1.083303425027D-09 2.604279537307D-11 -2.404346400046D-13 Max. rel. Error: 8.0720 % Mean rel. Error: 1.8795 % \end{verbatim}\end{small} \begin{figure} \label{2.2.15d} \epsfxsize=16truecm \epsffile{Amjuel_PS/h3pn5fu.ps} \end{figure} \newpage \subsection{ Reaction 2.2.15e $ H_3^+ + e \rightarrow ...+ H(6) $, \ Ratio $H(6)/H_3^+ $ } Multi-step hydrogenic population coefficients Data: K. Sawada, T.Fujimoto, \cite{kn:Sawada} and R. Janev et al, 1987 Production of initial $H(n=2)$ from $H_3^+$ via $1/3.5 \times \langle Hydhel~ 2.2.15\rangle$, then CR redistribution in H Ratio of population coefficients: p(6)/nH3+ \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.731306702718D+01 2.226799613424D+00 -2.713541077245D-01 1 2.721916003669D+00 2.752077117728D-01 -2.817824763132D-01 2 -1.445171758730D+00 -3.455207346437D-02 2.128468170611D-02 3 4.869784512858D-01 -1.117099787519D-01 1.101949732661D-01 4 -1.366199370764D-01 1.963591329586D-02 -1.452797917604D-02 5 2.789289520108D-02 8.956074919162D-03 -9.295896282076D-03 6 -3.785560599727D-03 -2.449188168800D-03 1.956661410764D-03 7 3.086189807154D-04 1.287091624921D-04 -1.507685975982D-05 8 -1.139982513894D-05 3.981631091951D-06 -1.109641079725D-05 E-Index: 3 4 5 T-Index: 0 1.160222068193D-01 -2.351441393066D-02 2.434601322965D-03 1 1.173245156970D-01 -2.491839320070D-02 2.905055223332D-03 2 -5.633298373088D-03 7.917813609696D-04 -6.244317946507D-05 3 -4.412365175467D-02 8.991092209700D-03 -1.015055902253D-03 4 4.769180959321D-03 -8.470242324439D-04 8.762486764680D-05 5 3.796552815269D-03 -7.759741376950D-04 8.718058637354D-05 6 -6.790907264022D-04 1.241005294221D-04 -1.291557445220D-05 7 -1.814513841588D-05 6.730818401122D-06 -9.728795555375D-07 8 5.957908324528D-06 -1.396807603409D-06 1.699967143140D-07 E-Index: 6 7 8 T-Index: 0 -1.345468571268D-04 3.762918405002D-06 -4.176542071199D-08 1 -1.885547024432D-04 6.375389426295D-06 -8.745135270264D-08 2 3.292884698321D-06 -1.190866363308D-07 2.060340214319D-09 3 6.410030327458D-05 -2.116865424138D-06 2.846524837720D-08 4 -5.282031902152D-06 1.714977601939D-07 -2.311882826237D-09 5 -5.462320288173D-06 1.789108252698D-07 -2.387626221779D-09 6 7.684830295858D-07 -2.431186166102D-08 3.170509451364D-10 7 7.002458436648D-08 -2.501985930755D-09 3.541620765501D-11 8 -1.121847222632D-08 3.812117569450D-10 -5.230180135049D-12 Max. rel. Error: 7.7841 % Mean rel. Error: 2.1550 % \end{verbatim}\end{small} \begin{figure} \label{2.2.15e} \epsfxsize=16truecm \epsffile{Amjuel_PS/h3pn6fu.ps} \end{figure} \newpage \subsection{ Reaction 7.2a $ H^- + p \rightarrow ...+ H(3) $, \ Ratio $H(3)/H^- $, cold $H^-$ } Multi-step hydrogenic population coefficients Data: K. Sawada, T.Fujimoto, \cite{kn:Sawada} and Janev et al, 1987, and P.T. Greenland Production of initial $H(n=2), H(n=3)$ from $H^-$ via $ \langle Hydhel~ 7.2.2\rangle + \langle Hydhel~ 7.2.3\rangle$, then CR redistribution in H Ratio of population coefficients: p(3)/nH- \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -1.698348739110D+01 1.121505448583D+00 -1.562056461483D-01 1 -1.986622381979D-01 -2.318217689253D-02 1.896031486639D-02 2 -3.050975728615D-03 -3.329699545201D-02 3.779763018328D-02 3 1.002499912290D-02 1.045462457960D-02 -9.650053061780D-03 4 -6.398953884751D-04 1.441395323793D-03 -1.689635207883D-03 5 -7.711075007663D-05 -1.265328413655D-03 1.172945655383D-03 6 -2.049983387516D-05 2.044766998421D-04 -1.600026196636D-04 7 6.408878869927D-06 -7.052533095200D-06 1.334460994662D-07 8 -3.926518102708D-07 -4.161804947648D-07 7.965715911231D-07 E-Index: 3 4 5 T-Index: 0 7.384423345663D-02 -1.696804365272D-02 2.090058776152D-03 1 -3.664162784606D-03 -4.356306374247D-04 2.146755452836D-04 2 -1.612181968354D-02 3.403282708663D-03 -3.903169292552D-04 3 3.237264411283D-03 -4.804144315515D-04 2.972541984716D-05 4 7.163905079239D-04 -1.561640485896D-04 1.914209762341D-05 5 -4.120367467656D-04 7.008894220942D-05 -6.189441302916D-06 6 5.033444502959D-05 -7.181438176276D-06 4.108056332733D-07 7 1.170985498327D-06 -4.690125988575D-07 8.503464517525D-08 8 -3.594245312260D-07 7.814690334520D-08 -9.611375720209D-09 E-Index: 6 7 8 T-Index: 0 -1.399195453462D-04 4.756587306459D-06 -6.422505400847D-08 1 -2.514789071754D-05 1.212290889597D-06 -2.106280292156D-08 2 2.457727782342D-05 -7.941349227263D-07 1.025519706079D-08 3 -1.694973729097D-07 -5.142251421864D-08 1.423052870937D-09 4 -1.305410385352D-06 4.544728618553D-08 -6.246887421462D-10 5 2.736219149295D-07 -4.974014655394D-09 1.101207197277D-11 6 1.974698869452D-09 -1.016713293612D-09 2.621621803143D-11 7 -7.763141441637D-09 3.392374094524D-10 -5.632384756330D-12 8 6.750917451519D-10 -2.475979110847D-11 3.641741567554D-13 Max. rel. Error: 3.9821 % Mean rel. Error: 1.1463 % \end{verbatim}\end{small} \begin{figure} \label{7.2a} \epsfxsize=16truecm \epsffile{Amjuel_PS/hmn3fu.ps} \end{figure} \newpage \subsection{ Reaction 7.2b $ H^- + p \rightarrow ...+ H(2) $, \ Ratio $H(2)/H^- $, cold $H^-$ } Multi-step hydrogenic population coefficients Data: K. Sawada, T.Fujimoto, \cite{kn:Sawada} and R. Janev et al, 1987, and P.T. Greenland Production of initial $H(n=2), H(n=3)$ from $H^-$ via $ \langle Hydhel~ 7.2.2\rangle + \langle Hydhel~ 7.2.3\rangle$, then CR redistribution in H Ratio of population coefficients: p(2)/nH- \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -1.926343612010D+01 9.700693610120D-01 3.086732967457D-02 1 -1.496546124174D-01 -1.162600124695D-02 2.092625890254D-02 2 1.400659517460D-02 -1.908809713587D-03 4.474825228504D-03 3 3.712727041944D-02 -3.993957797149D-03 -4.541915418960D-04 4 1.113294261028D-02 1.611302161934D-03 -5.800693212819D-04 5 -2.330535554138D-03 9.558196184261D-04 -6.770389256165D-04 6 -7.776821303119D-04 -4.777860585666D-04 3.191698603955D-04 7 1.906239407094D-04 6.855600321265D-05 -4.406502657234D-05 8 -1.086976945156D-05 -3.231539920350D-06 1.960565560845D-06 E-Index: 3 4 5 T-Index: 0 -1.026100449251D-02 1.333365556163D-03 -4.164574430779D-05 1 -1.057668991857D-02 2.292243771977D-03 -2.438392602831D-04 2 -3.880343783906D-03 1.355446874959D-03 -2.254517664957D-04 3 1.729089007572D-03 -5.825182714335D-04 8.058493209277D-05 4 3.161122491789D-05 -4.291165076538D-06 3.882643863521D-06 5 1.355992925800D-04 -1.875746974531D-06 -2.072988238143D-06 6 -7.101794671976D-05 5.892592961569D-06 -1.070175076067D-07 7 9.542955450383D-06 -7.940664442729D-07 2.114115776211D-08 8 -3.805705631298D-07 2.128669195423D-08 9.157761577608D-10 E-Index: 6 7 8 T-Index: 0 -4.925686587468D-06 4.112831538264D-07 -8.777239592815D-09 1 1.320368718562D-05 -3.516108767654D-07 3.593691259527D-09 2 1.896658591425D-05 -7.769484207076D-07 1.231580177702D-08 3 -5.398656503144D-06 1.737911735033D-07 -2.130553272068D-09 4 -6.162993739156D-07 3.529468645256D-08 -6.926859162458D-10 5 2.283983783682D-07 -9.387255029589D-09 1.353162447593D-10 6 -5.193261748972D-09 -8.326872653843D-12 8.362383797066D-12 7 -2.705240932212D-10 5.067994995276D-11 -2.001347795107D-12 8 -1.122561005445D-10 1.928570020702D-12 3.288397756094D-14 Max. rel. Error: 4.1304 % Mean rel. Error: .7570 % \end{verbatim}\end{small} \begin{figure} \label{7.2b} \epsfxsize=16truecm \epsffile{Amjuel_PS/hmn2fu.ps} \end{figure} \newpage \subsection{ Reaction 7.2c $ H^- + p \rightarrow ...+ H(4) $, \ Ratio $H(4)/H^- $, cold $H^-$ } Multi-step hydrogenic population coefficients Data: K. Sawada, T.Fujimoto, \cite{kn:Sawada} and R. Janev et al, 1987, and P.T. Greenland Production of initial $H(n=2), H(n=3)$ from $H^-$ via $ \langle Hydhel~ 7.2.2\rangle + \langle Hydhel~ 7.2.3\rangle$, then CR redistribution in H Ratio of population coefficients: p(4)/nH- \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -2.969108713736D+01 1.931658904309D+00 7.005369877806D-02 1 8.583491624134D-01 -8.544233834909D-02 9.904671957939D-02 2 -3.327946567475D-01 1.355262241947D-02 -1.899077114113D-02 3 8.772623007048D-02 -4.247217004031D-03 6.314342474404D-03 4 -2.582394435391D-02 1.090757038295D-03 -1.202894310870D-03 5 6.746292673873D-03 -3.228772733572D-04 1.070577412178D-04 6 -1.132324670043D-03 6.889983086344D-05 -6.086331074514D-07 7 1.006838799981D-04 -5.193593477524D-06 -2.845251555754D-06 8 -3.599766107118D-06 3.508499294249D-08 3.027924280383D-07 E-Index: 3 4 5 T-Index: 0 -2.422134716752D-02 3.199185442634D-03 -6.987784095340D-05 1 -4.450036905348D-02 9.670609772772D-03 -1.101676052891D-03 2 8.393372221366D-03 -1.661524835400D-03 1.641367406906D-04 3 -2.639744634139D-03 5.083813172965D-04 -5.282312671120D-05 4 3.818974330343D-04 -6.097846279683D-05 6.274556790674D-06 5 9.032592725060D-06 -6.659380541156D-06 8.007827323926D-07 6 -7.241191756806D-06 1.656854215049D-06 -1.498873287066D-07 7 1.401115633607D-06 -2.121062436653D-07 1.534383868464D-08 8 -1.101496052033D-07 1.593127950555D-08 -1.277557055555D-09 E-Index: 6 7 8 T-Index: 0 -1.803884638427D-05 1.309228115068D-06 -2.572694262914D-08 1 6.597236559178D-05 -1.961355019834D-06 2.274461149865D-08 2 -8.182135682187D-06 1.912043686849D-07 -1.561456368451D-09 3 3.184968943859D-06 -1.061178779633D-07 1.506697376442D-09 4 -4.432073749742D-07 1.802283140716D-08 -2.998106690730D-10 5 -3.770998670281D-08 7.419022111792D-10 -5.644157060356D-12 6 7.339285822808D-09 -2.538540703677D-10 5.059927143765D-12 7 -7.934859405533D-10 3.738687857068D-11 -8.858974656396D-13 8 7.567293625031D-11 -3.326379990558D-12 6.790144662322D-14 Max. rel. Error: 4.0429 % Mean rel. Error: 1.7450 % \end{verbatim}\end{small} \begin{figure} \label{7.2c} \epsfxsize=16truecm \epsffile{Amjuel_PS/hmn4fu.ps} \end{figure} \newpage \subsection{ Reaction 7.2d $ H^- + p \rightarrow ...+ H(5) $, \ Ratio $H(5)/H^- $, cold $H^-$ } Multi-step hydrogenic population coefficients Data: K. Sawada, T.Fujimoto, \cite{kn:Sawada} and R. Janev et al, 1987, and P.T. Greenland Production of initial $H(n=2), H(n=3)$ from $H^-$ via $ \langle Hydhel~ 7.2.2\rangle + \langle Hydhel~ 7.2.3\rangle$, then CR redistribution in H Ratio of population coefficients: p(5)/nH- \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.043880324651D+01 2.037032074318D+00 -5.086322906145D-02 1 1.011406665313D+00 -6.365628088545D-02 7.087018763490D-02 2 -4.732792128048D-01 -1.434223357911D-02 1.444177153118D-02 3 1.440745315416D-01 3.264873576448D-03 1.234505116701D-04 4 -4.082830889986D-02 1.991190906181D-03 -2.756435764540D-03 5 9.541548408277D-03 -9.069208554478D-04 6.996980010317D-04 6 -1.454117847671D-03 1.551884580262D-04 -5.857488300427D-05 7 1.198928707328D-04 -1.400228251698D-05 6.473439676219D-07 8 -4.030214875087D-06 6.097512779644D-07 4.415255128121D-08 E-Index: 3 4 5 T-Index: 0 2.509733144867D-02 -6.315994199856D-03 8.827794491945D-04 1 -2.975345239990D-02 5.983399626204D-03 -6.277759777604D-04 2 -5.166305865235D-03 9.106705396634D-04 -8.761725049017D-05 3 -1.123250849126D-03 4.288583660416D-04 -6.890481712127D-05 4 1.147789672027D-03 -2.316365246467D-04 2.543759697649D-05 5 -1.993228761853D-04 2.517330858438D-05 -1.247794740929D-06 6 9.762118554856D-06 -3.741044970390D-07 -9.913305397062D-08 7 2.196741015054D-07 6.182578609139D-08 -2.188081446861D-08 8 -1.180565156491D-09 -1.449312603808D-08 3.350274299704D-09 E-Index: 6 7 8 T-Index: 0 -6.942768316956D-05 2.730469037199D-06 -4.155159141638D-08 1 3.369864501513D-05 -8.510546585606D-07 7.531215060388D-09 2 4.914337425208D-06 -1.501058689051D-07 1.891596830989D-09 3 5.529304847315D-06 -2.178898125651D-07 3.358437789658D-09 4 -1.555058635679D-06 4.945103866119D-08 -6.348990139489D-10 5 -1.032098974250D-08 3.032884418381D-09 -7.544164802502D-11 6 1.356968032839D-08 -6.737882205239D-10 1.229312195398D-11 7 2.266731611803D-09 -9.840633948791D-11 1.532952032542D-12 8 -3.079193750552D-10 1.282055029730D-11 -2.003506603284D-13 Max. rel. Error: 3.6382 % Mean rel. Error: 1.4968 % \end{verbatim}\end{small} \begin{figure} \label{7.2d} \epsfxsize=16truecm \epsffile{Amjuel_PS/hmn5fu.ps} \end{figure} \newpage \subsection{ Reaction 7.2e $ H^- + p \rightarrow ...+ H(6) $, \ Ratio $H(6)/H^- $, cold $H^-$ } Multi-step hydrogenic population coefficients Data: K. Sawada, T.Fujimoto, \cite{kn:Sawada} and R. Janev et al, 1987, and P.T. Greenland Production of initial $H(n=2), H(n=3)$ from $H^-$ via $ \langle Hydhel~ 7.2.2\rangle + \langle Hydhel~ 7.2.3\rangle$, then CR redistribution in H Ratio of population coefficients: p(6)/nH- \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -3.067097488487D+01 2.133892956222D+00 -1.858785381782D-01 1 1.107995704752D+00 -7.267316900367D-02 8.619894154229D-02 2 -5.345011110243D-01 -3.782902464706D-02 3.756478330674D-02 3 1.764954640174D-01 -1.032649676351D-02 6.464524722712D-03 4 -5.202491523226D-02 9.880352020439D-03 -7.493150468782D-03 5 1.098049582592D-02 6.531384081385D-04 -4.330923663414D-04 6 -1.298474536154D-03 -1.099967577090D-03 7.673435067944D-04 7 6.641085066002D-05 1.987746890586D-04 -1.359755033628D-04 8 -6.055672527870D-07 -1.099732061179D-05 7.398032652292D-06 E-Index: 3 4 5 T-Index: 0 9.184112431405D-02 -2.187443850319D-02 2.732957962088D-03 1 -3.580517565764D-02 6.746409669729D-03 -6.444562044629D-04 2 -1.526915092790D-02 3.195158804825D-03 -3.642351248993D-04 3 -1.591669787688D-03 2.306297194231D-04 -2.527875779410D-05 4 2.344024954832D-03 -3.904912867153D-04 3.759207667760D-05 5 8.191445720958D-05 3.579949470965D-07 -1.520984760597D-06 6 -2.001600190074D-04 2.348421586345D-05 -1.161204797043D-06 7 3.467501043759D-05 -3.909320595026D-06 1.690954968052D-07 8 -1.839785030150D-06 1.966330012309D-07 -6.837510677821D-09 E-Index: 6 7 8 T-Index: 0 -1.868296143542D-04 6.535291194065D-06 -9.119318650851D-08 1 3.052346096314D-05 -6.246714758968D-07 3.118274317587D-09 2 2.310260448654D-05 -7.637664587365D-07 1.022317615231D-08 3 1.917516778339D-06 -7.990930597360D-08 1.329300639507D-09 4 -2.089962077496D-06 6.184502696051D-08 -7.491029220022D-10 5 1.631598610791D-07 -6.823070866810D-09 1.018157208247D-10 6 1.519122575792D-09 1.768275307240D-09 -4.254302334326D-11 7 2.544277095276D-09 -4.245685956755D-10 9.325245214987D-12 8 -3.147128047635D-10 2.969365004153D-11 -6.059328354768D-13 Max. rel. Error: 4.5793 % Mean rel. Error: 1.9756 % \end{verbatim}\end{small} \begin{figure} \label{7.2e} \epsfxsize=16truecm \epsffile{Amjuel_PS/hmn6fu.ps} \end{figure} \newpage \subsection{ Reaction 2.0a $e + H_2 \rightarrow H_2^+ + ... $ , Ratio \ $H_2^+/H_2$ } Multi-step hydrogenic density ratios Data: K. Sawada, T.Fujimoto, \cite{kn:Sawada} and Janev et al, 1987, and P.T. Greenland CR equilibrium ratio H2+ to H2 density (coll.rad model, Sawada/Fujimoto/Greenland) here: H2+ gain from electr. impact only only contribution from EI on H2 and H2* to production rate of $H_2^+$ \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -1.929803964240D+01 2.097006502950D-01 -1.100904809661D-01 1 1.727612905933D+01 -4.662670859833D-01 8.567341672326D-02 2 -8.438025952533D+00 6.115179297110D-01 -1.153478632323D-01 3 2.883389908864D+00 -4.286361930144D-01 6.596018559458D-02 4 -7.403401021470D-01 1.809442086665D-01 -1.864042138902D-02 5 1.387371448471D-01 -4.879175895909D-02 4.430141421894D-03 6 -1.746217632264D-02 8.151856339270D-03 -1.015594807894D-03 7 1.287561948974D-03 -7.544209459715D-04 1.374937928555D-04 8 -4.136061327089D-05 2.914443517923D-05 -7.106408217685D-06 E-Index: 3 4 5 T-Index: 0 4.477781641551D-02 -9.060826089295D-03 1.170547725039D-03 1 -6.827368520293D-03 -3.618060467670D-03 6.852659500488D-04 2 1.993457166448D-02 1.643837202714D-04 -3.516424328964D-04 3 -1.341784022457D-02 1.582201264314D-03 -7.056994955968D-05 4 1.875666968084D-03 -2.978688155916D-04 2.721069163086D-05 5 1.476743155802D-04 -3.955049388000D-05 2.382368688632D-06 6 6.205132641268D-06 7.210178682186D-06 -6.812476857444D-07 7 -1.222677896703D-05 8.247029259344D-07 -5.043186962921D-08 8 1.041267499432D-06 -1.158374992604D-07 9.052478729563D-09 E-Index: 6 7 8 T-Index: 0 -8.893455666588D-05 3.479454987799D-06 -5.361512296401D-08 1 -4.473404420068D-05 1.209602016239D-06 -1.069974187479D-08 2 3.207886028645D-05 -1.101305933603D-06 1.299192188737D-08 3 4.431489645883D-07 2.326874797653D-08 1.068518137706D-10 4 -1.428413713222D-06 4.845148645034D-08 -8.048035605554D-10 5 -5.790867265229D-08 -6.986008432331D-10 4.535659079263D-11 6 3.277446170025D-08 -8.583517963518D-10 9.700723935742D-12 7 2.025920058300D-09 -3.655728430701D-11 8.337869178540D-14 8 -4.280094258996D-10 1.063115935764D-11 -1.030790224273D-13 Max. rel. Error: 1.8077 % Mean rel. Error: .3852 % \end{verbatim}\end{small} \begin{figure} \label{h12_2.0a} \epsfxsize=16truecm \epsffile{Amjuel_PS/ratioH12_2a.ps} \end{figure} \newpage \subsection{ Reaction 2.0b $e + H_2(v=0) \rightarrow H_2^+ + ... $ , Ratio \ $H_2^+/H_2$ } Multi-step hydrogenic density ratios Data: K. Sawada, T.Fujimoto, \cite{kn:Sawada} and R. Janev et al, 1987, and P.T. Greenland CR equilibrium ratio $H_2^+$ to $H_2$ density (coll.rad model, Sawada/Fujimoto/Greenland) contribution from EI on $H_2$ and $H_2^*$ plus from CX on cold $H_2(v=0)$, ($E_{H_2}(v)=0.1$ eV) and assuming $n_e=n_p, T_e=T_p$ \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -8.073335051460D+00 6.423193640255D-03 -8.948271203923D-03 1 1.653303173229D+00 -2.467726829997D-02 2.781981866915D-03 2 -2.823571725913D+00 4.179798625064D-02 -3.843754761904D-02 3 3.990452244578D+00 3.234966368980D-02 1.652438305320D-02 4 -1.928017324234D+00 -5.924941119276D-02 2.747810096639D-03 5 4.270719810226D-01 3.111963342548D-02 -5.375451827926D-03 6 -4.448144242484D-02 -7.757664930424D-03 2.077957627729D-03 7 1.689930248766D-03 9.331136287171D-04 -3.275780863917D-04 8 1.023775315217D-05 -4.333393780782D-05 1.830671388026D-05 E-Index: 3 4 5 T-Index: 0 4.582288903630D-03 -1.133062383784D-03 1.472017794904D-04 1 2.885192609023D-03 -9.313120366375D-04 1.193603851194D-04 2 1.457779901878D-02 -2.689882985994D-03 2.781888663389D-04 3 -1.096201612859D-02 1.873511746692D-03 -1.169697988538D-04 4 5.081237207186D-03 -1.022266662048D-03 5.028620238286D-05 5 -1.087834901368D-03 3.309186604685D-04 -2.068184308171D-05 6 -4.372642244363D-05 -3.372497244723D-05 2.250956728263D-06 7 4.092745909295D-05 -2.274671467977D-06 2.463960054850D-07 8 -3.393709830706D-06 3.905523509303D-07 -3.774892100311D-08 E-Index: 6 7 8 T-Index: 0 -1.037336914709D-05 3.752297970376D-07 -5.454015313711D-09 1 -7.537317404876D-06 2.293533267915D-07 -2.631009817091D-09 2 -1.566116716437D-05 4.383284185329D-07 -4.647720359472D-09 3 3.575003652413D-07 2.295739667060D-07 -6.354279184897D-09 4 1.852056305253D-06 -2.235055431776D-07 5.044313531628D-09 5 -1.431641793698D-07 4.978742338393D-08 -1.196745758163D-09 6 4.433372743456D-08 -7.031624330495D-09 1.525402495797D-10 7 -2.449746761192D-08 1.051457900024D-09 -1.574612982461D-11 8 2.386870809793D-09 -7.721695858310D-11 9.552566353384D-13 Max. rel. Error: 20.6614 % Mean rel. Error: 8.5812 % \end{verbatim}\end{small} \newpage this page is intentionally left blank \texttt{} \newpage \subsection{ Reaction 2.0c $e + H_2(v) \rightarrow H_2^+ + ... $ , Ratio \ $H_2^+/H_2$ } Multi-step hydrogenic density ratios Data: K. Sawada, T.Fujimoto, \cite{kn:Sawada} and R. Janev et al, 1987, and P.T. Greenland CR equilibrium ratio H2+ to H2 density (coll.rad model, Sawada/Fujimoto/Greenland) for vibrational population $P(v)$ contribution from CX on cold H2(v) ($E_{H_2}(v)=0.1$ eV) and EI on H2 and H2* Should be larger than corresponding H11 ratio for contrib. from CX alone. Slightly violated due to fitting problem near 1-2 eV \begin{small}\begin{verbatim} E-Index: 0 1 2 T-Index: 0 -5.179118614571D+00 1.286086917362D-02 -1.247224025136D-02 1 2.724390078109D+00 2.834163745797D-02 -3.864050364482D-02 2 -4.386686018740D+00 -2.926061072808D-02 2.894878695435D-02 3 2.264569877939D+00 1.815438259403D-02 -1.085596419844D-02 4 7.274238145138D-02 -8.711469240181D-03 1.228482582919D-03 5 -3.332379782334D-01 3.737790746246D-03 -2.689540529741D-04 6 9.526327139861D-02 -1.046333532366D-03 2.549358736065D-04 7 -1.096455316607D-02 1.457992401832D-04 -5.912048929304D-05 8 4.636081955869D-04 -7.621573981592D-06 3.973565261183D-06 E-Index: 3 4 5 T-Index: 0 4.533679343348D-03 -8.361635510932D-04 8.553044625491D-05 1 1.706652099436D-02 -3.663038423578D-03 4.202564138138D-04 2 -9.446648200804D-03 1.518996106179D-03 -1.265997327758D-04 3 3.413100865417D-03 -5.414461499166D-04 5.583904028460D-05 4 -2.783712092681D-04 4.118527168273D-05 -1.416596336268D-05 5 -7.626065770945D-05 3.568228589947D-05 -1.406315371249D-06 6 -3.059560467433D-05 -3.460893323989D-06 4.064186524949D-07 7 1.303239138604D-05 -1.086383020673D-06 6.161003040376D-08 8 -1.046764002685D-06 1.291713097220D-07 -9.932517910526D-09 E-Index: 6 7 8 T-Index: 0 -4.999715093023D-06 1.571098567732D-07 -2.060813085997D-09 1 -2.662584829521D-05 8.795062121815D-07 -1.182222955604D-08 2 5.854399926391D-06 -1.486122653306D-07 1.689012430939D-09 3 -3.494312204501D-06 1.176151828469D-07 -1.631239647294D-09 4 1.434270108351D-06 -5.449461807998D-08 6.856555143001D-10 5 -3.197342970575D-08 -4.539301068809D-10 9.975543797298D-11 6 -3.342848157445D-08 2.469622408760D-09 -6.675572336239D-11 7 2.239916154599D-10 -2.455363614572D-10 7.954115052237D-12 8 3.412487324650D-10 1.748563436447D-12 -2.514652180013D-13 Max. rel. Error: 18.5554 % Mean rel. Error: 8.9531 % \end{verbatim}\end{small} \begin{figure} \label{2.0c} \epsfxsize=16truecm \epsffile{Amjuel_PS/ratioH12_2bc.ps} \end{figure} \newpage \section{Appendix} \newpage \begin{thebibliography}{99} \bibitem{kn:Ehrhardt} A.B.Ehrhardt, W.D.Langer, PPPL 2477 (1987) \bibitem{kn:Janev} R.K. Janev, B. Langer et al. Springer Series on Atoms+Plasmas, Vol 4, 1987 \bibitem{kn:Riviere} A.C.Riviere, Nucl.Fus. 11 (1971), p363 \bibitem{kn:Mahn} C.Mahn, V.Welge, IPP 2/239, June 1978 \bibitem{kn:Reiter91c} Reiter, D., Eckstein, W., Giesen, G., Belitz, H.J., Database for recycling and penetration of neutral helium atoms in the boundary of a fusion plasma, J\"ul-2605 (1991) \bibitem{kn:Reiter-Janev} Reiter, D. in ``Atomic and Plasma Material Interaction Processes", eds. R.K. Janev, H.W. Drawin, Elsevier Science Publishers 1993 \bibitem{kn:Sawada} Sawada,K., Fujimoto,T., J. Appl. Phys.78 (5), (1995) ,p2913 \bibitem{kn:Bell} Bell et al.,``Atomic and molecular data for fusion, part I: recommended cross-sections and rates for electron ionization of light atoms and ions" report CLM-R 216, UKAEA Culham, 1982 \bibitem{kn:Bachmann} Bachmann, P., Reiter, D., Contrib. Plas. Phys. 35, (1995), 1, pp45 \bibitem{kn:Cosby} P.C. Cosby, ``Electron-impact dissociation of nitrogen", J. Chem. Phys 98 (1993) 9544 \bibitem{kn:Bahati} E.M. Bahati, J.J. Jureta, D.S. Belic, H. Cherkani-Hassani, M.O. Abdellahi and P. Defrance, ``Electron impact dissociation and ionization of N2+", J. Phys. B: At. Mol. Opt. Phys. 34 (2001) 2963 \bibitem{kn:Rapp1} D. Rapp and P. Englander-Golden, ``Total cross-sections for ionization and attachment in gases by electron impact. I. Positive ionization", J. Chem. Phys 43 (1965) 1464 \bibitem{kn:Rapp2} D. Rapp, P. Englander-Golden and D.D. Briglia, ``Cross-sections for dissociative ionization of molecules by electron impact", J. Chem Phys. 42 (1965) 4081 \bibitem{kn:Brook} E. Brook, M.F.A. Harrison and A.C.H. Smith, J. Phys. B: : At. Mol. Opt. Phys. 11 (1978) 3115 \bibitem{kn:Petersen} J.R. Petersen, A. Le Padellec, H. Danared et al., J. Chem. Phys. 108 (5), (1998), p1978 \bibitem{kn:Green} Greenland, T., Reiter, D., ``The Role of Molecular Hydrogen in Plasma Recombination", Report, JUEL-3258 (1996), FZ-J\"ulich \bibitem{kn:Behringer} Behringer, K., ``Description of the Impurity Transport Code ``STRAHL" ". Report JET-R (1987) 08 and Report JET-R (1989) 03, JET Joint Undertaking, Abingdon Oxon OX 14 3EA \bibitem{kn:Schultz} Schultz, D. in ``Atomic and Molecular Processes in Fusion Edge Plasmas", ed.: Janev, R.K., Plenum Press, New York, 1995 \bibitem{kn:Freeman} Freeman, R., Jones, E., (1974), CLMR-137, Culham Laboratory report, Abingdon, England \bibitem{kn:Fujimoto} T. Fujimoto, J. Quant. Spectrosc. Radiat. Transfer, 21 (1979) 439 and: M. Goto, J. Quant. Spectrosc. Radiat. Transfer, 76 (2003) 331 \bibitem{kn:OakRidge} Kristic~P.~S., Schultz~D.~R., Physical Review A, 60 (1999), p2118 \bibitem{kn:McWhirter} R.W.P. McWhirter, A.G. Hearn, Proc. Phys. Soc. 82 (1963), p641 \end{thebibliography} \end{document}