Last revised 12/14/00 If you have questions or find errors contact A. V. Phelps at avp@jila.colorado.edu NITROGEN ATOMS AND MOLECULES These tables are from A. V. Phelps, J. Phys. Chem. Ref. Data 20, 557 (1991), with permission. The cross sections are in units 1E-20 m2. The cross sections are designated by the product of the collision, e.g., Q(e) for electron production by ionization of N2, Qm for momentum transfer scattering of N+ by N2, and Lm the energy loss function used in "continuous" models. See the above reference for details. In the absence of differential cross section data the following total (angular integrated) inelastic cross sections should be treated as peaked in the forward direction as expected at high energies. Cross sections for N2 + N2 collisions tabulated by product. Lab. energy Cross section eV Q(2nd Pos.) Q(e) Qm theshold (18) (15.6) 0.1 - - 44.5 0.1333 - - 39.2 0.1778 34.3 0.237 30.2 0.316 26.8 0.422 24.2 0.562 21.8 0.750 19.7 1 17.9 1.334 16.6 1.778 15.2 2.37 14 3.16 13 4.22 12.1 5.62 11.3 7.50 10.6 10 9.8 13.34 9.25 17.78 8.7 23.7 0.0 8.2 31.6 0.01 0.0 7.75 42.2 0.03 0.0016 7.25 56.2 0.06 0.0054 6.75 75.0 0.0955 0.0116 6.23 100 0.131 0.0305 5.6 133.4 0.153 0.077 5.03 177.8 0.163 0.158 4.33 237 0.167 0.275 3.65 316 0.162 0.44 2.93 422 0.153 0.675 2.35 562 0.14 0.97 1.63 750 0.131 1.34 1.08 1000 0.151 1.74 0.68 1334 0.203 2.18 0.405 1778 0.31 2.74 0.237 2370 0.5 3.37 0.137 3160 0.75 4.06 0.077 4220 1.13 4.9 0.043 5620 1.58 5.87 0.0235 7500 2.13 6.93 0.013 10000 2.72 8.05 0.0072 Reaction coefficients for N2 + N2 collisions. E/n T+ Q(2nd Pos.) Q(e) Qm Td eV m2 m2 m2 500 0.877 -a - 2.03E-19 1000 2.04 - - 1.73E-19 2000 4.65 3.21E-25 - 1.44E-19 3000 7.69 4.92E-24 2.70E-27 1.28E-19 5000 13.89 4.06E-23 6.33E-25 1.11E-19 10000 28.7 2.08E-22 2.71E-23 9.39E-20 20000 61.7 5.65E-22 2.78E-22 7.75E-20 50000 166.7 1.06E-21 1.91E-21 5.63E-20 100000 362 1.32E-21 5.43E-21 3.98E-20 a Too small for meaningful calculation. ARGON ATOMS - ELASTIC updated 7/1/00 These cross section have been taken from the paper "Collision cross sections for argon atoms with argon atoms for energies from 0.01 eV to 10 keV" by A. V. Phelps, C. H. Greene, and J. P. Burke, Jr., J. Phys. B 33, 2965 (2000). We present the results of fitting the cross sections with empirical formulas so as to facilitate the application of the theoretical results to transport and discharge models. We first fit the theoretical integral and differential cross section results over the energy range from 1 eV to 10 keV. No attempt was made to fit the oscillatory structure at lower energies. We then give fits to the differential scattering cross sections over the same energy range. Finally, tabulations of elastic and inelastic cross sections for Ar-Ar collisions. The cross section discussion given below is extracted and modified from the REVTEX/LATEX version of the above paper. BEGIN LATEX FORMAT \documentstyle[preprint,aps,amssymb]{revtex} \begin{document} The cross sections for total scattering $\sigma_t^{fit}$ and viscosity scattering $\sigma_v^{fit}$ in m$^2$ obtained by fitting the theoretical values are given by \begin{eqnarray} {\sigma_t^{fit}(E)} = 2.1 \times 10^{-18} E^{-0.4} [1+(E/15)^2]^{0.16} \label{eq:totalfit} \end{eqnarray} and \begin{eqnarray} {\sigma_v^{fit}(E)} = 1.85\times10^{-19} E^{-0.15}/ [1+(E/9)^{0.7}+(E/200)^{1.5}+(E/1000)^{2.5}]^{0.5}, \label{eq:viscosityfit} \end{eqnarray} where the relative energy E is in eV. Because of the near equality of the cross sections for both the symmetric and asymmetric cases presented earlier, equations\ (\ref{eq:totalfit}) and (\ref{eq:viscosityfit}) are valid for both cases. This $\sigma_v^{fit}(E)$ is useful in the ``single beam'' approximation \cite{PHE99,PHE87,PHE88} for the modeling of fast Ar atoms in discharges. The cross section for use in modeling the diffusion of $^{38}$Ar in $^{40}$% Ar as obtained by fitting the theoretical values shown in figure \ref{fig:Qasymm} is \begin{eqnarray} {\sigma_d^{fit}(E)} = 2.13\times10^{-19}\: E^{-0.2}/[1+(E/10)^{0.7}+(E/300)^{1.5}+(E/500)^2]^{0.5}. \label{eq:diffusionfit} \end{eqnarray} As pointed out previously, $\sigma_d^{fit}(E)$ is meaningful only for the asymmetric scattering case. The fits to the theory given by equations\ (\ref{eq:viscosityfit}) and (\ref{eq:diffusionfit}) are good to $\pm 5\%$ for energies from 0.1 eV to 10 keV, while that given by equation (\ref{eq:totalfit}) is good to $\pm 5\%$ for 1 eV to 10 keV. The functional form of the differential scattering cross section used to fit the theoretical results for the identical-atom scattering is symmetric about $\theta = \pi/2$ as required by the identical Ar atoms and contains an isotropic scattering term. The formula is based on the theory for scattering by a screened-Coulomb potential in the Born approximation \cite{MCD93} and is expected to be most useful at high energies. For the symmetric scattering case, we assume \begin{eqnarray} {\frac{{d\sigma}}{{d \Omega}}}(\theta)= {(a/2)[1 + 2 \eta - \cos(\theta)]^{-2} + (a/2)[1 + 2 \eta - \cos(\pi - \theta)]^{-2} + b}, \label{eq:fitdiffsymm} \end{eqnarray} where $\theta$ is in the center-of-mass frame and $a(E)$, $b(E)$, and $\eta(E)$ are to be determined from fits to the results of sections\ \ref{subsec:diffQs} and \ref{subsec:intQs}. When using the fits to the theoretical results for the asymmetric scattering, we use the first term of equation\ (\ref{eq:fitdiffsymm}) and half the last term. We find that, just as for the fits to the integrated cross sections, the $a(E)$, $b(E)$, and $\eta(E)$ are negligibly different for our symmetric and asymmetric scattering cases. By fitting to the three theoretical cross sections for the asymmetric case rather than the two cross sections for the symmetric case, we can use a three parameter expression for the differential cross section. Analytic expressions for $\sigma_t^{th}(E)$, $\sigma_v^{th}(E)$ and $\sigma_d^{th}(E)$ as functions of $a(E)$, $b(E)$ and $\eta(E)$ are first calculated by substituting equation (\ref{eq:fitdiffsymm}) into equations\ (\ref{eq:attenuation}), (\ref{eq:DiffusionSigma1}), and (\ref{eq:ViscositySigma1}). These $\sigma_t^{th}$, $\sigma_v^{th}$, and $\sigma_d^{th}$ are then set equal to corresponding theoretical cross sections from figure \ref{fig:Qasymm} at representative energies E and the resultant set of equations solved numerically for values of $a(E)$, $b(E)$ and $\eta(E)$. The empirical fits to these values of $a(E)$, $b(E)$ and $\eta(E)$ yield cross sections that agree with the data to $\pm 5\%$. We note that this reconstructed $\sigma_t$ is particularly sensitive to the choice of parameters. The analytic expressions for $a(E)$ and $b(E)$ in units of $10^{-20}$ m$^2$/str are \begin{eqnarray} {a(E)} = 0.27 E^{0.2}/[1+(E/9)^{0.8}+(E/350)^{1.3}+(E/800)^{2.2}], \label{eq:coefa} \end{eqnarray} and \begin{eqnarray} {b(E)} = 3.0 E^{-0.2}/[1+(E/15)^{0.5}+(E/800)^{1.1}+(E/10000)^2]. \label{eq:coefb} \end{eqnarray} The analytic expression for $\eta(E)$ resulting from the fitting is \begin{eqnarray} {\eta(E)} = 0.002 E^{0.75}/[1+(E/6)^{1.15}+(E/80)^{1.95}+(E/500)^{2.5}]. \label{eq:coefbeta} \end{eqnarray} The $b(E)$ parameter becomes very small at energies above 1 keV, as expected when screened-Coulomb scattering is dominant. Although the quality of the analytic fit to the theoretical differential cross sections varies considerably with energy and angle, we believe the ``three-moment'' fit described in this section conveys the essence of the differential scattering cross sections. When applying the present results to plasma models using the Monte Carlo techniques \cite{BOG95,SER96,REV97,PET98,SKU68,LIN77}, it is often necessary to calculate the probability that the Ar-Ar scattering will occur with an angle of less than $\theta_c$. This ``cumulative scattering probability'' for the symmetric scattering case $p^{{\bf ident}}(\theta_c)$ is given by \begin{equation} {p^{{\bf ident}}(\theta_c)}={\frac{{\ \int_0^{\theta_c} {\frac{{d \sigma^{% {\bf ident}}}}{{d \Omega}(\theta)}} \sin{\theta} d\theta} }{{\ \int_0^{\pi/2} {\frac{{d \sigma^{{\bf ident}}}}{{d \Omega}(\theta)}} \sin{% \theta} d\theta}}} \leq 1, \label{eq:cumprobsym} \end{equation} where $0 \leq \theta_c \leq \pi/2$. If we use the differential scattering cross section given by equation (\ref{eq:fitdiffsymm}), and set $p^{{\bf ident}}(\theta_c)$ equal to random number $R$, we obtain a cubic equation in $\cos(\theta_c)$. This cubic equation is to be solved for $\theta_c(R,E)$ in terms of $R$ and values of $a(E)$, $b(E)$, and $\eta(E)$ from equations\ \ref{eq:coefa} through \ref{eq:coefbeta}. The integrated inelastic cross sections are less than 10\% of $\sigma_{t}^{sum}$ for energies below 500 eV. We suggest that one use the fit to theory in equations (\ref{eq:fitdiffsymm}) to (\ref{eq:coefbeta}), so that one needs only one application of equation\ (\ref{eq:cumprobsym}) for each collision. The small values of these inelastic cross sections is fortunate because of the poor knowledge regarding their differential cross sections. In order to reduce computer time, Monte Carlo procedures often make the approximation that the differential cross section is independent of angle rather than the sharply peaked form in equation (\ref{eq:fitdiffsymm}). In this case, we recommend that at low energies the theoretical total cross section $Q_t$ be replaced by $3/2 \times Q_v$ from equation (\ref{eq:viscosityfit}). Equations (\ref{eq:totalfit}), (\ref{eq:diffusionfit}), (\ref{eq:fitdiffsymm}), (\ref{eq:coefa}), (\ref{eq:coefb}), and (\ref{eq:coefbeta}) would then be unused. This approximation keeps the viscosity cross section, i.e., the cross section limiting energy transport, constant \cite{CHA70,PHE94}. The results show that it is a poor approximation to use measured values of the attenuation cross section (often referred to as the total cross section) for the transport cross sections. \end{document} END LATEX FORMAT There is a potentially serious problem with applying this form of differential scattering to a fast Ar model. It arises from the fact that the total cross section Qt given above is roughly an order of magnitude larger than the viscosity cross section. This means that there will be an order of magnitude more collisions to compute for each fast atom than if one used an isotropic cross section yielding the same viscosity cross section. What is probably worse, is that there will be many orders of magnitude more product atoms to follow. The problem is how to make use of the facts that most of these high energy collisions are through small angles and that if the angle is small enough the slow product atom has a negligibly small energy. An alternative set of elastic cross sections, based on thermal viscosity measurements is used by A. Kersch, W. Morokoff, and Chr. Werner, J. Appl. Phys. 75, 2278 (1994) and by V. V. Serikov and K. Nanbu, J. Vacuum Sci. Technol. A 14, 3108 (1996). The viscosity cross section calculated from their variable-hard- sphere cross section is within 30% of ours. However, the self-diffusion or momentum transfer cross section calculated from their variable-hard-sphere cross section is about a factor of three smaller than ours. Also, our total cross section is about an order of magnitude larger than theirs. These differences arise from the highly anisotropic differential cross section we find to be consistent with the input data. See MODSCRCL.NB for a comparison. Argon-argon elastic scattering table The table give below is sampled from a more detailed table that shows better the oscillations in the total cross section for Ar-Ar collisions at relative energies below about 1 eV. The more extensive tables are availble on request to avp@jila.colorado.edu. The energy values are relative, i.e., center-of-mass values, in eV. SigmaTOT and SigmaVisc are the total (integrated) and viscosity cross sections for elastic scattering in m^2. Delta(Lmax) is the computed phase shift at the maximum angular momentum quantum number Lmax used in the calculations for a particular collision energy. %Gianturco-Aziz-Slaman potential 02/17/00 14:19:50 %energy(eV), SigmaTOT, SigmaVisc, Delta(Lmax), Lmax 1.00000D-02 4.15120D-18 6.37327D-19 1.02822D-01 100 1.77828D-02 3.89469D-18 5.71408D-19 8.15500D-02 132 3.16228D-02 3.58990D-18 4.16518D-19 6.13997D-02 176 5.62341D-02 2.88137D-18 3.02981D-19 4.48829D-02 236 1.00000D-01 2.95445D-18 2.49074D-19 3.30338D-02 316 1.77828D-01 2.39723D-18 2.19577D-19 2.52370D-02 420 3.16228D-01 2.10701D-18 1.98465D-19 1.86161D-02 562 5.62341D-01 2.21634D-18 1.80237D-19 1.41061D-02 748 1.00000D+00 2.06321D-18 1.62849D-19 1.04434D-02 1000 1.77828D+00 1.69308D-18 1.44824D-19 7.87665D-03 1332 3.16228D+00 1.32380D-18 1.25877D-19 5.87556D-03 1778 5.62341D+00 1.04412D-18 1.06645D-19 4.41441D-03 2370 1.00000D+01 8.58338D-19 8.81874D-20 3.30113D-03 3162 1.77828D+01 7.41028D-19 7.13037D-20 2.47671D-03 4216 3.16228D+01 6.67289D-19 5.73133D-20 1.85713D-03 5622 5.62341D+01 6.18802D-19 4.56046D-20 1.39153D-03 7498 1.00000D+02 5.84667D-19 3.56592D-20 1.04270D-03 10000 1.77828D+02 5.58245D-19 2.72726D-20 7.82202D-04 13334 3.16228D+02 5.35810D-19 2.03284D-20 5.86385D-04 17782 5.62341D+02 5.14848D-19 1.47155D-20 4.39766D-04 23712 1.00000D+03 4.94013D-19 1.03082D-20 3.29681D-04 31622 1.77828D+03 4.72663D-19 6.96322D-21 2.47236D-04 42168 3.16228D+03 4.50369D-19 4.52219D-21 1.85361D-04 56234 5.62341D+03 4.26661D-19 2.81766D-21 1.39011D-04 74988 1.00000D+04 4.02005D-19 1.68319D-21 1.04232D-04 100000 An evaluation of the effects of inelastic collisions on transport cross sections is availble on request. ARGON ATOMS - INELASTIC This table is from A. V. Phelps, J. Phys. Chem. Ref. Data 20, 557 (1991), with permission. The cross sections are in units 1E-20 m2. Note that the momentum transfer cross section in the original table should be replaced by the formula given above. In the absence of differential cross section data the following total (angular integrated) inelastic cross sections should be treated as peaked in the forward direction as expected at high energies. Some data on the angular distribution of inelastically scattered Ar is given by Brenot et al, Phys. Rev. A 11, 1245 (1975). Added 11/11/01 Note that Aberth and Lorents, Phys. Rev. 144, 109 (1966) state that the large-angle differntial scattering at 400and 600 eV is dominated by inelastic scattering Cross sections for Ar + Ar collisions tabulated by product, i.e., Q(e) means the production of electrons by ionization of Ar. Lab. atom Cross Section energy eV Q(e) Q(811) Q(795) threshold (15.8) (13.1) (11.6) 10 13.34 17.78 23.7 31.6 42.2 0.003 0.006 56.2 0.03 0.033 75.0 0.13 0.085 0.0025 100 0.37 0.14 0.0063 133.4 0.63 0.185 0.0111 177.8 0.88 0.235 0.0189 237 1.12 0.285 0.0305 316 1.33 0.315 0.0467 422 1.54 0.34 0.0605 562 1.74 0.355 0.0673 750 1.96 0.365 0.0725 1000 2.14 0.37 0.075 1334 2.33 0.38 0.0775 1778 2.5 0.38 0.08 2370 2.64 0.385 0.0825 3160 2.8 0.385 0.0845 4220 2.9 0.387 0.0865 5620 3.03 0.39 0.0887 7500 3.13 0.395 0.0905 10000 3.2 0.4 0.092 Helium-helium elastic scattering added 2/13/00 These are results using the theory described under the preceding argon entry. I have not yet attempted to fit the He-He results with analytical expressions. The following table is taken directly from the Fortran output. The present viscosity cross sections are within 10% of the results inferred from viscosity and thermal conductivity measurements for energies 0.008 and 0.8 eV. The present total cross sections are within 10% of the measurements of Feltgen et al, Phys. Rev. Lett. 30, 820 (1973) for energies from 0.01 to 0.2 eV. The discrepancies that increase with further decreases in energy have not yet been investigated. We have made no adjustments to these theoretical elastic cross sections to take into account the effects of inelastic channels at energies above about 50 eV. An evaluation of the effects of inelastic collisions on transport cross sections is availble on request. %Gianturco-Aziz-Slaman potential 02/13/00 10:36:44 %energy(eV),SigmaTOT(m^2),SigmaVisc(m^2),Delta(Lmax), Lmax 1.00000D-02 3.78947D-19 1.42034D-19 2.28101D-06 100 1.77828D-02 3.20317D-19 1.28344D-19 1.81080D-06 132 3.16228D-02 3.31205D-19 1.17020D-19 1.36522D-06 176 5.62341D-02 3.21391D-19 1.06409D-19 9.99402D-07 236 1.00000D-01 3.15322D-19 9.59901D-20 7.36216D-07 316 1.77828D-01 3.14796D-19 8.57765D-20 5.62394D-07 420 3.16228D-01 3.06484D-19 7.57821D-20 4.15187D-07 562 5.62341D-01 2.89008D-19 6.60981D-20 3.14699D-07 748 1.00000D+00 2.81425D-19 5.67957D-20 2.33217D-07 1000 1.77828D+00 2.67478D-19 4.79359D-20 1.75998D-07 1332 3.16228D+00 2.52890D-19 3.95764D-20 1.31392D-07 1778 5.62341D+00 2.39439D-19 3.17867D-20 9.87730D-08 2370 1.00000D+01 2.26179D-19 2.46549D-20 7.39066D-08 3162 1.77828D+01 2.12447D-19 1.82524D-20 5.54722D-08 4216 3.16228D+01 1.98532D-19 1.26727D-20 4.16092D-08 5622 5.62341D+01 1.84733D-19 8.18177D-21 3.11862D-08 7498 1.00000D+02 1.71121D-19 4.88337D-21 2.33734D-08 10000 1.77828D+02 1.57759D-19 2.69124D-21 1.75366D-08 13334 3.16228D+02 1.44580D-19 1.36624D-21 1.31479D-08 17782 5.62341D+02 1.31693D-19 6.39995D-22 9.86129D-09 23712 1.00000D+03 1.18961D-19 2.78777D-22 7.39234D-09 31622 1.77828D+03 1.06794D-19 1.14286D-22 5.54413D-09 42168 3.16228D+03 9.51110D-20 4.46743D-23 4.15674D-09 56234 5.62341D+03 8.36960D-20 1.68450D-23 3.11609D-09 74988 1.00000D+04 7.26911D-20 6.18256D-24 2.33595D-09 100000 Our analytical approximation to the elastic viscosity cross section SigmaVisc = Qv versus relative Erel or center-of-mass energy is Qv = 6.5E-20*(Erel)^(-0.17)* [1+(Erel/15)^(0.7)+(Erel/100)^(1.7)+(Erel/300)^2]^(-1) If one plans to model He-He elastic collisions using these results at low energies and assuming isotropic scattering, the assumed angular- integrated isotropic cross section should be Qiso-assumed = 3/2 * Qv. Because of angular weighting effects this will lead to the correct viscosity cross section. At high energies, the 3/2 factor approaches 1/2. See the Ar-Ar reference cited above for more on this point. AVP thanks A Bogaerts for comments leading to improvement of this recommendation. Neon-neon elastic scattering added 2/15/00 These are results using the theory described under the preceding argon entry. I have not yet attempted to fit these results with analytical expressions. The following table is taken directly from the Fortran output. The present viscosity cross sections are within 10% of the results inferred from viscosity and thermal conductivity measurements for energies 0.008 and 0.8 eV. The present total cross sections are about 20% higher than the measurements of Morrow et al, J. Chem. Phys. 59, 2145 (1973) for energies from 0.04 to 0.07 eV. We have made no adjustments to the theoretical elastic cross sections to take into account the effects of inelastic channels that become important at energies above about 500 eV. An evaluation of the effects of inelastic collisions on transport cross sections is availble on request. %Gianturco-Aziz-Slaman potential 02/13/00 11:32:50 %energy(eV),SigmaTOT(m^2),SigmaVisc(m^2),Delta(Lmax), Lmax 1.00000D-02 1.55694D-18 2.68125D-19 1.26811D-03 100 1.77828D-02 1.63863D-18 1.98469D-19 1.00647D-03 132 3.16228D-02 1.46181D-18 1.65511D-19 7.58333D-04 176 5.62341D-02 1.16344D-18 1.47114D-19 5.54694D-04 236 1.00000D-01 8.86174D-19 1.33787D-19 4.08350D-04 316 1.77828D-01 6.97949D-19 1.22156D-19 3.11840D-04 420 3.16228D-01 5.75335D-19 1.11140D-19 2.30109D-04 562 5.62341D-01 4.98216D-19 1.00445D-19 1.74379D-04 748 1.00000D+00 4.47672D-19 9.00474D-20 1.29190D-04 1000 1.77828D+00 4.18918D-19 7.99990D-20 9.74816D-05 1332 3.16228D+00 3.96481D-19 7.03633D-20 7.27640D-05 1778 5.62341D+00 3.78867D-19 6.11952D-20 5.46952D-05 2370 1.00000D+01 3.63874D-19 5.26536D-20 4.09219D-05 3162 1.77828D+01 3.50036D-19 4.46333D-20 3.07132D-05 4216 3.16228D+01 3.36359D-19 3.63468D-20 2.30367D-05 5622 5.62341D+01 3.22705D-19 2.86684D-20 1.72655D-05 7498 1.00000D+02 3.08862D-19 2.20182D-20 1.29399D-05 10000 1.77828D+02 2.94717D-19 1.64427D-20 9.70842D-06 13334 3.16228D+02 2.80262D-19 1.18851D-20 7.27882D-06 17782 5.62341D+02 2.65795D-19 8.26622D-21 5.45927D-06 23712 1.00000D+03 2.51569D-19 5.49591D-21 4.09295D-06 31622 1.77828D+03 2.37024D-19 3.47031D-21 3.06955D-06 42168 3.16228D+03 2.23110D-19 2.06947D-21 2.30144D-06 56234 5.62341D+03 2.08300D-19 1.16126D-21 1.72599D-06 74988 1.00000D+04 1.94248D-19 6.12777D-22 1.29419D-06 100000 Krypton-krypton elastic scattering added 2/20/00 These are results using the theory described under the preceding argon entry. I have not yet attempted to fit these results with analytical expressions. The following table is taken directly from the Fortran output. The present viscosity cross sections are oscillate about but are up to 20% higher and 10% lower than the results inferred from a power-law fit to viscosity and thermal conductivity measurements for energies below 0.2 eV. The present total cross sections have not yet been compared with experiments. We have made no adjustments to the theoretical elastic cross sections to take into account the effects of inelastic channels at energies above about 500 eV. The table give below is sampled from the much more detailed table required to show the roughly +- 10% oscillations in the total cross section for Xe-Xe collisions at relative energies below 10 eV and in the viscosity cross section at energies below about 0.1 eV. The more extensive tables are availble on request to avp@jila.colorado.edu. %Gianturco-Dham et al potential 02/20/00 17:15:43 %energy(eV),SigmaTOT(m^2), SigmaV(m^2), Delta(Lmax), Lmax 1.00000D-02 6.47722D-18 7.46018D-19 4.01796D-05 856 1.77828D-02 5.42234D-18 6.47207D-19 4.36732D-05 1060 3.16228D-02 5.37439D-18 5.83318D-19 4.72183D-05 1314 5.62341D-02 4.87650D-18 4.05917D-19 5.02517D-05 1634 1.00000D-01 4.38289D-18 3.10576D-19 5.32073D-05 2034 1.77828D-01 3.81230D-18 2.64175D-19 5.54455D-05 2540 3.16228D-01 3.19457D-18 2.36022D-19 5.74046D-05 3176 5.62341D-01 3.22962D-18 2.13788D-19 5.87834D-05 3980 1.00000D+00 2.54419D-18 1.93375D-19 5.94499D-05 5000 1.77828D+00 2.40764D-18 1.73497D-19 5.95268D-05 6294 3.16228D+00 2.48404D-18 1.53916D-19 5.88921D-05 7942 5.62341D+00 2.22220D-18 1.34722D-19 5.75594D-05 10046 1.00000D+01 1.78950D-18 1.16025D-19 5.55863D-05 12738 1.77828D+01 1.39603D-18 9.86616D-20 5.30783D-05 16188 3.16228D+01 1.11181D-18 8.27038D-20 5.00543D-05 20624 5.62341D+01 9.26064D-19 6.83688D-20 4.66475D-05 26338 1.00000D+02 8.09351D-19 5.56868D-20 4.29802D-05 33712 1.77828D+02 7.35415D-19 4.46042D-20 3.91489D-05 43250 3.16228D+02 6.85832D-19 3.50482D-20 3.52528D-05 55614 5.62341D+02 6.49790D-19 2.69403D-20 3.13932D-05 71672 1.00000D+03 6.20950D-19 2.01931D-20 2.76623D-05 92562 1.77828D+03 5.94981D-19 1.47079D-20 2.41243D-05 119788 3.16228D+03 5.69723D-19 1.03713D-20 2.08282D-05 155334 5.62341D+03 5.45211D-19 7.05491D-21 1.78117D-05 201812 1.00000D+04 5.19601D-19 4.61542D-21 1.50928D-05 262678 Xenon-xenon elastic scattering added 2/17/00 These are results using the theory described under the preceding argon entry. I have not yet attempted to fit these results with analytical expressions. The following table is taken directly from the Fortran output. The present viscosity cross sections are up to 15% higher than the results inferred from viscosity and thermal conductivity measurements for energies below 0.2 eV. The present total cross sections have not yet been compared with absolute experiments, but show good agreement with the "glory" structure measured for energies from 0.15 to 2 eV and with calculations of the absolute magnitude by van den Riesen at al, Physica A 115, 396 (1982). We have made no adjustments to the theoretical elastic cross sections to take into account the effects of inelastic channels at energies above about 500 eV. The table give below is sampled from the much more detailed table required to show the roughly +- 10% oscillations in the total cross section for Xe-Xe collisions at relative energies below 10 eV and in the viscosity cross section at energies below about 0.1 eV. The more extensive tables are availble on request to avp@jila.colorado.edu. %Gianturco-Dham et al (1990) potential 02/16/00 16:33:36 %energy(eV),SigmaTOT(m^2),SigmaVisc(m^2),Delta(Lmax), Lmax 1.00000D-02 9.96731D-18 1.17190D-18 3.42908D-04 856 1.77828D-02 8.59084D-18 8.77198D-19 3.72828D-04 1060 3.16228D-02 7.84381D-18 7.54511D-19 4.03224D-04 1314 5.62341D-02 7.17105D-18 5.96334D-19 4.29282D-04 1634 1.00000D-01 6.35342D-18 4.24746D-19 4.54721D-04 2034 1.77828D-01 5.51434D-18 3.41874D-19 4.74067D-04 2540 3.16228D-01 4.88312D-18 2.98429D-19 4.91073D-04 3176 5.62341D-01 4.33354D-18 2.68829D-19 5.03159D-04 3980 1.00000D+00 3.98392D-18 2.43544D-19 5.09187D-04 5000 1.77828D+00 3.79373D-18 2.19413D-19 5.10202D-04 6294 3.16228D+00 3.17573D-18 1.95518D-19 5.05144D-04 7942 5.62341D+00 2.79482D-18 1.71778D-19 4.94115D-04 10046 1.00000D+01 2.92242D-18 1.48463D-19 4.77593D-04 12738 1.77828D+01 2.70825D-18 1.25456D-19 4.56467D-04 16188 3.16228D+01 2.22229D-18 1.04982D-19 4.30881D-04 20624 5.62341D+01 1.74008D-18 8.75770D-20 4.01963D-04 26338 1.00000D+02 1.37795D-18 7.24089D-20 3.70754D-04 33712 1.77828D+02 1.13733D-18 5.90995D-20 3.38072D-04 43250 3.16228D+02 9.85212D-19 4.75033D-20 3.04767D-04 55614 5.62341D+02 8.89419D-19 3.75291D-20 2.71706D-04 71672 1.00000D+03 8.26278D-19 2.90852D-20 2.39690D-04 92562 1.77828D+03 7.81108D-19 2.20656D-20 2.09272D-04 119788 3.16228D+03 7.45181D-19 1.63507D-20 1.80885D-04 155334 5.62341D+03 7.13897D-19 1.18082D-20 1.54862D-04 201812 1.00000D+04 6.84059D-19 8.29461D-21 1.31368D-04 262678 Neon-xenon elastic scattering added 3/3/00 These are results using the theory described under the preceding argon entry. I have not yet attempted to fit these results with analytical expressions. The following table is taken directly from the Fortran output. The present diffusion cross sections are in very good agreement with results inferred from diffusion coefficient measurements for energies below 0.2 eV. The experimental total cross sections scatter about the theoretical values and show satisfactory agreement with the "glory" structure measured for energies from 0.15 to 2 eV. We have made no adjustments to the theoretical elastic cross sections to take into account the effects of inelastic channels and have not looked at the magnitudes of excitation cross sections. We have not found ionization cross sections. The table give below is sampled from the much more detailed table required to show the oscillations in the total cross section for Ne-Xe collisions at relative energies below 10 eV. The more extensive tables are availble on request to avp@jila.colorado.edu. %extrapolated Gianturco-Barrow-Slaman-Aziz potential 02/26/00 17:00:28 %energy(eV), SigmaTOT(m^2),SigmaV(m^2), SigmaD(m^2), Delta(Lmax), Lmax 1.00000D-02 3.22216D-18 5.83818D-19 6.38764D-19 7.97784D-04 220 1.77828D-02 3.15871D-18 4.17700D-19 4.58968D-19 7.85380D-04 278 3.16228D-02 2.90329D-18 3.11646D-19 3.74672D-19 7.87298D-04 350 5.62341D-02 2.23057D-18 2.61171D-19 3.27719D-19 7.76987D-04 442 1.00000D-01 2.28300D-18 2.32760D-19 2.94148D-19 7.81945D-04 556 1.77828D-01 2.29355D-18 2.11892D-19 2.65425D-19 7.83531D-04 700 3.16228D-01 1.98785D-18 1.93387D-19 2.38558D-19 7.81984D-04 882 5.62341D-01 1.58179D-18 1.75535D-19 2.12532D-19 7.78103D-04 1112 1.00000D+00 1.23978D-18 1.57838D-19 1.87039D-19 7.85522D-04 1398 1.77828D+00 1.00073D-18 1.40194D-19 1.62023D-19 7.83143D-04 1762 3.16228D+00 8.47022D-19 1.22150D-19 1.38106D-19 7.85924D-04 2218 5.62341D+00 7.50802D-19 1.04626D-19 1.16443D-19 7.88992D-04 2792 1.00000D+01 6.89740D-19 8.85818D-20 9.71404D-20 7.90728D-04 3516 1.77828D+01 6.48493D-19 7.41943D-20 8.01158D-20 7.94420D-04 4426 3.16228D+01 6.18374D-19 6.14276D-20 6.52289D-20 7.98221D-04 5572 5.62341D+01 5.93135D-19 5.01957D-20 5.23409D-20 8.01814D-04 7016 1.00000D+02 5.70697D-19 4.04130D-20 4.13194D-20 8.07058D-04 8832 1.77828D+02 5.48850D-19 3.19973D-20 3.20310D-20 8.12317D-04 11120 3.16228D+02 5.27682D-19 2.48642D-20 2.43357D-20 8.19268D-04 13998 5.62341D+02 5.04881D-19 1.89232D-20 1.80846D-20 8.26514D-04 17624 1.00000D+03 4.82720D-19 1.40743D-20 1.31190D-20 8.35254D-04 22188 1.77828D+03 4.60088D-19 1.02080D-20 9.27292D-21 8.45803D-04 27932 3.16228D+03 4.36105D-19 7.20583D-21 6.37643D-21 8.57798D-04 35166 5.62341D+03 4.11042D-19 4.94255D-21 4.26095D-21 8.72336D-04 44270 1.00000D+04 3.85351D-19 3.29074D-21 2.76573D-21 8.89167D-04 55734 Helium-argon elastic scattering added 12/09/00 These are results using the theory described under the preceding argon entry. I have only fit the diffusion cross section with an analytical expression. See below. The following table is taken directly from the Fortran output. We have made no adjustments to the theoretical elastic cross sections to take into account the effects of inelastic channels and have not yet looked at the magnitudes of excitation and ionization cross sections. The total cross sections agree very well with Pirani and Vecchiocattivi, J. Chem. Phys. 66, 372 (1977). Because of the use of the long-range potential of Taylor, Wyrick, and Hurly, J. Chem. Phys. 92, 6786 (1990) the low energy viscosity and diffusion cross sections are expected to agree with experiment. We have not examined the differential cross sections in this case. %Gianturco-Taylor et al potential 12/07/00 22:13:37 %energy(eV),SigmaTOT,SigmaV,SigmaD,Delta(Lmax),Lmax 1.00000D-02 1.62907D-18 2.72732D-19 3.20519D-19 1.61983D-06 220 1.77828D-02 1.21523D-18 2.20958D-19 2.74029D-19 1.59386D-06 278 3.16228D-02 9.28617D-19 1.93496D-19 2.43401D-19 1.59666D-06 350 5.62341D-02 7.48736D-19 1.74780D-19 2.18555D-19 1.57460D-06 442 1.00000D-01 6.40407D-19 1.58932D-19 1.95951D-19 1.58312D-06 556 1.77828D-01 5.74921D-19 1.43956D-19 1.74427D-19 1.58457D-06 700 3.16228D-01 5.33513D-19 1.29276D-19 1.53681D-19 1.57945D-06 882 5.62341D-01 5.04996D-19 1.14812D-19 1.33727D-19 1.56936D-06 1112 1.00000D+00 4.83003D-19 1.00658D-19 1.14691D-19 1.58154D-06 1398 1.77828D+00 4.64023D-19 8.69601D-20 9.67253D-20 1.57372D-06 1762 3.16228D+00 4.46170D-19 7.38781D-20 7.99515D-20 1.57575D-06 2218 5.62341D+00 4.28483D-19 6.15456D-20 6.44148D-20 1.57781D-06 2792 1.00000D+01 4.10507D-19 4.97368D-20 5.04665D-20 1.57663D-06 3516 1.77828D+01 3.92097D-19 3.90903D-20 3.87735D-20 1.57863D-06 4426 3.16228D+01 3.73198D-19 3.01209D-20 2.91368D-20 1.58004D-06 5572 5.62341D+01 3.53898D-19 2.26789D-20 2.13254D-20 1.58012D-06 7016 1.00000D+02 3.34223D-19 1.66082D-20 1.51398D-20 1.58234D-06 8832 1.77828D+02 3.14433D-19 1.17770D-20 1.03846D-20 1.58333D-06 11120 3.16228D+02 2.94486D-19 8.05161D-21 6.85612D-21 1.58607D-06 13998 5.62341D+02 2.74548D-19 5.28621D-21 4.34307D-21 1.58762D-06 17624 1.00000D+03 2.54604D-19 3.32221D-21 2.63384D-21 1.58988D-06 22188 1.77828D+03 2.35647D-19 1.99488D-21 1.52809D-21 1.59301D-06 27932 3.16228D+03 2.16799D-19 1.14443D-21 8.49107D-22 1.59579D-06 35166 5.62341D+03 1.97677D-19 6.28495D-22 4.53210D-22 1.59960D-06 44270 1.00000D+04 1.78585D-19 3.31675D-22 2.33380D-22 1.60341D-06 55734 Our analytical approximation to the preceding elastic diffusion cross section SigmaD = Qd versus relative center-of-mass energy Erel is Qd = 1.35E-19*Erel^(-0.2)* [1+(Erel/1.2)^(0.5)+(Erel/7)^(1.5)+(Erel/70)^3]^(-0.3) This fit is to +- 5% over the energy range from 0.1 to 10000 eV. Corrected Qv to Qd on 10/01/01 HYDROGEN modified 11/06/01 Analytic cross sections for collisions of H+, H2+, H3+, H, H2, and H- with hydrogen molecules have been published by T. Tabata and T. Shirai, Atomic Data and Nuclear Data Tables 76, 1 (2000). Not included in the above compilation are the theoretical cross sections for H+ and H collisions with H2 by Kristic and Schultz, Phys. Rev. A 60, 2118 (1999) and J. Phys. B 32, 2415 (1999). Because the cross sections of Tabata and Shirai do not show the threshold behavior and the high energy behavior, we have revised most of our 1990 cross sections for these species. A Mathematica notebook with analytic formulas and plots is available on request to A. V. Phelps. This cross section set, along with many others, is plotted in a paper submitted for publication by A. Bogaerts.