Cross sections for collisions of N+ and N2+ with N2, Ar+ with Ar, He+ with He, Ar+ with He, Na+ with Xe, and various hydrogen ions with H2. A very simplified set is suggested for Ne+ with Xe amd Xe+ with Ne Last revised 04/27/02. If you have questions contact A. V. Phelps at avp@jila.colorado.edu Cross section tabulations for He+ + Ne are available on request. Note that some of the following tables are 81 columns wide. NITROGEN ATOMIC AND MOLECULAR IONS The tables from A. V. Phelps, J. Phys. Chem. Ref. Data 20, 557 (1991). The cross sections are in units 1E-20 m^2. 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. THE CROSS SECTIONS FOR N+ + N2 -> N2+ + N LISTED BELOW NEED TO BE REVISED TO TAKE INTO ACCOUNT THE WORK OF FREYSINGER ET AL, J. CHEM. PHYS. 101, 3688 (1994). The wide spread in published cross section data suggests the importance of excited N+ collisions in the laboratory. Cross sections for N+ + N2 collisions by product. Lab. ion Cross Section energy eV Q(N2+) Q(391) Q(B2ä) Q(e) Qm Lm 0.1 112 14.9 0.1333 97 17.2 0.1778 84 19.9 0.237 73 23.1 0.316 63 26.6 0.422 55 30.9 0.562 48 36.0 0.750 41.5 41.5 1 35.5 47.3 1.333 31.3 55.7 1.778 0.051 27 64.0 2.37 0.068 23.8 75.3 3.16 0.083 20.8 87.7 4.22 0.104 18 101.2 5.62 0.164 15.7 117.7 7.50 0.35 13.5 135.0 10 1.45 11.7 156.0 13.33 3 10 177.8 17.78 4.25 8.6 204 23.7 4.9 0.0001 7.3 231 31.6 4.95 0.004 0.004 6.2 261 42.2 4.8 0.0063 0.0063 5.15 290 56.2 4.73 0.0085 0.0085 4.25 319 75.0 4.7 0.0109 0.0109 3.5 350 100 4.65 0.0137 0.0137 2.9 387 133.3 4.6 0.0172 0.0172 2.3 409 177.8 4.6 0.00093 0.0217 0.0217 1.8 427 237 4.6 0.0015 0.0272 0.0272 1.36 430 316 4.63 0.0025 0.0337 0.0337 0.98 413 422 4.67 0.0039 0.0425 0.0425 0.68 382 562 4.83 0.0061 0.053 0.053 0.46 345 750 4.95 0.0097 0.066 0.066 0.298 298 1000 5.17 0.0154 0.083 0.083 0.19 254 1333 5.44 0.0243 0.103 0.103 0.117 208 1778 6 0.038 0.13 0.13 0.07 166.4 2370 6.5 0.06 0.167 0.167 0.041 130.2 3160 7.1 0.094 0.218 0.218 0.0235 99.9 4220 7.8 0.148 0.297 0.297 0.0135 77.3 5620 8.4 0.233 0.407 0.407 0.0073 56.9 7500 9.25 0.365 0.58 0.58 0.0041 44.5 10000 10.1 0.555 0.82 0.82 0.0024 37.7 Cross sections for N2+ + N2 collisions by product. Correted 11/01/99 (Cross sections in units 1E-20 m2) Lab. ion Cross Section energy Q(300- eV Q(Vib) QCT Q(N+) Q(N3+) Q(391) 500) Qm Lm threshold (0.29) (15) (15) (18.8) (18.8) 0.1 177 17.7 0.1333 159 21.2 0.1778 143 25.4 0.2371 132 31.3 0.3162 123 38.9 0.4216 114 48.1 0.5623 107.5 60.4 0.7498 1.75 101 76.2 1 3.7 55 96.5 97.6 1.334 3.8 52 92.5 124.4 1.778 3.73 50 89.3 159.9 2.37 3.6 47.5 86 205 3.16 3.53 45 84 267 4.22 3.52 43.3 81.3 344 5.62 3.55 41.6 79.3 447 7.50 3.62 40.5 77.5 582 10 3.7 38.7 75.5 756 13.34 3.74 37.5 0.0034 0.0034 74 988 17.78 3.82 36 0.037 0.035 72 1281 23.71 3.87 35 0.31 0.09 70 1661 31.62 3.92 34 1.01 0.0215 0.0122 69 2183 42.2 3.95 33 0.99 0.0042 0.042 67.5 2848 56.2 3.95 32 0.89 0.0895 66 3714 75.0 3.9 31.3 0.75 0.101 64.5 4840 100 3.8 30.6 0.61 0 0.1 63.3 6333 133.4 3.65 29.7 0.49 0.007 0.098 62.3 8312 177.8 3.4 29 0.4 0.008 0.097 60.7 10799 237 3.16 28.3 0.34 0.0107 0.097 60 14235 316 2.85 27.7 0.3 0.0137 0.1 58.7 18572 421 2.5 27 0.29 0.0175 0.1045 57.5 24262 562 2.14 26.3 0.29 0.0227 0.12 56.3 31680 750 1.72 26 0.34 0.0295 0.143 55 41271 1000 1.22 25.4 0.435 0.0387 0.18 54 54035 1334 0.8 24.8 0.55 0.051 0.228 52.7 70322 1778 0.51 24.2 0.695 0.067 0.292 51.3 91285 2370 0.345 23.8 0.9 0.091 0.374 50 118641 3160 0.238 23.3 1.16 0.123 0.484 49 155042 4217 0.17 22.9 1.53 0.165 0.635 47.7 201263 5623 0.124 22.7 2 0.227 0.83 46.7 262757 7499 0.095 22 2.64 0.317 1.13 45.7 342867 10000 0.076 21.4 3.4 0.44 1.48 44.6 446216 ------------ ARGON IONS ELASTIC (corrected 04/27/02 - thanks to Z. Donko, updated 08/20/05 - thanks to A. Blias) For a simple approximation to the differential cross esction for elastic scattering we recommend that one use either a) isotropic scattering using what we will call the momentum transfer cross section Qm or b) a differential scattering cross section with an isotropic compoment with an angular integrated magnitude of Qi and a backward scattered (delta function) compoment with an angular integrated magnitude of Qb. At high collision energies this backward scattering cross section equals the symmetric charge transfer cross section. From the experimental point of view symmetric charge transfer is only one aspect of elastic scattering, e.g., at high energies it produces a peak in the center-of-mass differential cross section in the backward scattering direction. As the scattering becomes isotropic at low energies the symmetric charge transfer portion of the elastic differential cross section is no longer recognizable and the charge transfer cross section can be determined experimentally only with the use of different isotopes, i.e., asymetric charge transfer. The elastic momentum transfer cross section is calculated from the cross section formulas as the sum of the elastic isotropic cross section and twice the elastic backward scattering cross section, i.e., Qm = Qi + 2 Qb. See A. V. Phelps, J. Appl. Phys. 76, 747 (1994) for more discussion of the model. We have modified the analytic expressions for the elastic cross sections given in Eqs. (2) and (3) of Phelps (1994) in order to take into account the results of differential scattering cross section measurements by Aberth and Lorents, Phys. Rev. 144, 109 (1966) and Vestal et al, Phys. Rev. A 17, 1337 (1978). The very approximate nature of the isotropic component Qi is particularly evident in slide 9 of the file collision_data/ionmolecule/ICPEACSymmIonQs.doc or SymmIonAtomICPEAC.ppt. A closer fit did not seem justified by the uncertainties in the experimental data and by the absence of theory. Qi = QLangevin = 21.6/(Erel)^0.5, Qb = 52/(Erel)^0.08/(1+0.08/Erel)/(1+Erel/1000)^0.3, where the cross sections are in 10^-20 m^2 and the center-of-mass energies are in eV. Qm is determined from the relation Qm = Qi + 2 Qb. ARGON IONS INELASTIC Inelastic cross sections for Ar+ + Ar tabulated by product. The table is from A. V. Phelps, J. Phys. Chem. Ref. Data 20, 557 (1991). 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 Ar by Ar+. See the above reference for details. Note that the momentum transfer cross sections and charge transfer cross sections originally given in this table have been replaced by the cross sections discussed 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. Experiments show that this is a questionable approximation at high energies for Ar - Ar collisions, but it is the best we can do until sufficient data becomes available to allow the quantative evaluation of these contributions. See Phelps, Greene, and Burke, J. Phys. B 33, 2965 (2000) for such results in the case of Ar + Ar. Lab. ion Product energy eV Q(e) Q(UV) Q(488) Q(811) threshold (15.8) (11.8) (22) (13.1) 10 13.33521 17.78279 23.71373 0.002 31.62277 0.001 0.08 42.16965 0.02 0.17 56.23413 0.05 0.29 74.98942 0.12 0.41 0.0012 100 0.23 0.53 0.00007 0.003 133.3521 0.38 0.615 0.00016 0.0059 177.8279 0.58 0.68 0.00039 0.0097 237.1373 0.78 0.72 0.00083 0.014 316.2277 1.07 0.75 0.00156 0.0177 421.6965 1.4 0.76 0.00268 0.0202 562.3413 1.75 0.775 0.0041 0.022 749.8942 2.05 0.775 0.00575 0.0235 1000 2.3 0.75 0.00755 0.024 1333.521 2.5 0.72 0.0094 0.024 1778.279 2.6 0.68 0.0109 0.0233 2371.373 2.75 0.63 0.0123 0.0227 3162.277 2.85 0.59 0.0134 0.0217 4216.965 2.9 0.55 0.0143 0.0207 5623.413 2.95 0.52 0.015 0.0202 7498.942 3 0.48 0.0154 0.0198 10000 3 0.44 0.0157 0.019 HELIUM He+ +He ELASTIC For a simple approximation to the differential cross esction for elastic scattering we recommend that one use either a) isotropic scattering using what we will call the momentum transfer cross section Qm or b) a differential scattering cross section with an isotropic compoment with an angular integrated magnitude of Qi and a backward scattered (delta function) compoment with an angular integrated magnitude of Qb. At high collision energies this backward scattering cross section equals the symmetric charge transfer cross section. From the experimental point of view symmetric charge transfer is only one aspect of elastic scattering, e.g., at high energies it produces a peak in the center-of-mass differential cross section in the backward scattering direction. As the scattering becomes isotropic at low energies the symmetric charge transfer portion of the elastic differential cross section is no longer recognizable and the charge transfer cross section can be determined experimentally only with the use of different isotopes, i.e., asymetric charge transfer. The elastic momentum transfer cross section is calculated from the cross section formulas as the sum of the elastic isotropic cross section and twice the elastic backward scattering cross section, i.e., Qm = Qi + 2 Qb. See A. V. Phelps, J. Appl. Phys. 76, 747 (1994) for more discussion of the model. An analytic expression for the angular-integral of the isotropic component of the approximate differential cross section Qi as a function of the relative or center-of-mass energy Erel is: Qi = 7.63E-20*(Erel)^(-0.5) An analytic expression for the angular integral of the backward scattered component is: Qb = 1E-19*(Erel/1000)^(-0.15)*[1+Erel/1000]^(-0.25)*[1+5/Erel]^(-0.15) Tables of these Qb, Qi, and Qm in units of 10E-20 m^2 versus Erel in eV follow. Erel Qb Qi Qm = Qi +2Qb 0.01 22.13 76.30 120.6 0.02 22.13 53.95 98.20 0.05 22.11 34.12 78.33 0.1 22.07 24.13 68.27 0.2 22.01 17.06 61.08 0.5 21.82 10.79 54.43 1 21.54 7.630 50.70 2 21.04 5.395 47.47 5 19.93 3.412 43.27 10 18.73 2.413 39.87 20 17.30 1.706 36.32 50 15.26 1.079 31.61 100 13.69 0.7630 28.15 200 12.12 0.5395 24.78 500 10.01 0.3412 20.36 1000 8.403 0.2413 17.05 2000 6.845 0.1706 13.86 5000 5.018 0.1079 10.14 10000 3.887 0.07630 7.850 HYDROGEN 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). This set of cross sections is partially based on the earlier set by A. V. Phelps, J. Phys. Chem. Ref. Data 19, 653 (1990). Not included in the above compilations are the theoretical cross sections for H+ and H collisions with H2 by P. S. Kristic and D. R. Schultz, Phys. Rev. A 60, 2118 (1999) and J. Phys. B 32, 2415 (1999). Our H3+ + H2 cross sections of 1990 have been updated using results from B. L. Peko, R. L. Champion, and Y. Yang, J. Chem. Phys. 104, 6149 (1996); B. L. Peko and R. L. Champion ibid 107, 1156 (1997); and T. Simko et al, Phys. Rev. E 56, 5908 (1997). Our revised recommendations are given in the files H2H3PQDATA.nb and, its translation, H2H3PDATA.doc. Many of these cross section recommendations have been adopted and plotted by A. Bogaerts and R. Gijbles, Spectrochem. Acta B 57, 1071 (2002). Ar+ +He ELASTIC added 10/05/01 modified 11/14/01 Here we present the results of the calculation of the elastic scattering cross sections for Ar+ collisions with He. The calculations make use of the same JWKB code used by Phelps, Greens, and Burke, J. Phys. B 33, 2965 (2000). For internuclear separations greater than about 1.3 a.u. we use the interaction potentials given by Viehland, Viggiano, and Mason, J. Chem. Phys. 95, 7286 (1991). For smaller separations weuse an interpolation of the curves for He-He, Ne-Ne, and Ar-Ar from Gianturco and Dilomardo, J. Chimie Physique 72, 315 (1975) and a screened Coulomb formula. The cross sections listed are an average of those calculated for the X 2Sigma+ 1/2 and A1 2Pi 3/2 states as adopted by Viehland et al. The cross sections for these two state differ by about 20% at 100 eV. %Cross sections for Ar+ with He 11/14/2001 21:55:22 %energy (eV) Total Q (m^2) Viscosity Q (m^2) Diffusion Q (m^2) 0.01 5.304e-18 5.595e-19 8.485e-19 0.01778 4.359e-18 4.786e-19 5.493e-19 0.03162 3.845e-18 3.586e-19 3.666e-19 0.05623 2.83e-18 2.37e-19 2.426e-19 0.1 2.579e-18 1.635e-19 1.845e-19 0.1778 2.146e-18 1.2856e-19 1.5357e-19 0.3162 1.812e-18 1.0973e-19 1.3287e-19 0.5623 1.5322e-18 9.668e-20 1.1619e-19 1. 1.2088e-18 8.568e-20 1.0136e-19 1.778 9.039e-19 7.553e-20 8.766e-20 3.162 6.708e-19 6.59e-20 7.489e-20 5.623 5.135e-19 5.673e-20 6.301e-20 10. 4.135e-19 4.808e-20 5.207e-20 17.78 3.511e-19 4.e-20 4.209e-20 31.62 3.112e-19 3.254e-20 3.315e-20 56.23 2.842e-19 2.577e-20 2.528e-20 100. 2.642e-19 1.972e-20 1.852e-20 177.8 2.48e-19 1.4434e-20 1.2971e-20 316.2 2.337e-19 1.0084e-20 8.682e-21 562.3 2.202e-19 6.712e-21 5.509e-21 1000. 2.071e-19 4.214e-21 3.283e-21 1778. 1.941e-19 2.47e-21 1.821e-21 3162. 1.812e-19 1.3398e-21 9.344e-22 5623. 1.684e-19 6.697e-22 4.433e-22 10000. 1.5578e-19 3.093e-22 1.954e-22 An analytical expression representing the tabular data for the diffusion cross section is: Qd = 9.*10^(-20)/E^0.5/[1+(E/0.0087)^2]^0.25*[1+(E/0.067)]/ [1+(E/6)^0.6]/[1+(E/1200)]^0.9 where the relative energy E is in eV and the cross section Qd is in m^2. He+ + Ar ELASTIC corrected 11/30/01 Here we present the results of the calculation of the elastic scattering cross sections for He+ collisions with Ar. The calculations make use of the same JWKB code used by Phelps, Greens, and Burke, J. Phys. B 33, 2965 (2000). Our first calculations were made using our interpretation of the potential of Smith et al, Phys. Rev. 161, 31 (1967). However. we found that the long-range portion was too large by a factor of two. In addition Boyle and Smith, Physica 75, 351 (1975)found a much lower potential at intermediate ranges. Here we have used the potential for Li+-Ar from Alhrichs et al J. Chem. Phys. 88, 6290 (1988) for internuclear separations greater than about 1.9 a.u.. At very small separations we use the results of Lane and Everhardt, Phys Rev. 120, 2064 (1960) for He+-Ar. We continue the short range screened Coluomb until it meets smoothly the long-range potential for He+ - Ar. Our results should not be trusted below 0.1 eV because of possible multiple turning points. We have not attempted to adjust the potential to fit calculated differential cross sections to experimental values. The differential scattering data of Aberth and Lorents (1966) and of Baudon et al (1970), provide evidence of large cross section reductions at large angles and high energies because of inelastic scattering. One therefore expects large decreases from our Q's at energies above a few hundred eV because of the effects of inelastic collisions that are not considered in our calculations. Relative energy(eV),Qtot(m^2),Qvisc(m^2),Qdiff(m^2),Phase shift for Lmax,Lmax 1.00000D-02 1.81668D-17 2.64962D-18 7.11201D-18 1.31486D-02 221 1.77828D-02 1.54839D-17 1.79564D-18 3.87784D-18 1.16355D-02 279 3.16228D-02 1.50350D-17 1.13953D-18 1.70147D-18 1.04009D-02 351 5.62341D-02 1.21399D-17 7.14873D-19 1.00421D-18 9.26846D-03 442 1.00000D-01 9.52974D-18 5.35083D-19 7.02738D-19 8.23956D-03 557 1.77828D-01 8.07336D-18 4.08373D-19 5.49057D-19 7.35269D-03 701 3.16228D-01 6.64403D-18 3.42832D-19 3.40904D-19 6.54339D-03 883 5.62341D-01 5.40630D-18 2.13984D-19 1.99310D-19 5.82672D-03 1112 1.00000D+00 4.59476D-18 1.30020D-19 1.36837D-19 5.19267D-03 1400 1.77828D+00 3.82548D-18 9.24644D-20 1.06914D-19 4.63217D-03 1762 3.16228D+00 3.12717D-18 7.45829D-20 8.90162D-20 4.12992D-03 2218 5.62341D+00 2.48074D-18 6.36992D-20 7.56397D-20 3.67825D-03 2793 1.00000D+01 2.22457D-18 5.52060D-20 6.41800D-20 3.27900D-03 3516 1.77828D+01 1.67496D-18 4.76060D-20 5.37655D-20 2.92148D-03 4427 3.16228D+01 1.45396D-18 4.04867D-20 4.41185D-20 2.60447D-03 5573 5.62341D+01 1.35781D-18 3.41244D-20 3.47342D-20 2.32159D-03 7016 1.00000D+02 1.12285D-18 2.71769D-20 2.47907D-20 2.06926D-03 8833 1.77828D+02 8.35645D-19 1.94700D-20 1.64486D-20 1.84470D-03 11120 3.16228D+02 5.95743D-19 1.29676D-20 1.02350D-20 1.64428D-03 14000 5.62341D+02 4.27892D-19 8.05409D-21 5.94801D-21 1.46618D-03 17624 1.00000D+03 3.21219D-19 4.60698D-21 3.20712D-21 1.30710D-03 22188 1.77828D+03 2.54372D-19 2.39559D-21 1.59392D-21 1.16546D-03 27933 3.16228D+03 2.13927D-19 1.13636D-21 7.33836D-22 1.03919D-03 35166 5.62341D+03 1.87242D-19 5.00618D-22 3.15780D-22 9.26723D-04 44271 1.00000D+04 1.68566D-19 2.08562D-22 1.28439D-22 8.26422D-04 55735 Na+ + Xe Here we present the results of the calculation of the elastic scattering cross sections for Na+ collisions with Xe. The calculations make use of the same JWKB code used by Phelps, Greens, and Burke, J. Phys. B 33, 2965 (2000). Here we have used the potential from Nyeland et al, Chem. Phys. 147, 229 (1990) and Skullerud et al, J. Phys. B 32, 4509 (1999). For smaller separations we use an extrapolation of the curves for He-He, Ne-Ne, and Ar-Ar from Gianturco and Dilomardo, J. Chimie Physique 72, 315 (1975) and a screened Coulomb formula. Our calculations should not be trusted below 1 eV because of possible multiple turning points. We have not attempted to adjust the potential to fit calculated differential cross sections to experimental values. One expects large decreases from our Q's at energies above a few hundred eV because of the effects of inelastic collisions that are not considered in our calculations. Relative energy(eV),Qtot(m^2),Qvisc(m^2),Qdiff(m^2),Phase shift for Lmax,Lmax 1.00000D-01 3.07754D-17 8.17064D-19 1.09704D-18 7.48366D-02 1114 1.77828D-01 2.53837D-17 6.70294D-19 8.51629D-19 6.67797D-02 1402 3.16228D-01 2.12356D-17 5.27601D-19 6.13046D-19 5.94292D-02 1766 5.62341D-01 1.73893D-17 3.80730D-19 3.47046D-19 5.29206D-02 2224 1.00000D+00 1.43836D-17 2.25432D-19 2.23307D-19 4.72637D-02 2798 1.77828D+00 1.20353D-17 1.51052D-19 1.67311D-19 4.20722D-02 3524 3.16228D+00 9.95944D-18 1.17332D-19 1.36789D-19 3.75116D-02 4436 5.62341D+00 8.20080D-18 9.86927D-20 1.15678D-19 3.34107D-02 5586 1.00000D+01 6.85670D-18 8.52267D-20 9.83145D-20 2.97866D-02 7032 1.77828D+01 5.54293D-18 7.35791D-20 8.27887D-20 2.65420D-02 8854 3.16228D+01 4.55879D-18 6.28713D-20 6.83725D-20 2.36659D-02 11146 5.62341D+01 3.85631D-18 5.23963D-20 5.48623D-20 2.11001D-02 14032 1.00000D+02 3.27249D-18 4.22544D-20 4.30578D-20 1.88119D-02 17666 1.77828D+02 2.61804D-18 3.32917D-20 3.31577D-20 1.67761D-02 22240 3.16228D+02 2.11260D-18 2.57176D-20 2.50292D-20 1.49627D-02 27998 5.62341D+02 1.99982D-18 1.94558D-20 1.84748D-20 1.33455D-02 35248 1.00000D+03 1.72908D-18 1.43760D-20 1.32991D-20 1.19042D-02 44376 1.77828D+03 1.32344D-18 1.03459D-20 9.31299D-21 1.06212D-02 55866 3.16228D+03 9.51390D-19 7.23276D-21 6.33101D-21 9.47753D-03 70332 5.62341D+03 6.79842D-19 4.90147D-21 4.17174D-21 8.45909D-03 88542 1.00000D+04 5.02383D-19 3.21527D-21 2.66259D-21 7.55095D-03 111470 NEON Ne+ +Ne elastic For a simple approximation to the differential cross esction for elastic scattering we recommend that one use either a) isotropic scattering using what we will call the momentum transfer cross section Qm or b) a differential scattering cross section with an isotropic compoment with an angular integrated magnitude of Qi and a backward scattered (delta function) compoment with an angular integrated magnitude of Qb. At high collision energies this backward scattering cross section equals the symmetric charge transfer cross section. From the experimental point of view symmetric charge transfer is only one aspect of elastic scattering, e.g., at high energies it produces a peak in the center-of-mass differential cross section in the backward scattering direction. As the scattering becomes isotropic at low energies the symmetric charge transfer portion of the elastic differential cross section is no longer recognizable and the charge transfer cross section can be determined experimentally only with the use of different isotopes, i.e., asymetric charge transfer. The elastic momentum transfer cross section is calculated from the cross section formulas as the sum of the elastic isotropic cross section and twice the elastic backward scattering cross section, i.e., Qm = Qi + 2 Qb. See A. V. Phelps, J. Appl. Phys. 76, 747 (1994) for more discussion of the model. An analytic expression for the angular-integral of the isotropic component of the approximate differential cross section Qi as a function of the relative or center-of-mass energy Ecm is set equal to the Langevin spiraling cross section and is: Qi = 1.06E-19/(Ecm)^0.5 An analytic expression for the angular integral of the backward scattered component is: Qb = +2.8E-19/Ecm^0.15/(1+0.8/Ecm)^0.3 The total cross section Qt is evaluated using Masey and Mohr (1932) and the polarizability of Ne. Qt = 2.43E-18/(Ecm)^(1/3) Tables of these analytic Qb, Qt, Qi, and Qm in m^2 versus Erel in eV follow. Erel Qb Qt Qi Qm = Qi +2Qb eV m^2 m^2 m^2 m^2 0.01 1.49E-19 1.12E-17 1.06E-18 1.36E-18 0.02 1.65E-19 8.95E-18 7.50E-19 1.08E-18 0.05 1.87E-19 6.59E-18 4.74E-19 8.49E-19 0.1 2.04E-19 5.23E-18 3.35E-19 7.44E-19 0.2 2.19E-19 4.15E-18 2.37E-19 6.77E-19 0.5 2.33E-19 3.06E-18 1.50E-19 6.16E-19 1 2.34E-19 2.43E-18 1.06E-19 5.75E-19 2.5 2.24E-19 1.79E-18 6.70E-20 5.16E-19 3 2.21E-19 1.68E-18 6.12E-20 5.04E-19 3.5 2.18E-19 1.60E-18 5.67E-20 4.93E-19 4 2.15E-19 1.53E-18 5.30E-20 4.84E-19 5 2.10E-19 1.42E-18 4.74E-20 4.68E-19 8 1.99E-19 1.21E-18 3.75E-20 4.36E-19 10 1.93E-19 1.12E-18 3.35E-20 4.21E-19 12 1.89E-19 1.06E-18 3.06E-20 4.09E-19 17 1.80E-19 9.45E-19 2.57E-20 3.87E-19 20 1.76E-19 8.95E-19 2.37E-20 3.77E-19 23 1.73E-19 8.54E-19 2.21E-20 3.68E-19 30 1.66E-19 7.82E-19 1.94E-20 3.53E-19 50 1.54E-19 6.59E-19 1.50E-20 3.25E-19 100 1.39E-19 5.23E-19 1.06E-20 2.91E-19 200 1.26E-19 4.15E-19 7.50E-21 2.60E-19 500 1.10E-19 3.06E-19 4.74E-21 2.25E-19 1000 9.93E-20 2.43E-19 3.35E-21 2.02E-19 2000 8.95E-20 1.92E-19 2.37E-21 1.81E-19 5000 7.80E-20 1.42E-19 1.50E-21 1.58E-19 10000 7.03E-20 1.13E-19 1.06E-21 1.42E-19 XENON Xe+ +Xe elastic For a simple approximation to the differential cross esction for elastic scattering we recommend that one use either a) isotropic scattering using what we will call the momentum transfer cross section Qm or b) a differential scattering cross section with an isotropic compoment with an angular integrated magnitude of Qi and a backward scattered (delta function) compoment with an angular integrated magnitude of Qb. At high collision energies this backward scattering cross section equals the symmetric charge transfer cross section. From the experimental point of view symmetric charge transfer is only one aspect of elastic scattering, e.g., at high energies it produces a peak in the center-of-mass differential cross section in the backward scattering direction. As the scattering becomes isotropic at low energies the symmetric charge transfer portion of the elastic differential cross section is no longer recognizable and the charge transfer cross section can be determined experimentally only with the use of different isotopes, i.e., asymetric charge transfer. The elastic momentum transfer cross section is calculated from the cross section formulas as the sum of the elastic isotropic cross section and twice the elastic backward scattering cross section, i.e., Qm = Qi + 2 Qb. See A. V. Phelps, J. Appl. Phys. 76, 747 (1994) for more discussion of the model. An analytic expression for the angular-integral of the isotropic component of the approximate differential cross section Qi as a function of the relative or center-of-mass energy Ecm is set equal to the Langevin spiraling cross section and is: Qi = 3.39E-19/(Ecm)^0.5 Our analytic expression for the angular integral of the backward scattered component is: Qb = +3.6E-19/Ecm^0.42*(1+(Ecm/0.1)^2)^0.2/(1+(0.09/Ecm)^1.3)/(1+(Ecm/1000)^0.25) The total cross section Qt is evaluated using Masey and Mohr (1932) and the polarizability of Xe from McDaniel and Mason. Qt = 2.16E-17/(Ecm)^(1/3) Tables of these analytic Qb, Qt, Qi, and Qm in m^2 versus Erel in eV follow. Ecm Qb QL QL+2Qb Qt eV m^2 m^2 m^2 m^2 0.01 1.28E-19 3.39E-18 3.64E-18 1.00E-16 0.02 2.18E-19 2.39E-18 2.83E-18 7.96E-17 0.05 3.88E-19 1.51E-18 2.29E-18 5.86E-17 0.1 5.28E-19 1.07E-18 2.13E-18 4.65E-17 0.2 6.44E-19 7.57E-19 2.05E-18 3.69E-17 0.5 7.26E-19 4.79E-19 1.93E-18 2.72E-17 1 7.37E-19 3.39E-19 1.81E-18 2.16E-17 2.5 7.16E-19 2.14E-19 1.65E-18 1.59E-17 3 7.10E-19 1.95E-19 1.61E-18 1.50E-17 3.5 7.03E-19 1.81E-19 1.59E-18 1.42E-17 4 6.98E-19 1.69E-19 1.56E-18 1.36E-17 5 6.88E-19 1.51E-19 1.53E-18 1.26E-17 8 6.66E-19 1.20E-19 1.45E-18 1.08E-17 10 6.55E-19 1.07E-19 1.42E-18 1.00E-17 12 6.45E-19 9.77E-20 1.39E-18 9.43E-18 17 6.27E-19 8.21E-20 1.34E-18 8.40E-18 20 6.18E-19 7.57E-20 1.31E-18 7.96E-18 23 6.11E-19 7.06E-20 1.29E-18 7.60E-18 30 5.96E-19 6.18E-20 1.25E-18 6.95E-18 50 5.68E-19 4.79E-20 1.18E-18 5.86E-18 100 5.28E-19 3.39E-20 1.09E-18 4.65E-18 200 4.87E-19 2.39E-20 9.99E-19 3.69E-18 500 4.34E-19 1.51E-20 8.83E-19 2.72E-18 1000 3.94E-19 1.07E-20 7.98E-19 2.16E-18 2000 3.55E-19 7.57E-21 7.17E-19 1.71E-18 5000 3.06E-19 4.79E-21 6.16E-19 1.26E-18 10000 2.71E-19 3.39E-21 5.45E-19 1.00E-18 We thank V. Nagorny for pointing out errors in a previous version of this table. Corrected 04/02/02 XENON+ in NEON added 03/31/02 Most of this material was included in J. De Urquijo et al, Bull. Am. Phys. Soc. 45, No. 6, 47 (2000). Here we present a very simplified model for elastic collisions of Xe+ with Ne. The momentum transfer cross section Qm is set equal to the Langevin spiraling cross section for the Ne+-Xe polarization potential with "roll-off" at high energies approximating that expected for Coulomb scattering. Qm = 1.1E-19/Ecm^0.5/(1+Ecm/10000)^1.5 (m^2) and the total cross section is set equal to the Massey-Mohr total cross section for the Ne+-Xe polarization potential. Qt = 3.29E-18/Ecm^(1/3) (m^2) Here the center-of-mass energy Ecm is in eV. These formulas are tabulated below. Ecm Qm Qt eV m^2 m^2 0.01 1.10E-18 1.53E-17 0.02 7.78E-19 1.21E-17 0.05 4.92E-19 8.93E-18 0.1 3.48E-19 7.09E-18 0.2 2.46E-19 5.63E-18 0.5 1.56E-19 4.15E-18 1 1.10E-19 3.29E-18 2.5 6.95E-20 2.42E-18 3 6.35E-20 2.28E-18 3.5 5.88E-20 2.17E-18 4 5.50E-20 2.07E-18 5 4.92E-20 1.92E-18 8 3.88E-20 1.65E-18 10 3.47E-20 1.53E-18 12 3.17E-20 1.44E-18 17 2.66E-20 1.28E-18 20 2.45E-20 1.21E-18 23 2.29E-20 1.16E-18 30 2.00E-20 1.06E-18 50 1.54E-20 8.93E-19 100 1.08E-20 7.09E-19 200 7.55E-21 5.63E-19 500 4.57E-21 4.15E-19 1000 3.02E-21 3.29E-19 2000 1.87E-21 2.61E-19 5000 8.47E-22 1.92E-19 10000 3.89E-22 1.53E-19 Theoretical elastic scattering of Xe+ by Ne We do not know anything about the long and intermediate range potential for Xe+ in Ne. We therefore approximate the potential with literature values for Cs+ in Ne at large and intermediate separations. At large separations the induced dipole component of the potential is imdependent of the ion. Here we have used the potential from Nyeland et al, Chem. Phys. 147, 229 (1990) and Skullerud et al, J. Phys. B 32, 4509 (1999). For smaller separations we use an extrapolation of the curves for He-He, Ne-Ne, and Ar-Ar from Gianturco and Dilomardo, J. Chimie Physique 72, 315 (1975) and a screened Coulomb formula. The calculations make use of the same JWKB code used by Phelps, Greens, and Burke, J. Phys. B 33, 2965 (2000). Our calculations should not be trusted below 1 eV because of possible multiple turning points. energy(eV) SigmaTOT SigmaV SigmaD Delta(Lmax) Lmax 1.00000D-02 1.31533D-17 8.67321D-19 1.07507D-18 9.00145D-03 442 1.77828D-02 1.10473D-17 6.71060D-19 8.76095D-19 7.96059D-03 558 3.16228D-02 9.21205D-18 5.56238D-19 5.52089D-19 7.11308D-03 702 5.62341D-02 7.62509D-18 3.57258D-19 3.72794D-19 6.33719D-03 884 1.00000D-01 6.30263D-18 2.50275D-19 2.91531D-19 5.63328D-03 1114 1.77828D-01 5.45983D-18 2.01599D-19 2.48368D-19 5.02732D-03 1402 3.16228D-01 4.48637D-18 1.75677D-19 2.19393D-19 4.47482D-03 1766 5.62341D-01 3.76481D-18 1.57763D-19 1.95959D-19 3.98589D-03 2224 1.00000D+00 2.92973D-18 1.42640D-19 1.75002D-19 3.56119D-03 2798 1.77828D+00 2.73168D-18 1.28595D-19 1.55472D-19 3.17148D-03 3524 3.16228D+00 2.43114D-18 1.16002D-19 1.36093D-19 2.82920D-03 4436 5.62341D+00 1.92731D-18 1.02687D-19 1.15722D-19 2.52139D-03 5586 1.00000D+01 1.43456D-18 8.78657D-20 9.65545D-20 2.24935D-03 7032 1.77828D+01 1.06293D-18 7.36496D-20 7.95039D-20 2.00574D-03 8854 3.16228D+01 8.16184D-19 6.09020D-20 6.46429D-20 1.78975D-03 11146 5.62341D+01 6.61780D-19 4.97175D-20 5.18222D-20 1.59701D-03 14032 1.00000D+02 5.66671D-19 4.00032D-20 4.08751D-20 1.42507D-03 17666 1.77828D+02 5.07247D-19 3.16533D-20 3.16501D-20 1.27207D-03 22240 3.16228D+02 4.67900D-19 2.45725D-20 2.40028D-20 1.13575D-03 27998 5.62341D+02 4.40063D-19 1.86687D-20 1.77870D-20 1.01415D-03 35248 1.00000D+03 4.15949D-19 1.38456D-20 1.28492D-20 9.05757D-04 44376 1.77828D+03 3.95933D-19 9.99858D-21 9.02832D-21 8.09253D-04 55866 3.16228D+03 3.79277D-19 7.01378D-21 6.15800D-21 7.23225D-04 70332 5.62341D+03 3.63660D-19 4.76939D-21 4.07129D-21 6.46607D-04 88542 1.00000D+04 3.47325D-19 3.13942D-21 2.60706D-21 5.78281D-04 111470 Plots of these two sets of data are shown in the files IonAtomCEC01.ppt and in its "translation", CEC01IonAtom.doc. One expects large decreases from our elastic Q's at energies above a few hundred eV because of the effects of inelastic collisions that are not considered in our calculations and for which we have no data. NEON+ in XENON Most of this material was included in J. De Urquijo et al, Bull. Am. Phys. Soc. 45, No. 6, 47 (2000) and in A. V. Phelps, . Here we present a very simplified model for elastic collisions of Xe+ with Ne. The momentum transfer cross section Qm is set equal to the Langevin spiraling cross section for the Ne+-Xe polarization potential with "roll-off" at high energies approximating that expected for Coulomb scattering. Qm = 3.3E-19/Ecm^0.5/(1+Ecm/3300)^1.5 and the total cross section is set equal to the Massey-Mohr total cross section for the Ne+-Xe polarization potential. Qt = 1.393E-17/Ecm^(1/3) Here the center-of-mass energy Ecm is in eV. These formulas are tabulated below. We have also fitted the charge transfer measurements of W. B. Maier, Phys. Rev. A 5, 1256 (1972) and tabulated them below. Q(Ne+ +Xe ->Xe+ +Ne) = 5E-21*UnitStep(Ecm-2.5)/(1+(Ecm/10)^4)^0.5 Q(Ne+ +Xe ->Xe++ +Ne) = 2.2E-22*UnitStep(Ecm-17)/(1+(Ecm/32)^4)^0.75 ----- elastic ------ Ne+ > Xe+ Ne+>Xe++ Ecm Qm Qt Qct Qct eV m^2 m^2 m^2 m^2 0.01 3.30E-18 6.46E-17 1.00E-30* 1.00E-30* 0.02 2.33E-18 5.13E-17 1.00E-30 1.00E-30 0.05 1.48E-18 3.78E-17 1.00E-30 1.00E-30 0.1 1.04E-18 3.00E-17 1.00E-30 1.00E-30 0.2 7.38E-19 2.38E-17 1.00E-30 1.00E-30 0.5 4.67E-19 1.75E-17 1.00E-30 1.00E-30 1 3.30E-19 1.39E-17 1.00E-30 1.00E-30 2.5 2.08E-19 1.02E-17 1.00E-30 1.00E-30 3 1.90E-19 9.65E-18 2.49E-21 1.00E-30 3.5 1.76E-19 9.17E-18 4.96E-21 1.00E-30 4 1.65E-19 8.77E-18 7.41E-21 1.00E-30 5 1.47E-19 8.14E-18 1.21E-20 1.00E-30 8 1.16E-19 6.96E-18 2.32E-20 1.00E-30 10 1.04E-19 6.46E-18 2.65E-20 1.00E-30 12 9.47E-20 6.08E-18 2.71E-20 1.00E-30 17 7.94E-20 5.41E-18 2.37E-20 1.00E-30 20 7.31E-20 5.13E-18 2.12E-20 5.93E-22 23 6.81E-20 4.89E-18 1.90E-20 1.11E-21 30 5.94E-20 4.48E-18 1.52E-20 1.86E-21 50 4.56E-20 3.78E-18 9.49E-21 1.69E-21 100 3.16E-20 3.00E-18 4.87E-21 5.94E-22 200 2.14E-20 2.38E-18 2.47E-21 1.65E-22 500 1.19E-20 1.75E-18 9.95E-22 2.79E-23 1000 7.02E-21 1.39E-18 4.99E-22 7.09E-24 2000 3.63E-21 1.10E-18 2.50E-22 1.79E-24 5000 1.17E-21 8.14E-19 1.00E-22 2.87E-25 10000 4.08E-22 6.46E-19 5.00E-23 7.20E-26 * The 1.0E-30 entries are actually 0.0, but facilitate logrithmic plots. We have not made JWBK calculations of the elastic scattering of Ne+ with Xe, but suggest a comparison with the Na+ + Xe calculation tabulated above and shown in the files IonAtomCEC01.ppt and in its "translation", CEC01IonAtom.doc. Because of the very large ratio of the peak inelastic cross section to the estimated elastic cross sections (~ 25%), we expect that there will be a large decrease in the elastic momentum transfer cross sections beginning at energies below 10 eV. As discussed in the de Urquijo et al poster cited above, the agreement between measured changes in ion mobilities with the Xe to Ne concentration and the predictions of Monte Carlo calculations using the above cross sections is being tested. Contact L. C. Pitchford.