CFADC Data Collections: Elastic and related transport cross sections -- D^+ + C

Elastic and related transport cross sections for D⁺ + C

Index

Introduction
Important notes and updates
Publications
Data tables

Following the general procedures outlined in our previous papers which provided theoretical differential and integral elastic and related transport (momentum transfer and viscosity) cross sections for collisions among various isotopic combinations of H^+,, H, and H₂, and He, tabulated here are similar data for D⁺ + C for center of mass collisions energies between 0.1 and 100 eV.

In brief, the calculations were performed by solving the radial Schrodinger equation for each partial wave component on the two ground state triplet (b³Sigma^- and 2³Pi) adiabatic electronic eigenenergy curves. These states are the ground state energy curves of CH⁺ which correlate asymptotically (separated atoms limit) to C(²P). The potentials we used as our starting point in the present calculations were taken from work by Buenker and collaborators (described in Reference 5 below) and were obtained using the multireference single- and double-excitation configuration interaction (MRD-CI) method, in the range of internuclear separations from 0.6 to 20 a.u.

In order to obtain convergence in partial waves (impact parameter) for low energy elastic scattering, we extended these potential energy curves to larger distances by fitting them to the dipole polarization potential (dipole polarizability from Reference 6). Similarly, to assure convergence at large angles, important for accuracy of the momentum transfer and viscosity cross sections, we extended the curves to small distances by fitting to the Hartree-Fock model potential (representing the distance-dependent screening of the nuclear charge by the electronic density) of Garvey et al. (Reference 7).

Much as in our previous calculations, the radial integration was carried out using Johnson's logarithmic derivative method, beginning the integration at an internuclear separation of 0.05 a.u. and with a step of 0.0003 a.u., and then matching the solution to plane waves at 200 a.u. Convergence in partial waves is monitored until the partial amplitude, a_l, satisfies 1-Re(a_l) < 10^-6 and Im(a_l) < 10^-6 for 20 consecutive values of l. The elastic differential cross section is computed at 768 angles between 0 and pi, to facilitate Gauss-Legendre integration and to assure that all the oscillations of the differential cross section are represented accurately enough to assure convergence during this integration. The procedure is repeated for 31 energies spanning the center of mass collision energy range of 0.1-100 eV.

For this system, owing to the asymmetry of the colliding nuclei as well as the orthogonality of the magnetic sublevels involved, states represented by the two potential energy curves do not cohere. Thus, we present below the statistical average over the two ground curves, Sigma and Pi. The Pi state, having magnetic sublevels +1 and -1, carries a weight of 2/3 and the Sigma (m=0) carries the weight 1/3.

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Important notes and updates

1. The data have been posted as of 4/25/00. Any updates will be documented here.

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Publications

The results for collisions among all isotopic combinations of hydrogen ions, atoms, and molecules are described in the following references and here. The data form the basis for a volume of recommended elastic and transport related cross sections (reference 1), and many details of the calculations, their physical interpretation, and their inter-relationships are detailed in references 2-4. Reference 5 pertains to our work on charge transfer between C⁺ with H and H⁺ with C, illustrating the relevant H⁺+C potential energy curves, calculated by our collaborators on that work, Gu, Hirsch, and Buenker.

1. ``Elastic and related transport cross sections for collisions among isotopomers of H⁺ + H, H⁺ + H₂, H⁺ + He, H + H, and H + H₂'', P.S. Krstic and D.R. Schultz, Atomic and Plasma-Material Data for Fusion 8,1 (1998). (Postscript file containing the introduction, basic theoretical description, comparison with existing results, scaling relations, description of tables and graphs, and references - approximately 70 pages, 1.68 Mb, approximately 650 pages of graphs and tables omitted).
2. ``Elastic scattering and charge transfer in slow collisions: Isotopes of H and H⁺ colliding with isotopes of H and with He,'' P.S. Krstic and D.R. Schultz, J. Phys. B 32, 3485 (1999). (Postscript (5.48 Mb)).
3. ``Consistent definitions for, and relationships among, cross sections for elastic scattering of hydrogen ions, atoms, and molecules,'' P.S. Krstic and D.R. Schultz, Phys. Rev. A 60, 2118 (1999). (Postscript (4.21 Mb)).
4. ``Elastic and vibrationally inelastic slow collisions: H + H₂, H⁺ + H₂,'' P.S. Krstic and D.R. Schultz, J. Phys. B 32, 2415 (1999). (Postscript (3.53 Mb)).
5. ``Electron capture in collisions of C⁺ with H and H⁺ with C,'' P.C. Stancil, J-P. Gu, C.C. Havener, P.S. Krstic, D.R. Schultz, M. Kimura, B. Zygelman, G. Hirsch, R.J. Buenker, and M.E. Bannister, J. Phys. B 31, 3647 (1998); ``Charge transfer in collisions of C⁺ with H and H⁺ with C,'' P.C. Stancil, C.C. Havener, P.S. Krstic, D.R. Schultz, M. Kimura, J-P. Gu, G. Hirsch, R.J. Buenker, and B. Zygelman, Ap. J 502, 1006 (1998).
6. ``Atomic polarizabilities from ground and excited states of C, N, and O,'' R.K. Nesbet, Phys. Rev. A 16, 1 (1977).
7. ``Independent-particle-model potentials for atoms and ions with 36 < Z =< 54 and a modified Thomas-Fermi atomic energy formula,'' R.H. Garvey, C.H. Jackman, and A.E.S. Green, Phys. Rev. A 12, 1144 (1975).

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Data tables

Integral Cross Sections

The statistically averaged (see explanation above) elastic integral cross section, momentum transfer cross section, and viscosity cross section are given in the following table as a function of center of mass collision energy (from 0.1 to 100 eV). The cross sections are given in atomic units (i.e. 1 a.u. of cross section = [Bohr radius]² = 2.80028 * 10^-17 cm²). The center of mass energies are given by the following formula, E_CM = 10^{(0.1*n - 1)} eV, in order to roughly uniformly span logarithmically the range of 0.1 to 100 eV.

Integral Cross Sections

Differential Cross Sections

The statistically averaged (see explanation above) elastic differential cross section are given in the files below for 31 center of mass collision energies from 0.1 to 100 eV. The first column in each files give the center of mass scattering angle in radians (at 768 values) and the second column gives the differential cross section multiplied by 2 pi sin(theta) in atomic units (i.e. 1 a.u. = [Bohr radius]²/srad = 2.80028 * 10^-17 cm²/srad). The center of mass energies are given by the following formula, E_CM = 10^{(0.1*n - 1)} eV, in order to roughly uniformly span logarithmically the range of 0.1 to 100 eV.