Elastic and related transport cross sections for
(H,D,T)+ + C |
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 H+ + C, D+ + C and,
T+ + 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, al, satisfies
1-Re(al) < 10-6 and Im(al) <
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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- 1. The data have been posted as of 4/25/00. Any updates will be
documented here.
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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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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,
ECM = 10(0.1*n - 1) eV, in order to roughly
uniformly span logarithmically the range of 0.1 to 100 eV.
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, ECM =
10(0.1*n - 1) eV, in order to roughly uniformly span
logarithmically the range of 0.1 to 100 eV.
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