Vibrational-Rotational Excitation in Atom-Diatomic-Molecule Collisions

Abstract

Differential and total cross sections are calculated for elastic scattering and also for rotational and vibrational excitation when an atom and a diatomic molecule collide at keV energies. Explicit calculations for vibrational excitation are here limited to the first vibration state only, although the method can easily be extended to higher vibrational states. The results are valid for small-angle scattering at keV energies, for which the motion of the nuclei can be treated in the Born approximation, while the electronic motion is treated in the adiabatic approximation. The cross sections are obtained as analytic expressions, the exact solutions which follow from a realistic potential form with several adjustable parameters. These parameters can be adjusted to fit the proposed potential form to the potential appropriate to the desired collision reactants. The potential form includes the long-range $R^{-6\mathrm{}}$ van der Waals interaction as well as the steep repulsive potential at short ranges and is a function also of the orientation angle between the molecular axis and the incident direction. Hydrogen-atom-hydrogen-molecule scattering is presented as an example. The potential for three hydrogen atoms is obtained by adjusting the parameters in the analytical expression for the potential to the ab initio calculation of the ${\mathrm{H}}_3$ energy surface of Shavitt et al., and numerical values for the differential and total cross sections are obtained. In the case of other collision reactants, for which no ab initio energy-surface calculations are available, the results of the present work conversely permit the parameters (and, therefore, the energy surface) to be determined by experimental cross-section measurements at keV energies.