Molecular Collisions. IX. Restricted Distorted-Wave Approximation for Rotational Excitation and Scattering of Diatomic Molecules

The general expression for rotational excitation and scattering cross sections for rigid diatomic molecules derived in Paper VIII is reduced to yield a restricted distorted-wave approximation, resulting in a relatively simple equation for the inelastic transition probabilities. The new expressions possess significant advantage over analogous ones of Davison and of Arthurs and Dalgarno due to the elimination of certain multiple summations. The results are, however, demonstrated to be identical by direct resummation methods. For a potential which is separable into a product of a radial and an angular function, the dependence of the transition probability upon the anisotropy parameters is given explicitly.