A recoupled states approximation for molecular scattering theory

Abstract

Recent work is reviewed on the theory of angular momentum decoupling approximations in inelastic molecular scattering theory. It is shown that the failure of these approximations is more extensive than previously believed, particularly for completely state-selected m transitions. A systematic study of a number of centrifugal sudden approximations is made and discussed. A new method is presented for improving these approximations, which recouples the approximate solutions. Completely state-selected differential and integral cross sections are computed under the centrifugal decoupling approximation and its correction for Ne+HD scattering at a total energy of 31.5 meV. Five choices of the partial wave decoupling parameter (including the three known ones) are studied. The numerical results show that with the partial wave parameter chosen to be the arithmetic mean of the initial and final l-quantum numbers, the coupled states approximation gives excellent results for orientation averaged transitions, but fails dramatically for state-selected m transitions. The corrected centrifugal decoupling approximation gives significantly more accurate inelastic differential and integral state-selected cross sections than its uncorrected counterpart. The extension of this correction technique to the energy sudden and the infinite order sudden approximations is discussed.