The stationary-point structure and calculation of distorted wave integrals in atom-diatom scattering

Abstract

A new semi-classical method for the calculation of perturbation-type integrals, recently presented by Child, is examined and applied to the calculation of rotationally and vibrationally inelastic distorted wave integrals in the He-H₂ systems. Using the uniform Airy approximation to the wavefunctions the system is mapped onto a model system and evaluation of the integral follows using stationary phase-type arguments. We have theoretically examined the stationary-point structure and the analysis was also used in the search for stationary points of the real system. Results of our investigation into the stationary-point structure of the system are presented along with the calculated integrals. Good agreement is found with exact calculations and comparison is also made with a recently developed analytical model.