The adiabatic semiclassical perturbation theory for vibrationally inelastic scattering. I. Collinear calculations

摘要

A semiclassical approximation is developed to treat vibrationally inelastic scattering. The vibrational basis set used is adiabatic with respect to a reference potential which is chosen to be as close as possible to the true potential and yet give easily obtainable solutions to the vibrational wave equation. The radial wave functions are obtained using the WKB approximation, and the coupled Schrouml;dinger equations are solved by a firsthyphen;order perturbation method (similar to the distortedhyphen;wave approximation) to yield a phase shift matrix which is then exponentiated to give the full scattering matrix. Results, including highhyphen;order transitions, were obtained for all the cases computed by Secrest and Johnson and by Clark and Dickinson. The agreement is excellent, being better than 10percnt; for half of the cross sections and, except for one system, rarely off by more than a factor of 2.