The adiabatic semiclassical perturbation theory for vibrationally inelastic scattering. I - Collinear calculations. II - Three-dimensional treatment

A semiclassical approximation to treat vibrationally inelastic scattering is developed. 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 also gives easily obtainable solutions to the vibrational wave equation. The radial wave functions are obtained using the WKB approximation, and the coupled Schroedinger equations are solved by a first-order perturbation method to yield a phase shift matrix which is exponentiated to give the full scattering matrix. Results were obtained for all the cases computed by Secrest and Johnson and by Clark and Dickinson, and the agreement is better than 10% for half of the cross-sections and rarely off by more than a factor of 2.