Perturbation Treatment of Large-Angle Elastic Scattering

Abstract

A perturbation treatment, valid for small impact parameters, is developed for the WKB phase shift and the classical deflection angle for a general Lennard-Jones potential. The unperturbed problem is the scattering at zero impact parameter from a repulsive interaction given by Cr−8. The centrifugal term in the effective potential and an attractive term are added as perturbations. The phase shift and deflection angle are obtained as a simple series to third order in both perturbations. A simple expression is obtained for the large-angle differential cross section which may be used to obtain the well depth ε and the power of the repulsive wall s.