Potential scattering cross sections in the semiclassical limit

Abstract

The semiclassical theory of uniform approximations to the cross section for small-angle scattering is investigated numerically for various potential models, including the familiar Lennard-Jones interatomic potential. Calculations of the differential cross section using the semiclassical formulae are compared with quantum mechanical calculations to investigate the accuracy and range of validity of the uniform approximations. It is demonstrated that such methods can predict very precisely the shape of the differential cross section over a surprisingly wide range of conditions.