Complex angular momentum analysis of diffraction scattering in atomic collisions

Abstract

The application of complex angular momentum techniques to diffraction scattering in elastic atom–atom collisions is investigated. Two different semiclassical methods have been used. In the first method, complex saddle points associated with the semiclassical integral representation for the scattering amplitude are employed. The second method is the Regge pole approach to elastic scattering. The first calculations are reported in which the semiclassical uniform Airy approximation using complex angular momenta has been applied to the dark side of a rainbow. Good agreement with partial wave results is obtained for the uniform Airy and Regge pole theories, with the Regge pole approach the easier to apply. The accuracy of the transitional Airy and primitive semiclassical approximations has also been studied. The effect of neglecting the scattering from the repulsive core of the potential is investigated. This case arises in the elastic scattering of chemically reactive systems when strong absorption is present. In addition, the effect on diffraction scattering of damping out the attractive part of a Lennard-Jones potential has ben studied until just the repulsive core remains.