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.

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A systematic study of elastic scattering by complex valued optical potentials has been carried out. A Lennard-Jones (12,6) potential with an imaginary r−s term has been used in the calculations. The collision parameters are chosen to model the elastic scattering of K by HBr and Li by HBr. First-order semiclassical single turning point phase shifts are compared with accurate quantum phase shifts and close agreement is found. It is straightforward to calculate semiclassical phase shifts for an optical potential; it is unnecessary to introduce additional approximations (for numerical convenience) as is usually done in the literature. Up to 15 000 terms in the partial wave series are used to calculate elastic angular distributions. It is shown that a rich interference structure and a backward glory can occur in the large angle scattering, provided the transition from absorbency to transparency is sufficiently rapid. Different optical potentials can result in similar angular distributions. A complex angular momentum (Regge pole) analysis of the large angle scattering has been carried out. It is shown that the interference effects have a physical interpretation in terms of surface waves that propagate around the core of the potential and the directly reflected elastic scattering.