Fast oscillations in the semiclassical limit of the total cross section

Abstract

A semiclassical approximation for the total cross section is derived starting from the exact partial-wave sum. Use of the Poisson-sum formula clearly demonstrates the contribution that arises from classical orbiting. This contribution results in a pattern of fast oscillations superimposed on the main glory oscillations and in certain cases may lead to a type of 'classical' resonance whose width-to-spacing ratio is independent of h(cross). Numerical examples are presented. The results also demonstrate (in the semiclassical limit) the insignificant role played by tunnelling resonances.