Rainbow scattering in atomic collisions: A Regge pole analysis

Abstract

The application of Regge pole techniques to rainbow scattering in atomic collisions is investigated. Semiclassical calculations of Regge pole positions and residues are carried out for Lennard-Jones potentials based on the collision systems CH₄-Ar, H⁺-Ar and He-Ne. The residues of maximum modulus have values in the range 1–10¹³. The larger values are associated with pronounced rainbow maxima in the scattering. Decaying surface waves, propagating around the repulsive core of the potential, are used for the interpretation of rainbow scattering. The background integral is approximated by the direct scattering from the repulsive core. The dark side of a rainbow can be characterized by the Regge poles lying closest to the real axis in the complex angular momentum plane. In favourable cases, such as the differential cross section possessing widely spaced oscillations, a single Regge pole is sufficient to characterize the scattering on both the bright and dark side of the classical rainbow angle.