Properties of Regge pole positions and residues for interatomic potentials

Abstract

A detailed investigation of the Regge properties of singular intermolecular potentials has been made. Inverse power potentials of the type r -s with s>2 and Lennard-Jones (12, 6) potentials are considered. Exact quantum and semiclassical calculations are carried out for collision systems for which the residue of maximum modulus is of order unity. Good agreement between the exact quantum and semiclassical results is found. The existence of non-linear as well as linear Regge trajectories is established. The accuracy and utility of some simple approximate formulae due to Brander (1966) and Tiktopoulos (1969) for the Regge properties of r -s potentials is investigated. A new approximate formula based on a complex harmonic oscillator formalism is also derived. It is shown that these approximate formulae can be used to understand the main Regge properties of singular intermolecular potentials.