On Regge trajectories for ion-atom and atom-atom potentials

Abstract

Some properties of Regge trajectories for interatomic potentials of the Lennard-Jones type are considered. An exact differential equation for the trajectories is derived. An approximation similar to the rigid rotator and neglect of centrifugal distortion approximation allows this equation to be integrated and predicts a linear relation between Re (λ _n ²) and the energy E. A semiclassical analysis complements the formal analysis and gives a physical interpretation to the integration constant Re C_n as well as to Im λ _n : Re C _n is related to the vibrational states of the potential and Im λ _n is related to the angle of rotation of the atoms about each other. A numerical example is presented for a Lennard-Jones (6, 4) potential, with parameters approximating low energy H⁺-Ar elastic scattering.