Low-energy scattering by long-range singular potentials

Abstract

This work considers the quantum-mechanical problem of low-energy scattering by inverse-power repulsive potentials. A method capable of generating all the terms in the low-energy asymptotic expansions of the phase shifts is presented. This method is based on the approach of inner-outer expansions and may be extended to more general singular long-range potentials. The computational procedure demonstrates clearly the mathematical origin of all the terms in the asymptotic expansions of the phase shifts.