Scattering of a slow quantum particle on an axially symmetric short-range potential

Abstract

A linear version of the variable-phase approach in potential-scattering theory is supplemented with a new asymptotic method. This method is intended for analyzing quantum mechanically and for constructing explicit low-energy approximations for partial-wave phase shifts, amplitudes, cross sections, and radial components of the wave function for the scattering of a quantum particle on an axially symmetric short-range potential. The procedure used to construct all low-energy approximations reduces to solving a recursion chain of energy-independent sets of equations, each such set consisting of two linear first-order differential equations. © 2014 Pleiades Publishing, Ltd.