Slow electron elastic scattering by a target represented by different zero-range potentials

TL;DR

This paper derives formulas for calculating phase shifts in slow electron elastic scattering by targets modeled with different zero-range potentials, highlighting the use of non-spherical functions and the S-matrix method.

Contribution

It introduces general formulas for phase shifts and continuum wave functions for non-spherical zero-range potential targets, expanding the theoretical framework.

Findings

Formulas for phase shifts in non-spherical zero-range potentials

Representation of wave functions using non-spherical orthonormal functions

Discussion of the S-matrix method for arbitrary potentials

Abstract

The general formulas to calculate the phase shifts of wave function of a particle scattering on a target formed by a pair of non-identical zero-range potentials are derived. It is shown that at asymptotically great distances from the target the continuum wave function of particle is presented as an expansion in a set of other than spherical, orthonormal functions. General formulas for these functions are obtained. The special features of the S-matrix method for the case of arbitrary non-spherical potentials are discussed.