The exact three-dimensional half-shell t-matrix for a sharply cut-off Coulomb potential in the screening limit

TL;DR

This paper derives an analytical expression for the three-dimensional half-shell t-matrix of a sharply cut-off Coulomb potential and confirms its accuracy through numerical solutions, enhancing understanding of scattering in screened Coulomb systems.

Contribution

It provides the first exact analytical derivation of the three-dimensional half-shell t-matrix for a sharply cut-off Coulomb potential without partial wave expansion.

Findings

Analytical form matches numerical solutions for large cut-off radii.

Asymptotic behavior of the t-matrix is explicitly characterized.

Numerical solutions agree well with the derived asymptotic form.

Abstract

The three-dimensional half-shell t-matrix for a sharply cut-off Coulomb potential is analytically derived together with its asymptotic form without reference to partial wave expansion. The numerical solutions of the three-dimensional Lippmann-Schwinger equation for increasing cut-off radii provide half-shell t-matrices which are in quite a good agreement with the asymptotic values.