A Direct Method For the Low Energy Scattering Solution of Delta Shell Potentials

TL;DR

This paper introduces a direct momentum-space method for solving low energy scattering and bound states in delta shell potentials, explicitly imposing outgoing boundary conditions, offering an alternative to standard partial wave analysis.

Contribution

It presents a novel direct approach in momentum space for delta shell potentials, explicitly imposing boundary conditions, differing from traditional methods.

Findings

Results agree with standard partial wave analysis.

Method effectively handles circular and spherical delta shells.

Provides a new perspective on boundary condition implementation.

Abstract

A direct method for the bound states and the low energy scattering from a circular and a spherical delta shell potentials is proposed and the results are compared with the one using the standard partial wave analysis developed for potentials with rotational symmetry. The formulation is presented in momentum space and the scattering solutions are obtained by considering the elementary use of distributions. In this approach, the outgoing boundary conditions are imposed explicitly in contrast to the $i\epsilon$ prescription often used in quantum mechanics.