Development of a Cox-Thompson inverse scattering method to charged particles

TL;DR

This paper extends the Cox-Thompson inverse scattering method to include long-range Coulomb interactions, enabling the derivation of inverse potentials with different behaviors at the origin, and suggests a repulsive core in p-alpha interactions.

Contribution

The paper introduces two new formulations of the Cox-Thompson method for charged particles, accommodating Coulomb forces and analyzing their effects on inverse potentials.

Findings

Inverse potentials can be singular or finite at the origin depending on the reference potential.

The p-alpha interaction likely has a repulsive hard core.

The method accurately reproduces experimental phase shifts.

Abstract

A Cox-Thompson fixed-energy quantum inverse scattering method is developed further to treat long-range Coulomb interaction. Depending on the reference potentials chosen, two methods have been formulated which produce inverse potentials with singular or finite value at the origin. Based on the quality of reproduction of input experimental phase shifts, it is guessed that the p-alpha interaction possesses an interesting repulsive hard core.