Accurate calculation of low energy scattering phase shifts of charged particles in a harmonic oscillator trap

TL;DR

This paper introduces two high-accuracy numerical methods for calculating low-energy scattering phase shifts of charged particles in a harmonic oscillator trap, validated against the Numerov method and applicable to nuclear and atomic physics.

Contribution

The paper presents two novel numerical approaches for solving the Coulomb-corrected BERW formula with high accuracy across all energies, demonstrated on p-alpha scattering.

Findings

Methods reproduce phase shifts from Numerov method for l=0 and l=1.

Full Python scripts provided for broad application.

Validated accuracy across entire energy spectrum.

Abstract

Considering the elastic scattering of two charged particles, we present two methods for numerically solving the generalized Coulomb-corrected BERW formula with high accuracy across the entire energy spectrum. We illustrate these methods using p-alpha scattering, employing a phenomenological p-alpha short-range interaction. Our results reproduce the phase shifts computed with the Numerov method for all l=0 and l=1 channels. We also provide full access to the Python script used to obtain these results, which can be readily applied to a wide range of core-fragment scattering problems in nuclear and atomic physics.