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

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.