Comparative Study of alpha-alpha interaction potentials constructed using various phenomenological models

TL;DR

This study compares various phenomenological models for alpha-alpha interactions by analyzing scattering phase shifts and inverse potentials, demonstrating that different models yield similar results and emphasizing the importance of capturing basic interaction features.

Contribution

It provides a comparative analysis of multiple phenomenological potentials for alpha-alpha scattering, highlighting their similar effectiveness in modeling interactions.

Findings

All models produce similar inverse potentials.

Models yield closely matching phase shift errors.

Any function capturing basic interaction features is effective.

Abstract

In this paper, we have made a comparative study of alpha-alpha scattering using different phenomenological models like Morse, double Gaussian, double Hulthen, Malfliet-Tjon and double exponential for the nuclear interaction and atomic Hulthen as screened coulomb potential. The phase equations for S, D and G channels have been numerically solved using 5th order Runge-Kutta Method to compute scattering phase shifts for elastic scattering region consisting of energies up to 25.5 MeV. The model parameters in each of the chosen potentials were varied in an iterative fashion to minimize the mean absolute percentage error between simulated and expected scattering phase shifts. A comparative analysis revealed that, all the phenomenological models result in exactly similar inverse potentials with closely matching mean absolute percentage error values for S, D and G state. One can conclude that any mathematical function that can capture the basic features of two body interaction would always guide correctly in construction of inverse potentials.