Constructing Inverse Scattering Potentials for {\alpha}-{\alpha} System using Reference Potential Approach

TL;DR

This paper introduces a reference potential method using Morse functions to accurately construct inverse alpha-alpha scattering potentials, effectively incorporating Coulomb and nuclear interactions, and achieving high precision in phase shift predictions.

Contribution

It presents a novel approach combining Morse potentials for Coulomb and nuclear interactions to construct inverse scattering potentials with minimal error.

Findings

Achieved mean absolute percentage errors below 1% for phase shifts.

Resonance predictions for D and G states closely match experimental data.

Method effectively accounts for long-range Coulomb and short-range nuclear forces.

Abstract

Background: An accurate way to incorporate long range Coulomb interaction alongside short-range nuclear interaction has been a challenge for theoretical physicists. Purpose: In this paper, we propose a methodology based on the reference potential approach for constructing inverse potentials of alpha-alpha scattering. Methods: Two smoothly joined Morse potentials, regular for short-range nuclear interaction and inverted for long range Coulomb, are used in tandem as a reference potential in the phase function method to obtain the scattering phase shifts for the S, D and G states of alpha-alpha scattering. The model parameters are optimized by choosing to minimize the mean absolute percentage error between the obtained and experimental scattering phase shift values. Results: The constructed inverse potentials for S, D and G states have resulted in mean absolute percentage errors of 0.8, 0.5, and 0.4 respectively. The obtained resonances for D and G states closely match the experimental ones. Conclusion: The reference potential approach using a combination of smoothly joined Morse functions is successful in accurately accounting for the Coulomb interaction between charged particles in nuclear scattering studies.