Modeling of Real and Imaginary Phase Shifts for $\alpha-\alpha$ Scattering using Malfliet-Tjon Potential

TL;DR

This paper develops a novel algorithm combining a Riccati-type phase equation with Variational Monte Carlo to derive inverse potentials for alpha-alpha scattering, accurately matching experimental phase shifts across multiple partial waves.

Contribution

It introduces a new method for modeling real and imaginary phase shifts using inverse potentials and an optimization approach to fit experimental data.

Findings

Achieved low mean absolute percentage error for phase shifts in different partial waves.

Successfully modeled both real and imaginary components of phase shifts.

Validated the approach with experimental data across multiple angular momentum channels.

Abstract

The real and imaginary scattering phase shifts (SPS) and potentials for $\ell=0,2,4$ partial waves have been obtained by developing a novel algorithm$^{\ref{Fig1}}$ to derive inverse potentials using a phenomenological approach. The phase equation, which is a Riccati-type non-linear differential equation, is coupled with the Variational Monte Carlo method. Comparisons between the resulting SPS for various $\ell$ channels and experimental data are made using mean absolute percentage error (MAPE) as a cost function. Model parameters are fine-tuned through an appropriate optimization technique to minimize MAPE. The results for $\ell=0^+$, $2^+$, and $4^+$ partial waves are generated to align with experimental SPS with mean absolute error (MAE) calculated with respect to experimental data is 3.19, 8.74, 13.06 respectively corresponding to real part and 0.76, 0.76, 0.59 corresponding to imaginary parts of scattering phase shifts.