Analysing supersymmetric transformed $\alpha$-nucleus potentials with electric-multipole transitions

TL;DR

This paper investigates supersymmetric transformations of alpha-nucleus potentials to produce shallow potentials that preserve phase shifts but modify wave functions, analyzed through electric-multipole transitions for better multi-cluster system modeling.

Contribution

It introduces a method to generate shallow supersymmetric potentials from deep ones, maintaining phase shifts while altering wave functions for improved nuclear cluster analysis.

Findings

Supersymmetric transformations produce phase-shift-equivalent shallow potentials.

Wave functions are significantly altered by the transformations.

Electric-multipole transitions reveal differences in radial sensitivities.

Abstract

Alpha($^{4}$He)-cluster models have often been used to describe light nuclei. Towards the application to multi-cluster systems involving heavy clusters, we study the relative wave functions of the $\alpha+^{16}$O and $\alpha+^{40}$Ca systems generated from phase-shift-equivalent potentials. In general, a potential between clusters is deep accommodating several redundant bound states which should be removed in an appropriate way. To avoid such a complicated computation, we generate a shallow-singular potential by using supersymmetric transformations from the original deep potential. Changes in the relative wave functions by the transformations are quantified with electric-multipole transitions which give a different radial sensitivity to the wave function depending on their multipolarity. Despite the fact that the original and transformed potentials give exactly the same phase shift, some observables are unfavorably modified. A possible way to obtain a desired supersymmetric potential is proposed.