Study of resonance states of $^{11}$Be with isospectral bound state microscopic potential

TL;DR

This paper applies supersymmetric quantum mechanics to study resonance states in the weakly bound nucleus $^{11}$Be using a microscopic potential derived from the DDM3Y interaction, achieving good agreement with experimental data.

Contribution

It introduces a novel application of SQM with a microscopic potential to analyze quasi-bound states in $^{11}$Be, providing new insights into its resonance structure.

Findings

Resonance energies match experimental data well.

Generated isospectral potentials reveal detailed resonance structures.

Method demonstrates effectiveness for weakly bound nuclear systems.

Abstract

The theoretical procedure of supersymmetric quantum mechanics (SQM) is adopted for the first time to study quasi-bound states of a weakly bound nuclear system using microscopic potential. The density dependent M3Y (DDM3Y) effective interaction was found earlier to give a satisfactory description of radioactivity, nuclear matter and scattering. In the present work, we have generated a two-body potential microscopically in a single folding model using the DDM3Y effective interaction. From this potential, SQM generated a family of isospectral potentials for $^{11}$Be ($^{10}$Be + n). We investigated the 5/2$^+$, 3/2$^-$ and 3/2$^+$ resonance states of $^{11}$Be. The experimental data and the present calculations of excitation energies of the above resonance states are found to be in good agreement.