An Exactly Solvable Supersymmetric Model of Semimagic Nuclei

TL;DR

This paper introduces an exactly solvable supersymmetric model for semimagic nuclei with a dominant orbit-dependent pairing interaction, enabling straightforward calculation of eigenstates and revealing supersymmetry in nuclear spectra.

Contribution

It presents a new exactly solvable model for semimagic nuclei with a dominant pairing interaction and demonstrates its supersymmetry, along with a simplified method for eigenvalue calculation.

Findings

Model accurately describes Ni isotopes from 58Ni to 68Ni.

Supersymmetry connects spectra of certain semimagic nuclei.

New technique simplifies solving Bethe ansatz equations.

Abstract

A simple model of nucleons coupled to angular momentum zero (s-pairs) occupying the valance shell of a semi-magic nuclei is considered. The model has a separable, orbit dependent pairing interaction which dominates over the kinetic term. It is shown that such an interaction leads to an exactly solvable model whose (0+) eigenstates and energies can be computed very easily with the help of the algebraic Bethe ansatz method. It is also shown that the model has a supersymmetry which connects the spectra of some semimagic nuclei. The results obtained from this model for the semimagic Ni isotopes from 58Ni to 68Ni are given. In addition, a new and easier technique for calculating the energy eigenvalues from the Bethe ansatz equations is also presented.