Resonance energy and wave functions of $^{31}$Ne: a calculation using supersymmetric quantum mechanics

TL;DR

This paper introduces a novel computational approach combining supersymmetric quantum mechanics and bound states in continuum techniques to accurately calculate energies and wave functions of weakly bound nuclei, exemplified on $^{31}$Ne.

Contribution

The study develops an efficient method for nuclear energy and wave function calculations using SSQM and BIC, applied to $^{31}$Ne with results matching experimental data.

Findings

Identified bound states at -0.33, -0.30, -0.15 MeV

Predicted several low-lying resonance states including f7/2 and p1/2

Resonance energy of f7/2 state agrees with literature

Abstract

In this communication, we present an efficient method for computation of energy and wave function of weakly bound nuclei by the application of supersymmetric quantum mechanics (SSQM) and bound states in continuum (BIC) technique. As a case study the scheme is implemented to the two-body ($^{30}$Ne + n) cluster model calculation of neutron-rich nucleus $^{31}$Ne. Woods-Saxon central potential with spin-orbit component is used as the core-nucleon interaction. The two-body Schr\"{o}dinger equation in relative coordinate is solved numerically to get the energy and wave function of the low-lying bound states. A one-parameter family of isospectral potential (IP) is constructed from the bound state solutions following algebra of SSQM to find energies and wave functions of the resonance states. In addition to the 2p$_{3/2^-}$ (-0.33 MeV) ground state, two bound excited states: s$_{1/2}$ (-0.30 MeV), $p_{1/2}$ (-0.15 MeV) are also obtained. Few low-lying resonance states: f$_{7/2_1}$ (2.57 MeV), f$_{7/2_2}$ (4.59 MeV), f$_{5/2_1}$ (5.58 MeV), p$_{1/2_1}$(1.432 MeV), p$_{1/2_2}$ (4.165 MeV), p$_{3/2_1}$ (1.431 MeV), p$_{3/2_2}$ (4.205 MeV) are predicted. Among the predicted resonance states, the f$_{7/2^{-}}$ state having resonance energy $E_R \simeq 4.59$ MeV is in excellent agreement with the one found in the literature.