Application of supersymmetric quantum mechanics to study bound state properties of exotic hypernuclei

TL;DR

This paper applies supersymmetric quantum mechanics to analyze bound state properties of hypernuclei, using hyperspherical harmonics and phenomenological potentials to predict energies, wavefunctions, and geometrical observables.

Contribution

It introduces a novel approach combining SSQM with hyperspherical harmonics to study hypernuclei bound states, extending the analysis to excited states.

Findings

Number of bound states increases with core mass.

Predicted ground and excited state energies match experimental trends.

Calculated RMS radii and geometrical properties of hypernuclei.

Abstract

Bound state properties of few single and double-$\Lambda$ hypernuclei is critically examined in the framework of core-$\Lambda$ and core+$\Lambda+\Lambda$ few-body model applying hyperspherical harmonics expansion method (HHEM). The $\Lambda\Lambda$ potential is chosen phenomenologically while the core-$\Lambda$ potential is obtained by folding a phenomenological $\Lambda N$ interaction into the density distribution of the core. The depth of the effective $\Lambda N$ potential is adjusted to reproduce the experimental data for the core-$\Lambda$ subsystem. The three-body Schr\"odinger equation is solved by hyperspherical adiabatic approximation (HAA) to get the ground state energy and wave function. The ground state wavefunction is used to construct the supersymmetric partner potential following prescription of supersymmetric quantum mechanics (SSQM) algebra. The newly constructed supersymmetric partner potential is used to solve the three-body Schr\"odinger equation to get the energy and wavefunction for the first excited state of the original potential. The method is repeated to predict energy and wavefunction of the next higher excited states. The possible number of bound states is found to increase with the increase in mass of the core of the hypernuclei. The Root Mean Squared (RMS) matter radius and some other relevant geometrical observables are also predicted.