Proton-neutron random phase approximation studied by the Lipkin-Meshkov-Glick model in the SU(2) $\times$ SU(2)

TL;DR

This paper investigates the proton-neutron RPA using an extended Lipkin-Meshkov-Glick model, focusing on correlated ground states and neutron-proton number differences, revealing the model's accuracy and limitations.

Contribution

It introduces an analysis of proton-neutron RPA with correlated ground states and neutron-proton asymmetry within the Lipkin-Meshkov-Glick framework.

Findings

RPA excitation energies agree with exact solutions up to a certain interaction strength

Transition strengths are accurately predicted for symmetric neutron-proton numbers

Accuracy decreases for asymmetric neutron-proton configurations, even at weak interactions

Abstract

We study the proton-neutron RPA with an extended Lipikin-Meshkov-Glick model. We pay attention to the effect of correlated ground state and the case in which neutron and proton numbers are different. The effect of the correlated ground state are tested on the basis of quasi-boson approximation. We obtain the result that RPA excitation energies and transition strengths are in a good agreement with the exact solution up to a certain strength of the particle-particle interaction. However, the transition strength becomes worse if we consider the case in which neutron and proton numbers are different even at a weak particle-particle interaction.