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

Title: 基于Lipkin-Meshkov-Glick模型在SU(2) $\times$ SU(2)中研究的质子-中子随机相位近似

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. Show Chinese abstract

Abstract: 我们研究了具有扩展的Lipkin-Meshkov-Glick模型的质子-中子RPA。 我们关注相关基态的影响以及中子和质子数不同的情况。 基于准玻色子近似检验了相关基态的影响。 我们得到的结果表明，直到粒子-粒子相互作用达到一定强度为止，RPA激发能和跃迁强度与精确解有很好的一致性。 然而，即使在较弱的粒子-粒子相互作用下，当考虑中子和质子数不同的情况时，跃迁强度变得更差。