A possible trial beyond the conventional random phase approximation for the su(2)-Lipkin model including the case of non-closed shell system

TL;DR

This paper develops an improved approximation method for the su(2)-Lipkin model, addressing discrepancies between exact and RPA results, and extends the model to non-closed shell systems using an additional su(2)-algebra.

Contribution

The authors propose a renewed RPA framework and a modified su(2)-Lipkin model that can handle non-closed shell systems with any total fermion number.

Findings

Discrepancy between exact and RPA results is resolved.

The new method accurately estimates previously unmanageable terms.

Model extension allows for non-closed shell system analysis.

Abstract

Concerning the su(2)-Lipkin model, the calculation of the excitation energy to the 1st excited-state gives rise to the following fact: The two results based on the exact treatment and the conventional random phase approximation (RPA) are in unexpected disagreement. In order to remove this discrepancy, the conventional RPA is renewed. With the aim of this renewal, the terms, which cannot be dealt with in the conventional one, are estimated. The basic framework of this new form is not reorganized from that of the conventional one. In addition, the su(2)-Lipkin model itself is also modified so as to be applicable to the case with non-closed shell system. To this modification, one more su(2)-algebra, which has been already proposed by the present authors, is applied. Through the use of this algebra, the su(2)-Lipkin model is applicable to the case with any total fermion number permitted in the model.