Self-consistent quasiparticle RPA for multi-level pairing model

TL;DR

This paper develops a self-consistent quasiparticle RPA method incorporating particle-number projection via Lipkin-Nogami, tested on a solvable multi-level pairing model, showing improved accuracy especially in strong coupling regimes.

Contribution

It introduces a self-consistent quasiparticle RPA approach with Lipkin-Nogami projection, enhancing agreement with exact solutions in a multi-level pairing model.

Findings

LN method improves agreement with exact results in intermediate coupling

SCQRPA yields the closest results to exact in strong coupling

Different approximations compared for accuracy and stability

Abstract

Particle-number projection within the Lipkin-Nogami (LN) method is applied to the self-consistent quasiparticle random-phase approximation (SCQRPA), which is tested in an exactly solvable multi-level pairing model. The SCQRPA equations are numerically solved to find the energies of the ground and excited states at various numbers $\Omega$ of doubly degenerate equidistant levels. The use of the LN method allows one to avoid the collapse of the BCS (QRPA) to obtain the energies of the ground and excited states as smooth functions of the interaction parameter $G$. The comparison between results given by different approximations such as the SCRPA, QRPA, LNQRPA, SCQRPA and LNSCQRPA is carried out. While the use of the LN method significantly improves the agreement with the exact results in the intermediate coupling region, we found that in the strong coupling region the SCQRPA results are closest to the exact ones.