Canonical and microcanonical ensemble descriptions of thermal pairing within BCS and quasiparticle RPA

TL;DR

This paper introduces a simplified method for describing thermal pairing in finite systems using canonical and microcanonical ensembles, based on BCS and quasiparticle RPA with particle-number projection, showing good agreement with exact solutions and experimental data.

Contribution

It presents a novel approach combining BCS and quasiparticle RPA with particle-number projection for finite systems in canonical and microcanonical ensembles.

Findings

Good agreement with exact solutions of pairing model

Consistent with experimental data for $^{56}$Fe

Applicable to systems where exact solutions are impractical

Abstract

We propose a description of pairing properties in finite systems within the canonical and microcanonical ensembles. The approach is derived by solving the BCS and self-consistent quasiparticle random-phase approximation with the Lipkin-Nogami particle-number projection at zero temperature. The obtained eigenvalues are embedded into the canonical and microcanonical ensembles. The results obtained are found in quite good agreement with the exact solutions of the doubly-folded equidistant multilevel pairing model as well as the experimental data for $^{56}$Fe nucleus. The merit of the present approach resides in its simplicity and its application to a wider range of particle number, where the exact solution is impracticable.