Pairing within the self-consistent quasiparticle random-phase approximation at finite temperature

TL;DR

This paper introduces a novel approach to finite-temperature pairing in nuclei, incorporating quasiparticle-number fluctuations and dynamic couplings, leading to more accurate predictions of pairing gaps, energy, and heat capacity.

Contribution

It develops a self-consistent quasiparticle RPA method that includes fluctuations and vibrations, improving agreement with exact and Monte Carlo results.

Findings

Thermal pairing gap persists above BCS critical temperature.

Smoothed phase transition due to quasiparticle-number fluctuations.

Enhanced accuracy in total energy and heat capacity predictions.

Abstract

An approach to pairing in finite nuclei at nonzero temperature is proposed, which incorporates the effects due to the quasiparticle-number fluctuation (QNF) around Bardeen-Cooper-Schrieffer (BCS) mean field and dynamic coupling to quasiparticle-pair vibrations within the self-consistent quasiparticle random-phase approximation (SCQRPA). The numerical calculations of pairing gap, total energy, and heat capacity were carried out within a doubly folded multilevel model as well as realistic nuclei $^{56}$Fe and $^{120}$Sn. The results obtained show that, under the effect of QNF, in the region of moderate and strong couplings, the sharp transition between the superconducting and normal phases is smoothed out, resulting in a thermal pairing gap, which does not collapse at the BCS critical temperature, but has a tail, which extends to high temperature. The dynamic coupling of quasiparticles to SCQRPA vibrations significantly improves the agreement with the results of exact calculations and those obtained within the finite-temperature quantal Monte Carlo method for the total energy and heat capacity. It also causes a deviation of the quasiparticle occupation numbers from the Fermi-Dirac distributions for free fermions.