Exact and approximate ensemble treatments of thermal pairing in a multilevel model

Abstract

A systematic comparison is conducted for pairing properties of finite systems at nonzero temperature as predicted by the exact solutions of the pairing problem embedded in three principal statistical ensembles, as well as the unprojected (FTBCS1+SCQRPA) and Lipkin-Nogami projected (FTLN1+SCQRPA) theories that include the quasiparticle number fluctuation and coupling to pair vibrations within the self-consistent quasiparticle random-phase approximation. The numerical calculations are performed for the pairing gap, total energy, heat capacity, entropy, and microcanonical temperature within the doubly-folded equidistant multilevel pairing model. The FTLN1+SCQRPA predictions agree best with the exact grand-canonical results. In general, all approaches clearly show that the superfluid-normal phase transition is smoothed out in finite systems. A novel formula is suggested for extracting the empirical pairing gap in reasonable agreement with the exact canonical results.

arXiv comment25 pages, 4 figures. accepted for publication in Phys. Rev. C

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• On the importance of using exact pairing in the study of pygmy dipole resonance
• Possible existence of pygmy dipole resonance built on excited states in a neutron-rich ${}^{80}$Ge nucleus
• Re-investigation of heat capacity and paring phase transition in hot ${}^{93-98}$Mo nuclei
• Exact nuclear pairing solution for large-scale configurations: I. The EP (v1.0) program at zero temperature
• Thermal nuclear pairing within the self-consistent quasiparticle RPA