Thermodynamics of pairing transition for Odd-A nuclei

TL;DR

This study investigates the thermodynamics of pairing transitions in odd-A nucleus $^{171}$Yb using covariant density functional theory, revealing an S-shaped heat capacity influenced by pairing correlations and single-particle level structure.

Contribution

It introduces a shell-model-like approach with exact particle number conservation to analyze pairing transitions in odd-A nuclei within a covariant density functional framework.

Findings

S-shaped heat capacity observed in $^{171}$Yb and $^{172}$Yb.

Pairing transition affects heat capacity, with odd-A nuclei showing weaker effects.

Single-particle level structure near the Fermi surface influences the heat capacity shape.

Abstract

The hot nucleus $^{171}$Yb is investigated by the covariant density functional theory with the PC-PK1 effective interaction. The thermodynamic quantities are evaluated with the canonical ensemble theory. The pairing correlations is treated by the shell-model-like approach, in which the particle numbers are conserved strictly and in which the blocking effect is handled exactly. An S-shaped heat capacity versus temperature of $^{171}$Yb appears. It has been studied in terms of the blocking effect, the single-particle levels, the pairing gap, and defined seniority components, and compared to the heat capacity of $^{172}$Yb. The pairing transition from the superfluid state to the normal state can result in the S-shaped heat capacity of $^{172}$Yb where the one-pair-broken and two-pair-broken states dominate, while the single-particle level structure near the Fermi surface is associated with the S-shaped heat capacity of $^{171}$Yb. For odd-A nuclei, although the one-pair-broken and two-pair-broken states still contribute, the pairing gap and the pairing transition is relatively weak. The S-shaped heat capacity could be affected due to the blocking of the single-particle level near the Fermi surface.