Pairing phase transition: A Finite-Temperature Relativistic Hartree-Fock-Bogoliubov study

TL;DR

This study develops the finite-temperature relativistic Hartree-Fock-Bogoliubov (FT-RHFB) theory to explore phase transitions and pairing correlations in nuclei, revealing new phenomena like pairing re-entrance and persistence.

Contribution

First implementation of FT-RHFB theory providing insights into thermal effects on nuclear pairing and phase transitions in finite nuclei.

Findings

Critical temperature follows a linear relation with zero-temperature pairing gap.

Identified two types of pairing persistence: in closed subshell and loosely bound nuclei.

Observed pairing re-entrance phenomena at finite temperature.

Abstract

Background: The relativistic Hartree-Fock-Bogoliubov (RHFB) theory has recently been developed and it provides a unified and highly predictive description of both nuclear mean field and pairing correlations. Ground state properties of finite nuclei can accurately be reproduced without neglecting exchange (Fock) contributions. Purpose: Finite-temperature RHFB (FT-RHFB) theory has not yet been developed, leaving yet unknown its predictions for phase transitions and thermal excitations in both stable and weakly bound nuclei. Method: FT-RHFB equations are solved in a Dirac Woods-Saxon (DWS) basis considering two kinds of pairing interactions: finite or zero range. Such a model is appropriate for describing stable as well as loosely bound nuclei since the basis states have correct asymptotic behaviour for large spatial distributions. Results: Systematic FT-RH(F)B calculations are performed for several semi-magic isotopic/isotonic chains comparing the predictions of a large number of Lagrangians, among which are PKA1, PKO1 and DD-ME2. It is found that the critical temperature for a pairing transition generally follows the rule $T_c = 0.60\Delta(0)$ for a finite-range pairing force and $T_c = 0.57\Delta(0)$ for a contact pairing force, where $\Delta(0)$ is the pairing gap at zero temperature. Two types of pairing persistence are analysed: type I pairing persistence occurs in closed subshell nuclei while type II pairing persistence can occur in loosely bound nuclei strongly coupled to the continuum states. Conclusions: This first FT-RHFB calculation shows very interesting features of the pairing correlations at finite temperature and in finite systems such as pairing re-entrance and pairing persistence.