Pairing phase transition: A finite-temperature relativistic Hartree-Fock-Bogoliubov study

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 behavior for large spatial distributions. Results: Systematic FT-RH(F)B calculations are performed for several semimagic 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 Tc = 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 analyzed: 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 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.