Pairing transitions in finite-temperature relativistic Hartree-Bogoliubov theory

Abstract

We formulate the finite-temperature relativistic Hartree-Bogoliubov theory for spherical nuclei based on a point-coupling functional, with the Gogny or separable pairing force. Using the functional PC-PK1, the framework is applied to the study of pairing transitions in Ca, Ni, Sn, and Pb isotopic chains. The separable pairing force reproduces the gaps calculated with the Gogny force not only at zero temperature, but also at finite temperatures. By performing a systematic calculation of the even-even Ca, Ni, Sn, and Pb isotopes, it is found that the critical temperature for a pairing transition generally follows the rule T c = 0.6∆ n (0), where ∆ n (0) is the neutron pairing gap at zero temperature. This rule is further verified by adjusting the pairing gap at zero temperature with a strength parameter.

Shape transition with temperature of the pear-shaped nuclei in covariant density functional theory

“…2(c), the neutron pairing gap at zero temperature is ∆ n (0) = 0.63 MeV, and it decreases to zero at a critical temperature T c = 0.40MeV, which shows a pairing phase transition. The critical temperature for the pairing phase transition in the case of deformed nuclei basically follows the rule T c = 0.6∆ n (0), which was discovered for spherical nuclei [32]. Since the global minimum deformation for T T c changes little, as seen in Fig.…”

“…The RMF theory, which has achieved great success in describing ground-state properties of both spherical and deformed nuclei all over the nuclear chart [29][30][31], is also applied to study the shape evolution and phase transitions with temperature. The finite-temperature relativistic Hartree-Bogoliubov theory [32] and relativistic Hartree-Fock-Bogoliubov theory [33] for spherical nuclei are formulated, and used to study the pairing transitions in hot nuclei. The relativistic Hartree-BCS theory is applied to study the temperature dependence of shapes and pairing gaps for 166,170 Er and rareearth nuclei [34,35].…”

Pairing properties and specific heat of the inner crust of a neutron star

“…Within the standard BCS theory [14,15], one can see that the superfluid phase disappears beyond a certain value of the temperature of the system, Tc, since Cooper pairs are broken due to thermal fluctuations. For an homogenous system, the critical temperature can be related to the pairing gap at zero temperature, A^o , as [16] «M>.57Ar=0, [17][18][19]. In the region between the outer and the inner crust, the evolution of the pairing gap with temperature is much richer then predicted by the simple BCS theory.…”

Multipole excitations in hot nuclei within the finite temperature quasiparticle random phase approximation framework

“…In this work, the critical temperature values are calculated using the FT-HFBCS method: T c = 0.96 and 0.84 MeV for 68 Ni and 120 Sn nuclei, respectively. The value of the neutron pairing gap at zero temperature and the critical temperature generally follow the T c ≈ 0.57 T =0 empirical rule, as expected [37,38,46,47]. It should be noted that the use of the grand-canonical description leads to sharp phase transitions in nuclei within our model calculations.…”