Finite-temperature Hartree-Fock-Bogoliubov theory using Skyrme interactions and Relativistic Hartree-Fock effective Lagrangians, predicts 48 Ni as being a possible candidate for the finite temperature pairing re-entrance phenomenon. For this proton-drip-line nucleus, proton resonant states are expected to contribute substantially to pairing correlations and the two predicted critical temperatures are T c1 ∼ 0.08 − 0.2 MeV and T c2 ∼ 0.7 − 0.9 MeV. It is also shown that pairing re-entrance modifies the proton single particle energies around the Fermi level, as well as occupation numbers, and quasi-particle levels. The understanding of pairing re-entrance in 48 Ni presently challenge our understanding of exotic matter under extreme conditions.

Expressions of temperature-dependent perpendicular (ℑ⊥) and parallel (ℑ‖) moments of inertia, including isovector pairing effects, have been established using the cranking method. They are derived from recently proposed temperature-dependent gap equations. The obtained expressions generalize the conventional finite-temperature BCS (FTBCS) ones. Numerical calculations have been carried out within the framework of the schematic Richardson model as well as for nuclei such as N = Z, using the single-particle energies and eigenstates of a deformed Woods–Saxon mean-field. ℑ⊥ and ℑ‖ have been studied as a function of the temperature. It has been shown that the isovector pairing effect on both the perpendicular and parallel moments of inertia is non-negligible at finite temperature. These correlations must thus be taking into account in studies of warm rotating nuclei in the N ≃ Z region.

Temperature-dependent isovector neutron-proton (np) pairing gap equations have been established by means of the path integral approach. These equations generalize the BCS ones for the pairing between like particles at finite temperature. The method has been numerically tested using the one-level model. It has been shown that the gap parameter np has a behavior analogous to that of nn and pp as a function of the temperature: one notes the presence of a critical temperature. Moreover, it has been shown that the isovector pairing effects remain beyond the critical temperature that corresponds to the pairing between like particles.

The influence of the isovector neutron–proton (np) pairing effect on nuclear statistical quantities is studied in N ≈ Z even–even systems. Expressions of the energy, the entropy, and the heat capacity are established using a recently proposed temperature-dependent isovector pairing gap equations. They generalize the conventional finite temperature BCS (FTBCS) ones. The model is first numerically tested using the schematic one-level model. As a second step, realistic cases are considered using the single-particle energies of a deformed Woods–Saxon mean-field. It is shown that: (i) the gap parameter Δnp(T) behaves like Δtt(T), t = n, p, in the conventional FTBCS model and the critical temperature value Tcnp is such as Tcnp<Tcp<Tcn; (ii) the behavior of Δtt(T), t = n, p in the present model is different from that of the FTBCS one. This fact leads to a systematic discrepancy between the predictions of both models in the Tcnp<T<Tcn region for all studied statistical quantities; and (iii) in the 0≤T≤Tcnp region, the np pairing effect on the energy is a lowering of about 1%, on average, for all considered nuclei. Dealing with the entropy and the heat capacity, the np pairing effect appears only if the Tcnp value is sufficiently important.

Higher-order approximation based on Taylor expansion over the saddle point is employed to approach the partition function of a hot nucleus in the presence of the like-particle pairing correlations. Analytical expressions have been derived for the correction terms of different thermodynamic quantities such as energy, entropy and heat capacity. Furthermore, the theory has been applied to the schematic and realistic models. It is found that the correction terms are temperature-dependent functions and are more deeply sensitive to the pairing gap in the vicinity of the critical temperature.

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The nuclear structure and thermal quantities of the superheavy nucleus of [Formula: see text] are studied in a recent developed framework of the Finite-Temperature Hartree–Fock–Bogoliubov (FT-HFB) by using a zero-range pairing and including the continuum effects. Analyzing the shell structure of this nucleus at both zero and finite temperature shows a dependence on the various Skyrme-type forces used and a shell closure occurrence at [Formula: see text] for protons and [Formula: see text] for neutrons with a large gap energy where the pseudo-spin-orbit effects play a primordial role in the shell sequence at finite temperature which confirm the double magicity of [Formula: see text]. Thermodynamic quantities are also studied in the same framework where the results are qualitatively similar to what are obtained in case of the hot ordinary nuclei.

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