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Isovector plus isoscalar neutron–proton pairing effect on nuclear statistical quantities using a path integral approach

Gap equations at finite temperature are established in the isovector plus isoscalar pairing case [Formula: see text] using a path integral approach. Expressions of the various statistical quantities, i.e., the energy, the entropy and the heat capacity are then deduced. It is shown that they do generalize the ones obtained in the pure isovector ([Formula: see text]) pairing case, as well as those obtained within the conventional finite temperature Bardeen–Cooper–Schrieffer (FTBCS) theory in the pairing between like-particles case. A numerical study is then performed using the schematic one-level model. It is shown that the isoscalar n–p gap parameter [Formula: see text] behaves as a function of the temperature, like its homologues [Formula: see text] and [Formula: see text] in the conventional FTBCS approach. As for the three other gap parameters, i.e., [Formula: see text], [Formula: see text] and [Formula: see text], their behaviors are clearly modified when the isoscalar pairing is taken into account. In particular, one observes a shift of the values of the critical temperatures. Dealing with the statistical quantities, the inclusion of the isoscalar pairing, in addition to the isovector one, leads to a lowering of the energy as well as a change of the shapes of the curves of the energy, the entropy and the heat capacity as a function of the temperature.