Temperature Effect on Nuclear Statistical Quantities in the Case of Pure Isoscalar Neutron-Proton Pairing

Gap equations at finite temperature are deduced in the pure isoscalar pairing case (T=0). Expressions of the nuclear statistical quantities, i.e. the energy, the entropy and the heat capacity are deduced. A numerical study is then performed using the schematic one-level model. It is found that the behavior of the isoscalar neutron-proton gap parameter ∆T =0np as a function of the temperature is similar to that of ∆pp and ∆nn in the conventional Finite Temperature BCS (FTBCS) approach. The presence of a critical temperature value beyond which ∆T =0np is null is noted. Dealing with the nuclear statistical quantities, their behavior as a function of the temperature is similar to that obtained using the conventional FTBCS theory in the pairing between like-particles case. An increase in the energy value is noted compared with other types of pairing.