Neutron-proton isovector pairing correlations treatment in heated nuclei within the path integral formalism

Abstract A method for the treatment of the neutron-proton ( np ) isovector pairing correlations at finite temperature is developed within the path integral formalism. It generalizes the recently proposed model using a similar approach for pairing between like-particles. The pairing terms in the total Hamiltonian are expressed in a square form to facilitate the use of the Hubbard-Stratonovitch transformation. The expression for the partition function of the system is then established. The gap equations, as well as the expressions for the energy, entropy, and heat capacity of the system are deduced. In a first step, the formalism is numerically applied to the schematic Richardson model. In a second step, the method is applied to nuclei with using the single-particle energies of a deformed Woods-Saxon mean-field. The variations in the gap parameters, excitation energy, and heat capacity are studied as functions of the temperature. We show that the overall behavior of these quantities is similar to their homologues in the standard FTBCS model. We note in particular the existence of critical temperatures beyond which the pairing vanishes. Moreover, in the framework of the present approach, the pairing effects appear to persist beyond the critical temperatures predicted by the FTBCS model for pairing between like-particles or its generalization for np pairing.