Temperature-dependent isovector pairing gap equations using a path integral approach

Abstract

Temperature-dependent isovector neutron-proton $(\mathit{np})$ 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 ${\ensuremath{\Delta}}_{\mathit{np}}$ has a behavior analogous to that of ${\ensuremath{\Delta}}_{\mathit{nn}}$ and ${\ensuremath{\Delta}}_{\mathit{pp}}$ 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.