Nuclear superfluidity at finite temperature

The equation of motion for the two-fermion two-time correlation function in pairing channel is considered at finite temperature. Within Matsubara formalism, Dyson-type Bethe-Salpeter (Dyson-BSE) with frequency-dependent interaction kernel obtained. Similarly to case zero temperature, it decomposed into static and dynamical components, where former given by contraction bare density latter represented double four-fermion function, or propagator, two matrix elements. four-body being formally exact, requires approximations avoid generating prohibitively complicated hierarchy equations. We focus on approximation truncated level two-body functions, neglecting irreducible three-body higher-rank correlations. Such a truncation leads coupling between correlated fermionic pairs, which can be interpreted as emergent bosonic quasibound states, phonons, normal superfluid nature. ones are, thus, mediators pairing. In this framework, we obtained closed system equations particle-hole particle-particle propagators. This allows us study temperature dependence gap beyond Bardeen-Cooper-Schrieffer that implemented medium-heavy nuclear systems. cases $^{68}\mathrm{Ni}$ $^{44,46}\mathrm{Ca}$ are discussed detail.