Many-body correlations in nuclear superfluidity

The two-fermion two-time correlation function in the pairing channel is discussed within the equation of motion framework. Starting from the bare two-fermion interaction, we derive the equation of motion for the two-fermion pair propagator in a strongly correlated medium. The resulting equation is of the Dyson type with the kernel having static and one-frequency dependent components and, thus, can be regarded as a Dyson BetheSalpeter equation (Dyson-BSE). The many-body hierarchy generated by the dynamical interaction kernel is truncated on the level of two-body correlation functions, thus neglecting the explicit three-body and higher rank correlations. The truncation is performed via a cluster expansion of the intermediate three-particle-one hole correlation function irreducible in the particle-particle channel, that leads to the coupling between single fermions and emergent bosonic quasibound states (phonons). The latter couplings are, thus, derived in terms of the exact mapping of the in-medium two-fermion correlation functions onto the domain of phonons without introducing new parameters. The approach is applied to calculations of the pairing gaps in medium-mass nuclear systems, that include calcium, nickel and tin isotopic chains.