Many-body correlations in nuclear superfluidity

TL;DR

This paper develops a Dyson-Bethe-Salpeter equation framework to analyze many-body correlations in nuclear superfluidity, focusing on pairing interactions and collective excitations without introducing new parameters.

Contribution

It introduces a novel approach to derive and truncate the equation of motion for two-fermion propagators, incorporating collective modes in nuclear pairing calculations.

Findings

Calculated pairing gaps in medium-mass nuclei like calcium, nickel, and tin.

Established a parameter-free method linking fermionic correlations to bosonic collective modes.

Demonstrated the importance of many-body correlations in nuclear superfluidity.

Abstract

The two-fermion two-point correlation function in the pairing channel is discussed in 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 a static and a one frequency dependent components and, thus, can be regarded as Dyson Bethe-Salpeter 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 collective modes of excitation. The latter couplings are, thus, derived in terms of the exact mapping of the in-medium two-fermion correlation functions onto the domain of bosonic quasibound states (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.