Generalized Galitskii approach for the vertex function of a Fermi gas with resonant interaction

TL;DR

This paper extends the Galitskii approach to derive the two-particle vertex function for a resonantly interacting Fermi gas, justifying the extrapolation of weakly attractive results into strong coupling and repulsive regimes.

Contribution

It introduces a generalized method for the Bethe-Salpeter equation that accounts for resonant states in Fermi gases, applicable to both normal and condensate phases.

Findings

Vertex function near resonance matches that of weakly attractive Fermi gases.

Supports extrapolation of weak coupling results to strong coupling and repulsive regimes.

Provides a unified framework for resonant Fermi systems.

Abstract

We present a generalized Galitskii approach for the Bethe-Salpeter equation for the two-particle vertex function of a Fermi system with resonant interaction by accounting for the resonant state in the scattering potential and utilizing the universal form of the resonant scattering amplitude. The procedure can be carried out both for the normal as well as for the condensate state. In both cases, the vertex function in the vicinity of the resonance is shown to formally coincide with that obtained for a weakly attractive Fermi gas. Thus we justify the popular calculational framework in which results for the weakly attractive Fermi gas are formally extrapolated into the domain of strong coupling, and further to the repulsive side of the resonance, where molecular states are formed.