The third virial coefficient of a two-component unitary Fermi gas across an Efimov-effect threshold

TL;DR

This paper analytically calculates the third virial coefficient of a two-component unitary Fermi gas, revealing its smooth dependence on the mass ratio across the Efimov-effect threshold, with the three-body parameter playing a crucial role.

Contribution

It provides an analytical determination of the third cluster coefficient across the Efimov threshold, highlighting the relevance of the three-body parameter even outside the Efimov regime.

Findings

The third virial coefficient is a smooth function of the mass ratio across the Efimov threshold.

The three-body parameter influences the coefficient even in the non-Efimovian regime.

Analytical expression derived for the third cluster coefficient.

Abstract

We consider a mixture of two single-spin-state fermions with an interaction of negligible range and infinite $s$-wave scattering length. By varying the mass ratio $\alpha$ across $\alpha_c\simeq 13.6069$ one can switch on-and-off the Efimov effect. We determine analytically the third cluster coefficient of the gas. We show that it is a smooth function of $\alpha$ across $\alpha_c$ since, unexpectedly, the three-body parameter characterizing the interaction is relevant even on the non-Efimovian side $\alpha<\alpha_c$.