The interaction-sensitive states of a trapped two-component ideal Fermi gas and application to the virial expansion of the unitary Fermi gas

TL;DR

This paper analyzes the eigenstates of a two-component ideal Fermi gas in a harmonic trap, identifying interaction-sensitive states and proposing a new conjecture for the virial coefficient of the unitary Fermi gas, supported by numerical comparisons.

Contribution

It introduces a method to determine interaction-sensitive eigenstates using a Faddeev ansatz and proposes a new conjecture for the fourth-order virial coefficient.

Findings

Identification of interaction-sensitive eigenstates using Faddeev ansatz.

A new conjecture for the fourth-order virial coefficient of the unitary Fermi gas.

Good agreement with existing numerical results.

Abstract

We consider a two-component ideal Fermi gas in an isotropic harmonic potential. Some eigenstates have a wavefunction that vanishes when two distinguishable fermions are at the same location, and would be unaffected by s-wave contact interactions between the two components. We determine the other, interaction-sensitive eigenstates, using a Faddeev ansatz. This problem is nontrivial, due to degeneracies and to the existence of unphysical Faddeev solutions. As an application we present a new conjecture for the fourth-order cluster or virial coefficient of the unitary Fermi gas, in good agreement with the numerical results of Blume and coworkers.