An Effective Series Expansion to the Equation of State of Unitary Fermi Gases

TL;DR

The paper introduces a new series expansion-based analytical equation of state for unitary Fermi gases, achieving improved agreement with experimental data and theoretical calculations across a wide temperature range.

Contribution

It presents a novel series solution approach to the equation of state, incorporating known virial coefficients and the Bertsch parameter, enhancing accuracy over existing models.

Findings

Accurately describes the equation of state up to fugacity z=18

Estimates the Bertsch parameter as 0.35, close to experimental value 0.37

Shows good agreement with T-matrix calculations in the normal phase

Abstract

Using universal properties and a basic statistical mechanical approach, we propose a general equation of state for unitary Fermi gases. The universal equation of state is written as a series solution to a self consistent integral equation where the general solution is a linear combination of Fermi functions. First, by truncating our series solution to four terms with already known exact theoretical inputs at limiting cases, namely the first \emph{three} virial coefficients and using the Bertsch parameter as a free parameter, we find a good agreement with experimental measurements in the entire temperature region in the normal state. This analytical equation of state agrees with experimental data up to the fugacity $z = 18$, which is a vast improvement over the other analytical equations of state available where the agreements is \emph{only} up to $z \approx 7$. Second, by truncating our series solution to four terms again using first \emph{four} virial coefficients, we find the Bertsch parameter $\xi =0.35$, which is in good agreement with the direct experimental measurement of $\xi =0.37$. This second form of equation of state shows a good agreement with self-consistent T-matrix calculations in the normal phase.