An effective series expansion to the equation of state of unitary Fermi gases

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 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 only up to $z\approx 7$. Second, by truncating our series solution to four terms again using first 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. (paper)