Renormalized mean-field theory for a two-component Fermi gas with s-wave interactions

A method is introduced to renormalize the zero-range interaction for use in mean-field and many-body theory, starting from two-body calculations. The density-renormalized delta-function interaction is then applied using mean-field theory to a two-component fermion gas, and compared with diffusion Monte Carlo simulations and conventional mean-field calculations. In the unitarity limit, the equation of state exhibits the expected behavior $\mu\propto\rho^{2/3}$, with a parameter $\beta= -0.492$, which is consistent with recent experiments \cite{partridge2006pap, bourdel2004esb, kinast2005hcs, Stewart06}.