  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}.
