  We develop a theoretical method going beyond the contact-interaction
approximation frequently used in mean-field theories of many-fermion systems,
based on the low-energy T-matrix of the pair potential to rigorously define the
effective radius of the interaction. One of the main consequences of our
approach is the possibility to investigate finite-density effects, which are
outside the range of validity of approximations based on delta-like potentials.
We apply our method to the calculation of density dependent properties of an
ultracold gas of 6Li atoms at unitarity, whose two-body interaction potential
is calculated using ab initio quantum chemistry methods. We find that density
effects will be significant in ultracold gases with densities one order of
magnitude higher than those attained in current experiments.
