  We consider interacting Fermi systems close to the unitary regime and compute
the corrections to the energy density that are due to a large scattering length
and a small effective range. Our approach exploits the universality of the
density functional and determines the corrections from the analyical results
for the harmonically trapped two-body system. The corrections due to the finite
scattering length compare well with the result of Monte Carlo simulations. We
also apply our results to symmetric neutron matter.
