  We investigate the effect of optical lattices on the BCS superfluidity by
using the Gorkov--Melik-Barkhudarov (GMB) correction for a two-component Fermi
gas. We find that the suppression of the order parameter is strongly enhanced
by the lattice effects. The predictions made by the GMB corrections are in
qualitative and, for the cases studied, quantitative agreement with previous
quantum Monte Carlo results. We discuss how the GMB correction extends the
validity of the mean-field theory to a wider range of tunable optical lattice
systems in different dimensions.
