  We investigate the ground state properties of a disordered superfluid Fermi
gas across the BCS-BEC (Bose Einstein condensate) crossover. We show that, for
weak disorder, both the depletion of the condensate fraction of pairs and the
normal fluid density exhibit a nonmonotonic behavior as a function of the
interaction parameter $1/k_Fa$, reaching their minimum value near unitarity. We
find that, moving away from the weak coupling BCS regime, Anderson's theorem
ceases to apply and the superfluid order parameter is more and more affected by
the random potential.
