BCS superfluidity in ultracold gases with unequal atomic populations

We consider the existence of a BCS superfluid phase in ${}^6$Li due to the pairing of two hyperfine states with unequal number of atoms. We show that the domain of existence for this phase will be increased to a very large extent in the vicinity of the threshold for collapse. This is due to the presence of a new phase with anisotropic order parameter. This phase is induced by the anisotropic part of the scattering, linked to the indirect interaction between atoms through density fluctuation exchange.