Abstract
We consider the existence of a BCS superfluid phase in 6Li 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 instability. 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.