  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.
