Fermion superfluids of non-zero orbital angular momentum near resonance

The BEC-BCS crossover of fermion superfluids with near-resonance $s$-wave interactions has been extensively studied in the past year. We extend these studies to the pairing of Fermi gases near the scattering resonance of the $\ell\neq 0$ partial wave at $T=0$. Using a model potential which reproduces the actual two-body low energy scattering amplitude, we have obtained an analytic solution of the gap equation. We show that the ground state of $\ell=1$ and $\ell=3$ superfluids are orbital ferromagnets with pairing wavefunctions $Y_{11}$ and $Y_{32}$ respectively. For $\ell=2$, there is a degeneracy between $Y_{22}$ and a ``cyclic state".