Pairing of Fermions with Arbitrary Spin

Motivated by the recent success of optical trapping of alkali Bose condensate, we have studied the superfluid state of optically trapped alkali fermions, which can have Cooper pairs with total spin $J\ge 2$. In this paper, we shall discuss the general structure of these large spin Cooper pairs and their close relation with singlet Cooper pairs with nonzero orbital angular momentum. We also present the exact solution for the $J=2\mathrm{}$ pairing which shows a surprising change of ground state as the spin $f$ of the constituent fermion increases.