Universality of a two-component Fermi gas with a resonant interaction

We consider a two-component Fermi gas interacting via a Feshbach molecular state. It is shown that only for broad resonances where the Feshbach state is strongly coupled to the free particle continuum can the gas be expected to enter a universal state in the unitarity limit on the atomic side of the resonance where there are no molecules present. The universal state is distinct from the molecular gas state on the other side of the resonance. We furthermore calculate the energy of the gas for this universal state and our results are related to current experiments on ${}^6\mathrm{Li}$ and ${}^{40}\mathrm{K}$.