  We consider a two-component Fermi gas interacting via a Feshbach molecular
state. It is shown that an important energy scale is $E_g=g^4m^3/(64\pi^2)$
where $g$ is the Feshbach coupling constant and $m$ the mass of the particles.
  Only when $E_g\gg \epsilon_{\rm F}$ where $\epsilon_{\rm F}$ is the Fermi
energy 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 $^{6}$Li
and $^{40}$K.
