  In some recent experiments an ultracold gas of $^{40}$K$_2$ (or $^{6}$Li$_2$)
molecules has been produced from a degenerate two-component Fermi gas of
$^{40}$K (or $^{6}$Li) atoms by adiabatic passage through a Feshbach resonance.
The maximum atom-molecule transfer efficiency is reported to be about 50%. We
propose a simple microscopic model to characterize the ground state of the gas
in the vicinity of the resonance, and show that the term describing the
atom-molecule coupling is responsible for the observed efficiency 50%. Our
result also suggests that the experiments have produced a molecular condensate.
