  We discuss the BCS-BEC crossover in a degenerate Fermi gas of two hyperfine
states interacting close to a Feshbach resonance. This system has
quasi-molecular Bosons associated with a Feshbach resonance, and this kinds of
coupled Boson-Fermion model has been recently applied to Fermi atomic gases
within a mean-field approximation. We show that by including fluctuation
contribution to the free energy similar to that condiered by Nozi'eres and
Schmitt-Rink, the character of the superfluid phase transition continuously
changes from the BCS-type to the BEC-type, as the threshold of the
quasi-molecular band is lowered. In the BEC regime, the quasi-molecules become
stable long-lived composite Bosons, and an effective pairing interaction
mediated by the molecules causes pre-formed Cooper-pairs to also be stable even
above the transition temperature Tc. The superfluid phase transition is shown
to be usefully interpreted as the Bose condensation of these two kinds of
Bosons. The maximum Tc is given by (in terms of the Fermi temperature T_F)
Tc=0.218T_F (uniform gas) and Tc=0.518T_F (trapped gas in a harmonic
potential).
