A self-consistent theory is derived to describe the BCS--Bose-Einstein-condensate crossover for a strongly interacting Fermi gas with a Feshbach resonance. In the theory the fluctuation of the dressed molecules, consisting of both preformed Cooper pairs and ``bare'' Feshbach molecules, has been included within a self-consistent
T-matrix approximation, beyond the Nozi\`eres and Schmitt-Rink strategy considered by Ohashi and Griffin. The resulting self-consistent equations are solved numerically to investigate the normal-state properties of the crossover at various resonance widths. It is found that the superfluid transition temperature
Tc increases monotonically at all widths as the effective interaction between atoms becomes more attractive. Furthermore, a residue factor
Zm of the molecule's Green function and a complex effective mass have been determined to characterize the fraction and lifetime of Feshbach molecules at
Tc. Our many-body calculations of
Zm agree qualitatively well with recent measurments of the gas of
6Li atoms near the broad resonance at
834G. The crossover from narrow to broad resonances has also been studied.
Experiments on ultra-cold fermionic /sup 6/Li confined in a crossed dipole trap. /sup 6/Li possesses Feshbach resonances both in the s-wave and p-wave channels. This features enables the exploration of both s-wave and p-wave pairing mechanisms. We first discuss our observation of Bose-Einstein condensation of /sup 6/Li/sub 2/ molecules in the low-magnetic field wing the s-wave Feshbach located at /spl sim/ 834 G. The molecular BEC offers a good starting point for the exploration of the BEC-BCS (Bardeen-Cooper-Schrieffer) crossover. We have also located p-wave Feshbach resonances in the two lowest hyperfine states of /sup 6/Li. The experimental positions of these resonances are in good agreement with those predicted by coupled channel calculations. We have studied the atom losses close to these resonances and have developed a semi-analytical model capturing our experimental findings.