A self-consistent theory of atomic Fermi gases with a Feshbach resonance at the superfluid transition

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A self-consistent theory is derived to describe the BCS-BEC 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 Nozières 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 the recent measurments on the gas of ⁶Li atoms near the broad resonance at 834 Gauss. The crossover from narrow to broad resonances has also been studied.