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

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 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 T_c increases monotonically at all widths as the effective interaction between atoms becomes more attractive. Furthermore, a residue factor Z_m of the molecule’s Green function and a complex effective mass have been determined to characterize the fraction and lifetime of Feshbach molecules at T_c. Our many-body calculations of Z_m agree qualitatively well with recent measurments of the gas of ⁶Li atoms near the broad resonance at 834 G. The crossover from narrow to broad resonances has also been studied.