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A self-consistent theory is derived to describe the BCS-BEC crossover for astrongly interacting Fermi gas with a Feshbach resonance. In the theory thefluctuation of the dressed molecules, consisting of both preformed Cooper-pairsand ``bare'' Feshbach molecules, has been included within a self-consistent$T$-matrix approximation, beyond the Nozi\`{e}res and Schmitt-Rink strategyconsidered by Ohashi and Griffin. The resulting self-consistent equations aresolved numerically to investigate the normal state properties of the crossoverat various resonance widths. It is found that the superfluid transitiontemperature $T_c$ increases monotonically at all widths as the effectiveinteraction between atoms becomes more attractive. Furthermore, a residuefactor $Z_m$ of the molecule's Green function and a complex effective mass havebeen determined, to characterize the fraction and lifetime of Feshbachmolecules at $T_c$. Our many-body calculations of $Z_m$ agree qualitativelywell with the recent measurments on the gas of $^6$Li atoms near the broadresonance at 834 Gauss. The crossover from narrow to broad resonances has alsobeen studied.Comment: 6 papes, 6 figure

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