We provide a practical approach to the molecular production via linear downward sweeps of Feshbach resonances in degenerate Fermi gases containing incoherent mixtures of two atomic spin states. We show that the efficiency of the association of atoms is determined just by the Landau-Zener parameter in addition to the density of the gas. Our approach of pairwise summation of the microscopic binary transition probabilities leads to an intuitive explanation for the observed saturation of the molecular production and recovers all atomic loss curves of Regal et al. [Nature (London) 427, 47 (2003))]] as well as Strecker et al. [Phys. Rev. Lett. 91, 080406 (2003))]] without adjustable parameters.
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