Why only half of the fermionic atoms were converted to molecules by a Feshbach resonance?

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In some recent experiments an ultracold gas of ⁴⁰K₂ (or ⁶Li₂) molecules has been produced from a degenerate two-component Fermi gas of ⁴⁰K (or ⁶Li) atoms by adiabatic passage through a Feshbach resonance. The maximum atom-molecule transfer efficiency is reported to be about 50%. We propose a simple microscopic model to characterize the ground state of the gas in the vicinity of the resonance, and show that the term describing the atom-molecule coupling is responsible for the observed efficiency 50%. Our result also suggests that the experiments have produced a molecular condensate.