  We present a consistent nonequilibrium theory for the production of molecular
dimers from a two-component quantum-degenerate fermion atomic gas, via a linear
downward sweep of the magnetic field across a Feshbach resonance. This problem
raises interest because it is presently unclear as to why deviations from the
universal Landau-Zener formula for the transition probability at two-level
crossing are observed in the experimentally measured production efficiencies.
We show that the molecular conversion efficiency is represented by a power
series in terms of a dimensionless parameter which, in the zero-temperature
limit, depends solely on the initial gas density and the Landau-Zener
parameter. Our result reveals a hindrance of the canonical Landau-Zener
transition probability due to many-body effects, and presents an explanation
for the experimentally observed deviations [K.E. Strecker \textit{et al.},
Phys. Rev. Lett. {\bf 91}, 080406 (2003)].
