  The problem of molecular production from degenerate gas of fermions at a wide
Feshbach resonance, in a single-mode approximation, is reduced to the linear
Landau-Zener problem for operators. The strong interaction leads to significant
renormalization of the gap between adiabatic levels. In contrast to static
problem the close vicinity of exact resonance does not play substantial role.
Two main physical results of our theory is the high sensitivity of molecular
production to the initial value of magnetic field and generation of a large BCS
condensate distributed over a broad range of momenta in inverse process of the
molecule dissociation.
