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We introduce the Global Spin Model to study the static and dynamic propertiesof the ultracold fermionic gas near the broad Feshbach resonance. We show thatthe problem of molecular production, in a single-mode approximation, is reducedto the linear Landau-Zener problem for operators. The strong interaction leadsto significant renormalization of the gap between adiabatic levels. In contrastto static problem the close vicinity of exact resonance does not playsubstantial role. Two main physical results of our theory is the highsensitivity of molecular production to the initial value of magnetic field andgeneration of a large BCS condensate distributed over a broad range of momentain a wide range of parameters. We calculate the amplitude of the condensate asfunction of the initial detuning and the rate of the magnetic field sweep.

Static and Dynamic properties of a Fermi-gas of cooled atoms near a wide Feshbach resonance