Nonuniversal behavior of cold Fermi condensates with narrow Feshbach resonances

In this paper, we construct an effective field theory for a condensate of cold Fermi atoms whose scattering is controlled by a narrow Feshbach resonance. We show how, from first principles, it permits a hydrodynamic description of the BEC-BCS crossover from which the equation of state, intimately related to the speed of sound, can be derived. Specifically, we stress the nonuniversal behavior of the equation of state at the unitary limit of infinite scattering length that arises when either, or both, of the range of the interatomic force and the scale of the molecular field become large.