Feshbach resonance described by the boson fermion coupling

We consider a possibility to describe the Feshbach resonance in terms of the Boson Fermion (BF) model. Using such model we show that after a gradual disentangling of the boson from fermion subsystem the resonant type scattering between fermions is indeed generated. We decouple the subsystems via: (a) the single step, and (b) the continuous canonical transformation. With the second one we investigate the feedback effects effectively leading to the finite amplitude of the scattering strength. We study them in detail in: the normal $T>T_{c}$ and superconducting $T \leq T_{c}$ states.