  We use the standard fermionic and boson-fermion Hamiltonians to study the
BCS-BEC cross-over near the 202 G resonance in a two-component mixture of
fermionic 40K atoms employed in the experiment of C.A. Regal et al., Phys. Rev.
Lett. 92, 040403 (2004). Our mean-field analysis of many-body equilibrium
quantities shows virtually no differences between the predictions of the two
approaches, provided they are both implemented in a manner that properly
includes the effect of the highest excited bound state of the background
scattering potential, rather than just the magnetic-field dependence of the
scattering length. Consequently, we rule out the macroscopic occupation of the
molecular field as a mechanism behind the fermionic pair condensation and show
that the BCS-BEC cross-over in ultra-cold 40K gases can be analysed and
understood on the same basis as in the conventional systems of solid state
physics.
