2 0 Ju l 2 00 5 Conventional character of the BCS-BEC cross-over in ultracold gases of 40 K

We use the standard fermionic and boson-fermion Hamiltonia ns 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 equil ibrium quantities shows virtually no differences between the predictions of the two approaches, prov ided they are both implemented in a manner that properly includes the e ffect of the highest excited bound state of the background scat tering potential, rather than just the magnetic-field dependence o f the scattering length. Consequently, we rule out the macroscopic occupation of the molecular field as a mechan ism 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.