Pairing and molecule formation along the BCS-BEC crossover for finite range potentials

We address the thermodynamics of the zero temperature BCS-BEC crossover of a balanced two component mixture of a finite range interacting fermions within a mean field approach. For the analysis we consider two wide types of finite range potentials describing the interaction between different Fermi species: purely attractive, as the square well, the exponential and the Yukawa potentials, and others having both a repulsive wall at the origin as well as a finite attractive tail, as Van der Waals and dipolar potentials. We study the energy gap, the chemical potential and the pressure as functions of the scattering length for all the interacting potentials considered. The system spatial structure is further analyzed via the the pair functions associated to each potential. We find that for those with pure attractive contributions the crossover can be recognized either, when the chemical potential changes its sign or when the scattering length diverges. In contrast, the pair functions linked to potentials with both repulsive and attractive terms, show wide crossover regions without sharp distinctions at the sign change of the chemical potential nor at unitarity.