The contact in the BCS–BEC crossover for finite range interacting ultracold Fermi gases

• We consider a degenerate Fermi gas with finite range many-body interaction.
• We use the BCS ansatz beyond the contact approximation.
• We calculate thermodynamic variables and Tanʼs Contact.
• We have an energy-dependent gap.
• The finite range is a precursor to quantum phase transition-like behaviour.

Using mean-field theory for the Bardeen–Cooper–Schriefer (BCS) to the Bose–Einstein condensate (BEC) crossover we investigate the ground state thermodynamic properties of an interacting homogeneous Fermi gas. The interatomic interactions modelled through a finite range potential allows us to calculate the thermodynamic behaviour as a function of the potential parameters in the whole crossover region. We concentrate in studying the Contact variable, the thermodynamic conjugate of the inverse of the s-wave scattering length. Our analysis leads to predict a quantum phase transition – like in the case of large potential range. This finding is a direct consequence of the k-dependent energy gap.

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