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

## TL;DR

This paper investigates the BCS-BEC crossover in a two-fermion system with finite-range interactions, analyzing thermodynamics and pair functions to understand the transition from non-universal to universal behavior.

## Contribution

It introduces a mean field analysis of the BCS-BEC crossover for finite-range potentials, identifying variables that capture the transition and characterizing pair functions across the crossover.

## Key findings

- Transition occurs between scattering resonance and sign change of chemical potential.
- Pair functions become exponentially localized in BEC and oscillatory in BCS regimes.
- Finite-range interactions influence the universality of the crossover.

## Abstract

We analyze the BCS-BEC crossover transition of a balanced two component mixture of fermions interacting via a finite range potential, within a mean field approach. For the analysis we consider three finite range potentials cases describing the interaction between different Fermi species: a square well, an exponential and a Yukawa potential. The T = 0 thermodynamics analysis along the BCS-BEC crossover allow us to recognize the proper variables, for finite range interactions, that capture the transition from a thermodynamic non-universal behavior at unitarity, to its universal restoration. On the other side, the determination of the pair functions along the crossover suggests that the smooth transition occurs always between the scattering resonance and the change of sign of the chemical potential. This identification follows directly from the pair wave functions behavior, which in the BCS and BEC sides become exponentially localized and oscillatory slowly decaying respectively.