Scattering between fermion pairs in the BEC/BCS crossover

We investigate how the interactions between correlated pairs of fermions in a superfluid Fermi gas are related to the atom-atom interactions in this gas. To obtain an expression linking the pair-pair scattering length apair to the atom-atom scattering length as, a Landau-Ginzburg expansion of the free energy with respect to the order parameter is performed and the resulting interaction energy is identified with a contact interaction between pairs. We find that apair/as derived in this way is strongly influenced by many-body effects and is not constant throughout the BEC/BCS transition. This result is related to the behaviour of the Landau-Ginzburg parameters in conventional BCS superconductors. The effect of fluctuations of the order parameter on the pair-pair scattering length are discussed