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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.