Effective interaction between molecules in the strong-coupling BEC regime of a superfluid fermi gas

We investigate the effective interaction between Cooper-pair molecules in the strong-coupling BEC regime of a superfluid Fermi gas with a Feshbach resonance. Our work uses a path integral formulation and a renormalization group (RG) analysis of fluctuations in a single-channel model. We show that a physical cutoff energy ω_c originating from the finite molecular binding energy is the key to understanding the interaction between molecules in the BEC regime. Our work thus clari.es recent results by showing that a _M = 2a_F is a bare molecular scattering length while a _M = (0.6-0.75)a_F is the low-energy molecular scattering length renormalized to include high-energy scattering up to ω_c (here, a_F is the scattering length between Fermi atoms). We also include many-body effects at finite temperatures. We find that a_M is strongly dependent on temperature, vanishing at T_c, consistent with the earlier Bose gas results of Bijlsma and Stoof.