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 omega(c) originating from the finite molecular binding energy is the key to understanding the interaction between molecules in the BEC regime. Our work thus clarifies 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 omega(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 as results of Bijlsma and Stoof.