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We investigate the effective interaction between Cooper-pair molecules in thest rong-coupling BEC regime of a superfluid Fermi gas with a Feshbachresonance. Our work uses a path integral formulation and a renormalizationgroup (RG) analy sis of fluctuations in a single-channel model. We show that aphysical cutoff en ergy $\omega_c$ originating from the finite molecularbinding energy is the key to understanding the interaction between molecules inthe BEC regime. Our work t hus clarifies recent results by showing that $a_{\rmM}=2a_{\rm F}$ is a {\it ba re} molecular scattering length while $a_{\rmM}=(0.6\sim0.75) a_{\rm F}$ is the low energy molecular scattering lengthrenormalized to include high-energy scat tering up to $\omega_c$ (here $a_{\rmF}$ is the scattering length between Fermi atoms). We also include many-bodyeffects at finite temperatures. We find that $a_{\rm M}$ is strongly dependenton temperature, vanishing at $T_{\rm c}$, consistent with the earlier Bose gasresults of Bijlsma and Stoof.Comment: 10 pages, 3 figure

Effective Interaction between Molecules in the Strong-Coupling BEC Regime of a Superfluid Fermi Gas