We investigate the effective interaction between Cooper-pair molecules in the st rong-coupling BEC regime of a superfluid Fermi gas with a Feshbach resonance. Our work uses a path integral formulation and a renormalization group (RG) analy sis of fluctuations in a single-channel model. We show that a physical cutoff en ergy $ω_c$ originating from the finite molecular binding energy is the key to understanding the interaction between molecules in the BEC regime. Our work t hus clarifies recent results by showing that $a_{\rm M}=2a_{\rm F}$ is a {\it ba re} molecular scattering length while $a_{\rm M}=(0.6\sim0.75) a_{\rm F}$ is the low energy molecular scattering length renormalized to include high-energy scat tering up to $ω_c$ (here $a_{\rm F}$ is the scattering length between Fermi atoms). We also include many-body effects at finite temperatures. We find that $a_{\rm M}$ is strongly dependent on temperature, vanishing at $T_{\rm c}$ , consistent with the earlier Bose gas results of Bijlsma and Stoof.We investigate the effective interaction between Cooper-pair molecules in the st rong-coupling BEC regime of a superfluid Fermi gas with a Feshbach resonance. Our work uses a path integral formulation and a renormalization group (RG) analy sis of fluctuations in a single-channel model. We show that a physical cutoff en ergy $ω_c$ originating from the finite molecular binding energy is the key to understanding the interaction between molecules in the BEC regime. Our work t hus clarifies recent results by showing that $a_{\rm M}=2a_{\rm F}$ is a {\it ba re} molecular scattering length while $a_{\rm M}=(0.6\sim0.75) a_{\rm F}$ is the low energy molecular scattering length renormalized to include high-energy scat tering up to $ω_c$ (here $a_{\rm F}$ is the scattering length between Fermi atoms). We also include many-body effects at finite temperatures. We find that $a_{\rm M}$ is strongly dependent on temperature, vanishing at $T_{\rm c}$, consistent with the earlier Bose gas results of Bijlsma and Stoof.

arXiv:cond-mat/0504123Journal of the Physical Society of JapanOct 1, 200517 citations

ω_c

originating from the finite molecular binding energy is the key to understanding the interaction between molecules in the BEC regime. Our work t hus clarifies recent results by showing that

a_{\rm M}=2a_{\rm F}

is a {\it ba re} molecular scattering length while

a_{\rm M}=(0.6\sim0.75) a_{\rm F}

is the low energy molecular scattering length renormalized to include high-energy scat tering up to

ω_c

(here

a_{\rm F}

is the scattering length between Fermi atoms). We also include many-body effects at finite temperatures. We find that

a_{\rm M}

is strongly dependent on temperature, vanishing at

T_{\rm c}

, consistent with the earlier Bose gas results of Bijlsma and Stoof.