Effective Theory of Feshbach Resonances and Many-Body Properties of Fermi Gases

For calculating low-energy properties of a dilute gas of atoms interacting via a Feshbach resonance, we develop an effective theory in which the parameters that enter are an atom-molecule coupling strength and the magnetic moment of the molecular resonance. We demonstrate that, for resonances in the fermionic systems ${}^6\mathrm{Li}$ and ${}^{40}\mathrm{K}$ that are under experimental investigation, the coupling is so strong that many-body effects are appreciable even when the resonance lies at an energy large compared with the Fermi energy. We calculate a number of many-body effects, including the effective mass and the lifetime of atomic quasiparticles in the gas.

Figure 1

$-\mathrm{Im}\Sigma (p,{\xi }_p)/{ϵ}_{\mathrm{F}}$ as a function of $k_{\mathrm{F}}|a_{\mathrm{res}}|$ for various momenta. The solid curves are numerical results based on Eqs. (6, 10), the dashed curves are the results if the effect of the medium on the scattering amplitude is neglected, and the dotted curves are the Galitskii results. All these results become identical for $k_{\mathrm{F}}|a_{\mathrm{res}}|\ll 1$.