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.