Fermion-mediated BCS-BEC crossover in ultracold ${}^{40}$K gases

Feshbach resonance phenomena in atomic Fermi gases involves the multiple scattering of atoms from open channel states into a molecular bound state formed from neighbouring closed channel states. Current theories treat the closed channel molecule as a featureless boson, but it can be argued that this interpretation is inappropriate when applied to ${}^{40}$K, since the molecule shares a hyperfine spin state with the open channel states. Introducing a 3-fermion model, where a fermion is shared between the open and closed channel states, we explore how the nature of the bound state impinges on the mean- field characteristics of the system.