Fermi excitations in a trapped atomic Fermi gas with a molecular Bose condensate

We discuss the effect of a molecular Bose condensate on the energy of Fermi excitations in a trapped two-component atomic Fermi gas. The single-particle Green's functions can be approximated by the well-known BCS form, in both the BCS (Cooper pairs) and BEC (Feshbach resonance molecules) domains. The composite Bose order parameter ${\tilde \Delta}$ describing bound states of two atoms and the Fermi chemical potential $\mu$ are calculated self-consistently. In the BEC regime characterized by $\mu<0$, the Fermi quasiparticle energy gap is given by $\sqrt{\mu^2+{\tilde \Delta}^2}$, instead of $|{\tilde \Delta}|$ in the BCS region, where $\mu>0$. This shows up in the characteristic energy of atoms from dissociated molecules.