  We analyze the excitation spectrum of a three-dimensional(3D) Bose-Fermi
mixture with tunable resonant interaction parameters and high hyperfine spin
multiplets. We focus on a 3-particle vertex describing fermionic and bosonic
atoms which can scatter to create fermionic molecules or disassociate. For a
single molecular level, in analogy to the single magnetic impurity problem we
argue that the low lying excitations of the mean-field theory are described by
the Fermi liquid picture with a quasiparticle weight and charge which is
justified by a $1/N_\psi$ expansion, expected to be exact in the limit of
infinite degeneracy (or very high fermionic spin) $N_\psi \to \infty$. Our
emphasis is placed on the novel conditions for chemical equilibrium and how
many-body chemical reactions renormalize the bosonic chemical potential,
modifying condensation and superfluid-insulator transitions.
