  We propose a multi-band Fermi-Bose Hubbard model with on-site fermion-boson
conversion and general filling factor in three dimensions. Such a Hamiltonian
models an atomic Fermi gas trapped in a lattice potential and subject to a
Feshbach resonance. We solve this model in the two state approximation for
paired fermions at zero temperature. The problem then maps onto a coupled
Heisenberg spin model. In the limit of large positive and negative detuning,
the quantum phase transitions in the Bose Hubbard and Paired-Fermi Hubbard
models are correctly reproduced. Near resonance, the Mott states are given by a
superposition of the paired-fermion and boson fields and the Mott-superfluid
borders go through an avoided crossing in the phase diagram.
