  A mixture of spin-1/2 fermionic atoms and molecules of paired fermionic atoms
is studied in an optical lattice. The molecules are formed by an attractive
nearest-neighbor interaction. A functional integral is constructed for this
many-body system and analyzed in terms of a mean-field approximation and
Gaussian fluctuations. This provides a phase diagram with the two merging Mott
insulators and an intermediate superfluid. The Gaussian fluctuations give rise
to an induced repulsive dimer-dimer interaction mediated by the unpaired
fermions. The effect of an unbalanced distribution of spin-up and spin-down
fermions is also discussed.
