  The formation and dissociation of bosonic molecules in an optical lattice,
formed by spin-1/2 fermionic atoms, is considered in the presence of an
attractive nearest-neighbor interaction. A mean-field approximation reveals
three different phases at zero temperature: an empty, a condensate and a
Mott-insulating phase. The density of fermionic atoms and the density of
bosonic molecules indicate a characteristic behavior with respect to the
interaction strength that distinguishes between a dilute and a dense regime. In
particular, the attractive interaction favors the formation of molecules in the
dilute regime and the dissociation of atoms in the dense regime.

Superconductivity;Statistical Mechanics