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The paramagnetic phase of the extended attractive Hubbard model on the cubiclattice is studied within the spin rotation invariant Kotliar-Ruckensteinslave-boson representation at zero temperature. It is obtained that thequasiparticle residue of the Fermi liquid phase vanishes for all densities atan interaction strength slightly smaller than $U_c$ that signals theBrinkman-Rice transition, and that it weakly depends on density. While forvanishing non-local interaction parameters homogeneous static chargeinstabilities are found in a rather narrow window centered around quarterfilling and $U \simeq 0.8\ U_c$, increasing them to $V = -0.2\ U$ results intoa severe narrowing of this window. On the contrary, when all interactionparameters are attractive, for example for $V = 0.2\ U$, a large parameterrange in which homogeneous static charge instabilities is found. Yet, thissystematically happens inside the Fermi liquid phase.

Charge instabilities of the extended attractive Hubbard Model on the cubic lattice