Singular Quasiparticle Scattering in the Proximity of Charge Instabilities

We analyze the dynamic scattering amplitude between quasiparticles at the Fermi surface in the proximity of a charge instability, which may occur in the high temperature superconductors. Within the infinite-$U$ Hubbard-Holstein model we find that in the absence of long-range Coulomb forces the scattering amplitude is strongly singular at zero momentum transfer close to the phase separation instability. In the presence of long-range Coulomb forces the singularity occurs at finite wave vectors. In both cases we show how normal state properties are largely affected by this scattering.