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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.
Castellani et al. (Mon,) studied this question.
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