Long-wavelength behavior, impurity scattering and magnetic excitations in a marginal Fermi liquid

The marginal Fermi liquid hypothesis about the excitation spectrum of the high temperature superconductors is supplemented to specify the long-wavelength behavior; it is shown that there are no anomalous renormalizations of the compressibility and the uniform paramagnetic susceptibility. Consideration of elastic scattering from impurities leads to the conclusion that as temperature is decreased, the scattering approaches the unitarity limit. We discuss the possibility that at T → 0, a marginal Fermi liquid is either a superconductor or an insulator. Predictions for the magnetic structure factor observable in neutron scattering consistent with the nuclear relaxation rate on copper and on oxygen are also given