Short-range order and the electronic structure of a one-dimensional liquid metal

The energy spectrum of a one-dimensional array of $\delta$-function potentials is studied as a function of the degree of short-range order in the arrangement of the scatterers. The integrated density of states is evaluated numerically and the results are used to compare alternate theoretical formalisms. In particular, we consider Lax's quasicrystalline approximation (QCA) and the more recent self-consistent approaches of Gyorffy and Schwartz and Ehrenreich. Surprisingly, we find that only the non-self-consistent QCA yields a reasonable description of the electronic spectrum. The failure of the self-consistent schemes appears to be due to an incomplete treatment of the multiple-occupancy corrections.