One-Dimensional Impurity Bands

The density of states of one-dimensional crystals consisting of functions randomly distributed has been calculated on the IBM 650 computer. The chains contained 500-1000 impurity atoms, and the most probable error in the integrated density of states at various energies was estimated to be at most %. Calculations were performed for various values of the parameter =n{₀}, where n is the density of atoms and ₀ the attenuation constant appropriate to the isolated bound state. The results at different densities are compared with those obtained from various physical models. At low densities the machine results display a singularity in the density of states at the isolated atom energy. For 1, a simple pair theory fits the machine results quantitatively in the wings and displays a similar singularity. At high density (1) the machine results are smooth and fitted well by a crude optical model, except for a tail below the band edge omitted by the latter. An optical model containing local density fluctuations provides a qualitative understanding of the tail and a fair over-all fit for 1.