One-Dimensional Impurity Bands

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