Model-Potential Calculation of the Density of States in Liquid and Solid Lithium, Cadmium, and Indium

A perturbation expansion of the electron energy has been used to calculate the density of states in liquid lithium, cadmium, and indium. The full nonlocal form of the optimum model potential proposed by Shaw has been used in these calculations. It is shown by comparing the nonlocal calculation to various approximate calculations that the nonlocal effects produce large changes in the second-order corrections to the electron energy and a considerable smoothing of the structure in the density of states. The first-order, $k$-dependent corrections to the electron energy have been included, and $k$-dependent effective masses have been calculated for several elements. The density of states for crystalline lithium, cadmium, and indium has also been calculated by determining the distortion of energy surfaces due to the first few zone planes. The results for liquid and solid are compared, and agreement with experiment is discussed.