Optimum Form of a Modified Heine-Abarenkov Model Potential for the Theory of Simple Metals

Abstract

A modified form of the Heine-Abarenkov model potential is proposed. The core potential is replaced with a constant potential ${A}_{l}$ only for those angular momenta for which there are core wave functions. Also, the model radius ${R}_{l}$ is allowed to be different for each $l$ and to depend on energy. It is shown that this potential can be optimized using a variational procedure. The optimum model parameters are obtained by choosing an ${R}_{l}$ such that ${A}_{l}=\ensuremath{-}v({R}_{l})$. The optimized form of this modified model potential has several advantages. It provides a unique prescription for selecting model radii, and it eliminates the necessity of approximating the ${A}_{l}$ for $l>2$. Also, the form factors tend to decay rather than oscillate at short wavelengths. The linear extrapolation of ${A}_{l}$ versus $E$ proposed by Animalu is shown to be valid for most simple metals. Optimum model potential parameters are obtained, and form factors and depletion holes are evaluated for a group of simple metals using the optimized model potential.