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 $A_l=-v\left(R_l\right)$. 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 $l>\mathrm{}2\mathrm{}$. 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.