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

A modified form of the Heine-Abarenkov model potential is proposed. The core potential is replaced with a constant potential Aₗ only for those angular momenta for which there are core wave functions. Also, the model radius Rₗ 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 Rₗ such that Aₗ=-v(Rₗ). 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 Aₗ for $l>2$. Also, the form factors tend to decay rather than oscillate at short wavelengths. The linear extrapolation of Aₗ 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.