Reformulation of the Screened Heine-Abarenkov Model Potential

The screening of a generalized Heine-Abarenkov model potential is systematically reformulated. The electron density in a metal is calculated in terms of model-potential parameters. One contribution to this charge is a depletion hole, analogous to the orthogonalization hole in pseudopotential theory. A general expression for the depletion hole is derived. The screened form factor for the model potential is calculated, taking into account the nonlocality and energy dependence of the model potential. The long-wavelength limit of the form factor is evaluated and found to be $-\frac{2}{3}{E}_F$ at the Fermi surface, as for local potentials. It is found that the depletion-hole contribution cancels a term arising from the energy dependence of the potential at long wavelengths. Consequently, it is unnecessary to renormalize the dielectric constant as done by Heine and Animalu. The magnitude of the depletion hole is evaluated for several elements using the Heine-Abarenkov model potential. The expression for the depletion hole is also shown to be valid for a certain class of pseudopotentials.