We have extended the work of Sahni and Bohnen to more emphatically demonstrate that as an electron is removed from within a metal to infinity outside, its average exchange charge density is not localized to the surface region but rather spreads throughout the entire semi-infinite crystal. Thus, asymptotically, the Fermi hole does not constitute part of the image charge at the surface. In addition to the planar-averaged density, we have also studied the structure of the charge in planes parallel to the surface as well as in the plane perpendicular to the surface encompassing the axis of electron removal. Comparison of the quantum-mechanical and classical charge distributions in the planes parallel to the surface show the two to differ significantly. We also prove analytically that independent of the electron position in the vacuum (positive half-space) region, there is always charge at minus infinity in the metal.

• Received 15 January 1987

DOI:https://doi.org/10.1103/PhysRevB.37.745