Therefore the optical potential depends only on one position and the energy. Several choices are possible for such a function. For a valence density functional Fig. 3 shows the charge density and the resulting optical potential for two energies. Shown is a cut in direct space with the vacuum at the top of the images.
Dark shades belong to high charge density and high damping.
The optical potential from the local density functional shows more structure than the charge itself. This comes from the nonlinearity of the functional which gives strongest damping at mediate density. The spatial structure of the damping is important for electron spectroscopy by its influence on the spatial structure of the scattering state or, for photoemission, of the initial and final states. It confirms a previous suggestion about a second experimental current minimum which has to be attributed to a second gap in the band structure. It is clearly a consequence of the electronic structure from the pseudopotential used here.