Exchange Potential in the Surface Region of a Free-Electron Metal

Abstract

The weighted average exchange charge and the average exchange potential proposed by Slater have been evaluated explicitly in the surface region of a free-electron gas bounded by an infinite barrier. It is found that in the surface the exchange hole ceases to accompany its electron and that the exchange potential beyond the surface is essentially that due to an exchange hole stationary in the surface region. This interpretation explains the failure of the statistical approximation to the exchange potential at low electron densities. At high densities, the statistical approximation agrees closely with the average exchange potential. In the surface region the normally spherically symmetrical exchange hole becomes distorted. This change of shape is discussed qualitatively for electrons in the immediate surface region and electrons very far from the surface of a distribution bounded by a finite low barrier. The exchange surface energy of this model of a metal surface is 96 ergs/${\mathrm{cm}}^2$ for an interior density equal to that of sodium.