Nodal Hydrogenic Wave Functions of Impurities on Bounded-Electron-Gas Surfaces

Recent suggestions by Levine for exactly treating hydrogenic impurities on idealized semiconductor surfaces are extended to the case of another exactly soluble model, a hydrogenic impurity on the boundary of a semi-infinite, dense electron gas. The surface selection rule l+m=odd is found to apply to this hypothetical surface. This rule is equivalent to the requirement that impurity wave functions have a nodal plane on the boundary. Unlike the dielectric case, the allowed wave functions of the present hypothetical model extend into the vacuum half-space but not into the electron-gas half-space. A surface dipole is thus formed which is directed into the surface, thus increasing the surface barrier for electron emission.The exact high-density results are extrapolated to densities that exist within conduction bands of real metals. With this extrapolation it is found that the exact high-density theory is useful in understanding the role of ion-core screening when small atoms, such as hydrogen or lithium, are adsorbed on real metal surfaces. The present results permit interpretation of previously unexplained data for lithium adsorption on metals.