Self-energy of a hydrogenic atom near a metal surface.

Abstract

General expressions for the self-energy of hydrogenic atoms near a metal surface have been derived. It is found that the self-energy at the metal surface saturates to a finite value with the inclusion of mul- tipolar excitations of the hydrogenic atoms. Numerical results have been presented for hydrogenic atoms moving normal to the metal surface at two speeds. It is also found that dispersion effects of surface-plasmon excitation further reduce the magnitude of the self-energy. a quantum-mechanical treatment of the problem has been proposed only recently by Manson and Ritchie. These authors have shown that the interaction energy near a metal surface is determined by quantum effects arising from virtual atomic excitations and surface plasmons. In their work they used a dipolar approxima- tion to simplify the interaction Hamiltonian, thereby con- sidering only virtual atomic excitations of simple dipoles. They have found that the interaction energy varies as I /Z when Z, the separation between the atom and met- al surface, is very large, and it varies as 1/Z when separa- tion between atom and metal surface is very small. Man- son and Ritchie have attributed the softening of the in- teraction to quantum effects near the surface. These au- thors have also shown that this interaction also depends on the speed of the atom relative to the metal surface. Recently, several papers have extended the work of Manson and Ritchie to incorporate multipolar excita- tions of the atom. With inclusion of these excitations, they have shown that at the surface, the interaction ener- gy saturates to a finite negative value. The numerical re- sults for the interaction energy of a positronium atom have been obtained by Pathak, Jindal, and Paranjape. It has been found that this interaction energy is smaller than the value obtained by Manson and Ritchie. In all earlier works the dispersion effects of surface and bulk plasmons have been neglected and results have been ob- tained with only the positronium atom kept in mind. In this paper we formulate a general theory for the calcula- tion of the self-energy of hydrogenic atoms near a metal surface, using a hydrodynamical model of metallic elec- trons. We incorporate the dispersion effects of surface plasmons. Our expressions for the self-energy of the atom moving normal to the surface at a speed below threshold reduce to the earlier results ' in the dispersion- less limits of surface plasmons. We present a theoretical formulation in Sec. II. The numerical results and discussions for the self-energy of the positronium and hydrogen atoms are presented in Sec. III.