Interaction of a charged particle with a solid surface: General formalism and spherical geometry

A formalism for evaluating the interaction potential of a charged particle with a solid is developed using linear response theory. It is applied to study the interaction with a metal sphere. The plasmon modes of the sphere are evaluated using the hydrodynamic model of metallic electrons and used in the general formulae. It is shown that the predominant contributions to the potential for r>or=R is due to a finite number of surface modes for dispersive plasmons. For r<R the bulk modes make the dominant contribution. The first-order quantum correction to the interaction potential is given.