Dielectric response of arbitrary surfaces and size quantized metals

Abstract

We propose a new, general method for obtaining closed form solutions of electrostatic response problems in solid bodies of arbitrary shape. The scheme is simple enough to be applied to problems with complicated geometries, yet it should be sufficiently reliable for most purposes. It is shown that its formulation in terms of boson pseudomodes provides a convenient generalization of a method proposed by Overhauser to treat electron correlation in metals. Explicit expressions are given for the image interaction between a point charge and a plane or spherical surface, and for the screening energies and the screened electric fields of impurities in size quantized metals. Several implications in the physical and chemical properties of small metal particles are briefly discussed. Quantum size effects are included by means of a suitable dielectric function, including quantum size, exchange and correlation effects, and are shown to be very significant when the particle radius is of the order of a few tens of angstroms.