Quantum size effects in metal particles and thin films by an extended RPA

The RPA is extended in the framework of linear response theory to allow for the treatment of a finite free electron gas. The dielectric function taking quantum size effects into account, is calculated and shown to be finite in the limit of small wavevectors. The theory is applied to a simple free electron model for a small metal particle and analytical expressions are obtained for the electronic polarizability of a thin film and for the optical properties in the plasma resonance region.