Theory for the polarizability of small spherical metallic clusters

The static electric dipole polarizability of small spherical metallic clusters is calculated using density-functional theory. We study systematically corrections to the local-density approximation which are particularly important when the spatial extension of the induced charge at the surface of the cluster becomes comparable to the size of the exchange hole. Additional corrections to the polarizability arising from the actual atomic structure of the metal cluster in comparison to a spherical jellium model are discussed.