Polarizability of a small sphere including nonlocal effects

We develop a simple semiclassical method for calculating the polarizability of a very small spherical particle by taking into account the nonlocal nature of the dielectric response. Our theory is very general in the sense that it can be applied to any material which can be characterized by a bulk dielectric function of the form εB(→k,ω): We introduce a new additional boundary condition (ABC) which is similar but not exactly equivalent to the Fuchs-Kliewer ABC. The theory is applied to calculate the polarizabilities of dielectric and metallic spheres.