Electric polarizability of small metal spheres

The electric polarizability of small sodium spheres is calculated in a semiclassical approximation based on the spherical jellium model and on the Vlasov equation. Static and dynamic polarizabilities are compared for two kinds of mean field with a smooth and a sharp surface. It is deduced that the position of the centroid of the surface-plasmon resonance is not sensitive to the surface diffuseness of the mean field. Comparison with analogous quantum calculations suggests that an unrealistic feature of the zero-range exchange-correlation force employed in the local-density approximation might play an important role in increasing the static polarizability and decreasing the frequency of the surface-plasmon resonance.