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Collective surface modes in small spherical metallic systems within the Bloch-Jensen hydrodynamical model

An exact generalization of the classical Bloch-Jensen hydrodynamical model for the homogeneous free-electron gas is obtained for a two-layer spherical metal system. The dispersion relation of surface plasmons together with the analytical expression of the self-consistent electric field are calculated exactly. It is found that small and large systems exhibit notably different behaviours. In particular, the surface-plasmon frequencies strongly depend on the layer thickness. As is the case for the metal-vacuum interface, the electric field is shown to present a sharp maximum at the interface between the two metals. A simple physical interpretation of this effect is provided. The present two-layer system also gives interesting indications about the part played in collective surface modes by the ion-density profile near the surface of small metal clusters, which may be helpful in interpreting recent puzzling experimental data.