SUM-RULES FOR SURFACE-PLASMON FREQUENCIES

Surfaces exhibit spatially localized collective electronic excitations . The Mie modes of a particulate is one well-known example. We derive sum rules which (1) relate the surface mode frequencies of complementa ry systems like a sphere and a void and (2) relate the surface mode fr equencies of a system with several interfaces to the ones for the indi vidual surfaces. Our approach is of general nature since the results a re based on properties of the Poisson equation and should be of intere st for spectroscopies of matter in different fields of physics, in par ticular for scanning transmission electron microscopy.