“…The longitudinal excitation spectra of allowable modes will be determined from a knowledge of the frequencydependent non-local dielectric function (r, r ; ω) of the composite system, which depends on the position coordinates r, r and frequency ω. Alternatively, the normal modes correspond to the resonances of the inverse dielectric function K(r, r ; ω) satisfying dr K(r, r ; ω) (r , r ; ω) = δ(r − r ). The significance of K(r, r ; ω) is that it embodies manybody effects 31,32 through screening by the medium of an external potential U (r ; ω) to produce an effective potential V (r; ω) = dr K(r, r ; ω)U (r ; ω). In Sec.…”