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Following Sham and Rice [L. J. Sham, T. M. Rice, Phys. Rev. 144 (1966) 708]the correlated motion of particle-hole pairs is studied, starting from thegeneral two-particle Greens function. In this way we derive a matrix equationfor eigenvalues and wave functions, respectively, of the general type ofcollective excitation of a N-particle system. The interplay between excitonsand plasmons is fully described by this new set of equations. As a by-productwe obtain - at least a-posteriori - a justification for the use of the TDLDAfor simple-metal clusters.Comment: RevTeX, 15 pages, 5 figures in uufiles format, 1 figure avaible from  ekardt@fhi-berlin.mpg.d

Effective particle-hole interaction and the optical response of simple-metal clusters