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

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 the general two-particle Greens function. In this way we derive a matrix equation for eigenvalues and wave functions, respectively, of the general type of collective excitation of a N-particle system. The interplay between excitons and plasmons is fully described by this new set of equations. As a by-product we obtain at least a-posteriori a justification for the use of the TDLDA for simple-metal clusters. 36.40.+d, 31.50.+w, 33.20.Kf Typeset using REVTEX 1