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

Following Sham and Rice [L. J. Sham and T. M. Rice, Phys. Rev. 144, 708 (1966)], the correlated motion of particle-hole pairs is studied, starting from the general two-particle Green's function. In this way, we derive a matrix equation for eigenvalues and wave functions, respectively, of the general type of collective excitation of an N-particle system. The interplay between excitons and plasmons is fully described by this set of equations. As a by-product we obtain - at least a posteriori - a justification for the use of the time-dependent local-density approximation for simple-metal clusters.