Ground State Correlations beyond the Random Phase Approximation and Collective Excitations

We present a method which allows one to treat correlations in finite Fermi systems in a more consistent way than the random phase approximation (RPA). We derive a closed, nonlinear set of equations which determines the energies and wave functions of the excited states, as well as the single-particle occupation numbers in the ground state. As an example, we apply it to metallic clusters. We show that our method allows one to correct for the inadequacy of standard RPA in cases where the use of the quasiboson approximation becomes questionable. The basic equations of the nuclear quasiparticle-phonon model are generalized for the case when RPA phonons are replaced by the phonons of the extended RPA (ERPA). The properties of the low-lying vibrational states in spherical nuclei are studied within the developed approach.