Towards a self-consistent random-phase approximation for Fermi systems

We present a method which allows us to treat correlations in finite Fermi systems in a more consistent way than the random-phase approximation (RPA). The quasiboson approximation (QBA), where expectation values in the ground state of the system are approximated by their values in the uncorrelated reference state, is avoided in our approach where the correlated ground state is always used. 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 to metallic clusters a simplified version of the approach which represents, however, a significant improvement over previous attempts to go towards a self-consistent RPA. We show that our method allows one to correct for the inadequacy of standard RPA in cases where the use of QBA becomes questionable.