On the interdependence between ground and one-phonon RPA states

Working within a schematic model and in a boson formalism, we provide a descrip tion of the ground and first-excited states of a nuclear system in terms of two independent phonon operators. The description reveals itself quite effective in reproducing the energies of the states. A comparison between these two phonon operators allows us to localize a region where a correct description of these states is compatible with the Random Phase Approximation (RPA) requirement of a single phonon. This region is found to coincide approximately with that spanned by the standard RPA. Outside this region, the two phonons start differing rapidly therefore making the application of the RPA scheme impossible. This allows a better understanding of recently performed higher-order RPA calculations