Abstract
Working within a schematic model and in a boson formalism, we provide adescrip tion of the ground and first-excited states of a nuclearsystem in terms of two independent phonon operators. The descriptionreveals itself quite effective in reproducing the energies of the states.A comparison between these two phonon operators allows us to localize a regionwhere 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 approximatelywith that spanned by the standard RPA. Outside this region, the two phononsstart differing rapidly therefore making the application of the RPA schemeimpossible. This allows a better understanding of recently performedhigher-order RPA calculations.
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