Properties of the multiphonon method applied to even-even spherical nuclei

The present contribution deals with the first applications of the multiphonon method to the description of low lying excitations in even-even spherical nuclei. For the first time, it becomes possible to make numerical calculations up to four phonons and to investigate properties of the model. It was found that one of the parts of a model Hamiltonian, called H-BB(P), which comes from the residual pairing interaction and which is usually neglected in calculations, is very important and can even lead to divergence when the phonons are piled up. A possible explanation of such a phenomenon is discussed.