On collective two-phonon states in deformed nuclei

The centroid energies of the two-phonon states in doubly even deformed nuclei are calculated within the quasiparticle-phonon nuclear model taking into account the Pauli principle in the two-phonon components of the wave functions. It is shown that the collective two-phonon energies are shifted by 1–2 MeV to higher energies due to the Pauli principle. A strong fragmentation of the two-phonon collective states over many nuclear levels occurs at the excitation energies of 3–4 MeV. It is concluded that the two-phonon states cannot exist in deformed nuclei. The analysis of the available experimental data on the two-phonon states shows that the experimental data do not contradict the results of these calculations.