Application of the multiphonon method to the study of the vibrational states withK=0in heavy deformed nuclei

The multiphonon method based on $K^{\pi }$ ${=0\mathrm{}}^{\mathrm{-}}$ and $K^{\pi }$ ${=0\mathrm{}}^{+}$ phonons is applied to heavy mass deformed even nuclei, such as Th, U, and Pu isotopes. Special emphasis is put on the location and properties of the ‘‘two phonon’’ states. Relative to an harmonic situation, the calculated energy spectra are systematically dilated. The octupole vibrations with $K^{\pi }$ ${=0\mathrm{}}^{\mathrm{-}}$ present larger anharmonicities than the vibrations $K^{\pi }$ ${=0\mathrm{}}^{+}$ which, in these nuclei, are found to be mainly of pairing nature. The two modes appear to be weakly coupled. The ‘‘two phonon’’ states are predicted to have an energy of about 1.7 to 2.0 MeV and keep some collective character through their electromagnetic transitions to the ‘‘one phonon’’ states. These conclusions are at variance with those of the quasiparticle phonon nuclear model of Soloviev et al.