The sdg interacting-boson model is presented in the SU(3) tensor formalism. The interactions are decomposed according to their SU(3) tensor character. The existence of the SU(3)-seniority preserving operator is found to be important. The model is applied to ${}_{}{}^{168}{}_{}{}^{}\mathrm{Er}$. Energy levels and electromagnetic transitions are calculated. This model is shown to solve the problem of anharmonicity regarding the excitation energy of the first $K^{\pi }$${=4\mathrm{}}^{+}$ band relative to that of the first $K^{\pi }$${=2\mathrm{}}^{+}$ one. E4 transitions are calculated to give different predictions from those by the quasiparticle-phonon nuclear model.

• Received 15 October 1987

DOI:https://doi.org/10.1103/PhysRevC.38.419