Interacting boson approximation description of the collective states ofEr168and a comparison with geometrical models

The interacting boson approximation has been used to calculate the positive parity states of ${}_{}{}^{168}{}_{}{}^{}\mathrm{Er}$ below 2 MeV. A simple parametrization has been used which corresponds to a description close to the SU(3) limit of the model. The predictions have been compared with new results available from a recent experimental study. Particular attention has been paid to the absolute magnitude of predicted $B\left(E2\right)$ values in assessing the significance of discrepancies between theory and experiment. Estimates of absolute strengths have also been obtained for $M1$ transitions in the scheme. The calculations correctly reproduce the complete sequence of $K^{\pi }=0^{+} \mathrm{and} 2^{+}$ bands below the pairing gap and provide an excellent overall description of their decay properties. Most importantly, the predicted dominance of the decay from the $\beta$ to the $\gamma$ band, over that to the ground state band, which represents a fundamental characteristic of the model in this region, is reflected by the experimental data. The reproduction of this feature from a band mixing approach in the framework of the geometrical description is also discussed, and the connection between the two descriptions is explored.