We discuss the fact that yrast levels in vibrational-like even-even nuclei do not follow the simple first-order anharmonic relation if $6^{+}$ and $8^{+}$ states are taken into account. The interpretation in terms of the vibrator model with three-phonon interactions is in contrast to the earlier description using the $U\left(5\right)\mathrm{}$ limit of the interacting boson model-1 with an anomalous energy of the $2_1^{+}$ state. The recently discovered peak in the statistical distribution of the $4_1^{+}$ to $2_1^{+}$ energy ratio at $R_{4/2}\approx 2.3,$ supports the latter viewpoint.

• Received 9 February 2000

DOI:https://doi.org/10.1103/PhysRevC.63.047304