β-band moment of inertia anomaly

The moment of inertia of the $K=0^{+}$ bands in some of the rare-earth nuclei differ from other low-lying bands. Using the $\frac{1}{N}$ expansion technique, we show that the interacting boson model with arbitrary kinds of bosons and interactions leads to the same moment of inertia for all bands and hence does not allow such a variation to leading order. Since there are usually more ${\mathrm{O}}^{+}$ bands in this region than can be accommodated in collective models, this could provide a useful criterion for the selection of the collective $\beta$ band.