Interacting-boson-approximationE2operator in deformed nuclei

The structure of the interacting boson approximation $E2$ operator appropriate to deformed nuclei is investigated. It is shown that, in the SU(3) limit of the Hamiltonian, the relative $B\left(E2\right)$ values of transitions between different representations of SU(3) are independent of the parametrization chosen for the operator. This feature leads to a better understanding of the geometrical analogs of the bands predicted by the interacting boson approximation. More generally, a study of empirical $B\left(E2\right)$ values in the deformed rare earth nuclei indicates the suitability of an almost constant form for the $E2$ operator across the region, and it is shown that the deduced form of the operator predicts very different features for the lowest ${\mathrm{O}}^{+}$ excitation than those associated with the geometrical concept of a $\beta$ band.