Yale University

One of the iconic observables in deformed nuclei is transitions for the K = 2 gamma vibration to the ground band. In the simplest models, relative values of these B(E2) values are given by the Alaga rules. In practice, deviations from these estimates are always found and have traditionally, and successfully, been interpreted in terms of rotation-vibration interactions (i.e., band mixing) in terms of a band mixing parameter, Z. However, a very different approach, with no mixing at all, called a Partial Dynamical Symmetry, was applied to all well-deformed rare earth nuclei, and succeeds almost as well, and with no parameters whatsoever. This development will be discussed. It also raises an important question since the deviations from the Alaga rules given by the PDS arise solely from the finite number of valence nucleons. Therefore, how can such dissimilar models, based on different physics, produce such similar results, and what are we to understand about the underlying physics. We will show that these apparently diverse models are, in fact, closely related and that they link the concept of rotation-vibration interactions directly to valence nucleon number.