A relation between E2 matrix elements connecting collective states of deformed nuclei

A relation is presented stating that a sum of certain products of E2 matrix elements connecting the 0+ and 2+ levels in the ground, β-, and γ-bands in the limit of strong quadrupole deformation vanishes. As a consequence β → g E2 matrix elements are much smaller than β → γ matrix elements, contrary to the naive expectation based on the vibrational picture of independent β and γ excitations. This relation is supported by experimental data on deformed nuclei, and suggests a re-examination of the traditional understanding of these basic collective modes and their inter-relationships.