Simple relations among E2 matrix elements of low-lying collective states

A method is developed to derive simple relations among the reduced matrix elements of the quadrupole operator between low-lying collective states. As an example, the fourth-order scalars of Q are considered. The accuracy and validity of the proposed relations is checked for the ECQF Hamiltonian of the IBM-1 in the whole parameter space of the Casten triangle. Furthermore these relations are successfully tested for low-lying collective states in nuclei for which all relevant data is available.