We have recently proposed a method to select core and cluster in a binary component description of atomic nuclei. The choice is based on the mismatch between measured binding energies and the underlying trend supplied by the liquid drop model. A key point is that the charge to mass ratios of parent, core, and cluster should be as nearly equal as possible. This approach implies that superdeformation should be ubiquitous across the Periodic Table. In these binary models, the transition quadrupole moments $Q_t$ of superdeformed (SD) bands depend strongly on the charge and mass splits, but are rather insensitive to other details. In fact, given the cluster charge $〈Z_2〉,$ $Q_t$ can be determined algebraically. We compare calculations of transition quadrupole moments with the measured values for the 41 SD bands in 21 even-even nuclei for which experimental data are available. The mass range is from $A\sim 60$ to $A\sim 240$ and the values of $Q_t$ vary from $\sim 3\hspace{0.5em}e\mathrm{b}$ to $\sim 30\hspace{0.5em}e\mathrm{b}.$ A good level of agreement is obtained.

• Received 13 April 2000

DOI:https://doi.org/10.1103/PhysRevC.63.014312