Empirical signature for shape transitions mediated by sub-shell changes

A simple approach that highlights the effects of shell or sub-shell changes in mediating shape/phase transitions in the equilibrium structure, and in the development of deformation, is presented. It uses only simple data such as R-4/2 equivalent to E(4(1)(+))/E(2(1)(+)) and 1/E(2(1)(+)) and reveals the character of transitional regions through the appearance of bubble and crossing topologies. Recent microscopic calculations are also considered from the same perspective. Since the method uses only the simplest data [E(2(1)(+)) is sufficient], it should be particularly valuable for future studies of exotic nuclei.