The effect of finite boson number in the interacting boson approximation is one of its most distinguishing features. These effects are investigated in terms of the deviations of $\gamma \to g$ band $E2\mathrm{}$ transitions from the rotational (Alaga) values which provide one of the most crucial tests of collective models of deformed nuclei. It is shown that the empirical systematics of these deviations displays a strong mass dependence, that the interacting boson approximation successfully reproduces these systematic trends, and does so primarily by virtue of the variations in boson number and not because of parameter variations. Moreover, the origin of the $N$ dependence lies in the characteristic way in which the SU(3) symmetry is broken in calculations for realistic deformed nuclei and involves, in an essential way, the $N$ dependence of the SU(3) $\gamma \to \beta$ transitions.

NUCLEAR STRUCTURE Interacting boson model, finite boson number effects, relation to geometric models.

• Received 22 February 1983

DOI:https://doi.org/10.1103/PhysRevC.28.894