Ground $\gamma$ Band Coupling in Heavy Deformed Nuclei and $SU(3)$ Contraction Limit

We derive analytic expressions for the energies and $B(E2)$-transition probabilities in the states of the ground and $\gamma$ bands of heavy deformed nuclei within a collective Vector-Boson Model with SU(3) dynamical symmetry. On this basis we examine the analytic behavior of the SU(3) energy splitting and the B(E2) interband transition ratios in the SU(3) contraction limits of the model. The theoretical analyses outline physically reasonable ways in which the ground-$\gamma$ band coupling vanishes. The experimental data on the lowest collective states of even-even rare earth nuclei and actinides strongly support the theoretical results. They suggest that a transition from the ground-$\gamma$ band coupling scheme to a scheme in which the ground band is situated in a separate irreducible representation of SU(3) should be realized towards the midshell regions. We propose that generally the SU(3) group contraction process should play an important role for such a kind of transitions in any collective band coupling scheme in heavy deformed nuclei