Predictions of the interacting boson approximation in a consistent Q framework

The predictions of the interacting boson approximation are studied in the consistent Q formalism in which the same parametrization of the boson quadrupole operator is used in both the Hamiltonian and in the E2 operator. In this scheme, wave functions, relative energies of states of the same spin, and all relative B(E2) values depend on only a single parameter, χ_Q, which appears in the internal structure of the operator Q. This feature allows a number of simple results to be obtained, principally through the construction of contour plots of various observables in terms of χ_Q and the boson number N. The entire SU(3)-O(6) region, including both limiting symmetries, can be treated by allowing χ_Q to vary between its respective limiting values for those two symmetries. For deformed nuclei, a number of characteristic features are obtained, involving the predicted decay of the γ band and the energy and decay of the first 0⁺ excitation. It is shown that the dominance of the β-->γ over β-->g matrix elements and the near equality of β-->γ and γ-->g E2 matrix elements are inherent features of the model. The automatic inclusion of band mixing in the interacting boson approximation is discussed in terms of the mixing parameter Z_γ and it is shown that the interacting boson approximation reproduces the empirical systematics in Z_γ. The concepts of the intrinsic state formalism are reviewed in the context of the consistent Q framework and shown to imply vanishing β-->g transitions, for any boson number, in the absence of K mixing effects. The O(6) limit obtained with the consistent Q formalism is shown to be a special case of the general limit. Finally, transition regions are discussed, particularly the SU(3)-O(6) case, in terms of "trajectories" in χ_Q between its limiting values. A number of qualitative parameter-free predictions for the evolution of energy or E2 branching ratios are thus obtained. NUCLEAR STRUCTURE Consistent Q formalism of the IBA. Energy and B(E2) predictions, contour plots, χ_Q trajectories, intrinsic state formalism.