A Correspondence Between IBA-I and IBA-II Model and Electromagnetic Transitions of Some Erbium Isotopes

Since the lowest levels are symmetric under the interchange of neutrons and protons from calculations in the interacting boson approximation IBA-2 model, IBA-1 model space, in which neutron and proton degrees of freedom are not distinguished can be considered as a subspace of the IBA-2 model space. Using the microscopic background of the IBA-2 model, a correspondence can be established between IBA-1 and IBA-2 model space. Since the space of the IBA-1 model can be regarded as a subspace of the IBA-2 model there is a unique way to “Project” the operators of the IBA-2 model onto those of IBA-1. This projection can be carried out by using the Fspin formalism. In the IBA-2, the lowest states are indeed fully symmetric, the calculations with the help of this projection, we explore the energy levels and the electric quadrupole transition probabilities B(E2;I_i
I_f) and -ray E2/M1 mixing ratios for selected transitions of ^166-168Er .Owing to admixtures of non-fully-symmetric states in IBA-2, we renormalized the parameters (ε) and (κ).This is the first time we show that this projection can be applied to some heavier isotopes and the results obtained for ^166-168Er isotopes are reasonably in good agreement with the previous experimental values.