A correspondence between IBA-1 and IBA-2 models and electromagnetic transitions in the decay of some erbium isotopes

The interacting boson approximation 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 using the F-spin formalism. In the IBA-2 model, the lowest states are indeed fully symmetric, and using 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 gamma-ray E2/M1 mixing ratios for selected transitions of Er-161,Er-161,Er-166,Er-168,Er-170. Owing to admixtures of non-fully-symmetric states in IBA-2, we renormalized the parameters (epsilon) and (kappa). This is the first time we show that this projection can be applied to some heavier isotopes and the results obtained for Er-162,Er-164,Er-166,Er-168,Er-170 isotopes are reasonably in good agreement with the previous experimental values.