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

Abstract

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 theF-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 probabilitiesB(E2; {ie393-01}) and γ-ray E2/M1 mixing ratios for selected transitions of162, 164, 166, 168, 170Er. Owing to admixtures of non-fully-symmetric states in IBA-2, we renormalized the parameters (e) and (κ). This is the first time we show that this projection can be applied to some heavier isotopes and the results obtained for162, 164, 166, 168, 170Er isotopes are reasonably in good agreement with the previous experimental values.