Comparison of different collective models describing the low spin structure ofEr168

Abstract

The ability of several collective models to reproduce the low-energy spectrum of ' Er is investigated. It is found that the interacting boson approximation, the general collective model, and the Gneuss-Greiner model all describe the data with comparable quality, while the rotation-vibration model appears to be too restrictive. The low-energy spectrum of ' Er has recently been the object of intensive discussions, ' because the geometrical collective models ' appeared to give different results from the interacting-boson approximation (IBA). ' On the other hand, it was shown by several authors that the IBA and the geometrical models can be related mathematically. The IBA Hamiltonian can be expressed in terms of the Bohr and Mottelson variables, although the IBA still has the additional condition of maximal number of d bosons. For low spins this should not play an important role as long as the total number of s and d bosons is sufficiently large. For high-spin states the pure s -d -boson description fails and other effects, such as g bosons, have to be taken into account. In the case of ' Er the number of bosons in the IBA is 16, quite a large number, so that the low-spin states should be reproducible with both the IBA and the geometrical models with about equal quality (even in the GneussGreiner model, usually only about 30 bosons are used). In that sense the results of Refs. 2 and 3 are surprising. In the present work we investigated ' Er in the framework of the general collective model (GCM), ' the GneussGreiner model (GGM), the rotation-vibration model