A simple, four-parameter algebraic collective model (ACM) Hamiltonian is used to describe 166Er. In this nucleus anharmonic double-γ vibrations are observed and the third excited 0+ state has been identified as a candidate for a bandhead of a β band. In contrast to γ-vibrational bands, systematically observed in deformed nuclei, β-vibrational bands are rarely well realized in nuclei and their observation and interpretation is still far from satisfactory. The purpose of the present paper is to show how the ACM model is capable to address complex properties of deformed nuclei in this region and what are its successes and weak points.
I will review developments and applications of an algebraic version of Bohr’scollective model (BM), known as the algebraic collective model (ACM) withinwhich fully converged calculations can be performed for a range of Hamiltonians.Examining the algebraic structure underlying the BM has clarified itsrelationship with the interacting boson model (IBM), with which it has relatedsolvable limits. I will review results of comparison of the two models for thecase of both axially-symmetric and triaxial rotor. Predictions for single andmulti-phonon excitations of deformed nuclei will be discussed and comparedwith data.