The relationship between the interacting boson model and the algebraic version of Bohrʼs collective model in its triaxial limit

Recent developments and applications of an algebraic version of Bohrʼs collective model, known as the algebraic collective model (ACM), have shown that fully converged calculations can be performed for a large range of Hamiltonians. Examining the algebraic structure underlying the Bohr model (BM) has also clarified its relationship with the interacting boson model (IBM), with which it has related solvable limits and corresponding dynamical symmetries. In particular, the algebraic structure of the IBM is obtained as a compactification of the BM and conversely the BM is regained in various contraction limits of the IBM. In a previous paper, corresponding contractions were identified and confirmed numerically for axially-symmetric states of relatively small deformation. In this paper, we extend the comparisons to realistic deformations and compare results of the two models in the rotor–vibrator limit. These models describe rotations and vibrations about an axially symmetric prolate or oblate rotor, and rotations and vibrations of a triaxial rotor. It is determined that most of the standard results of the BM can be obtained as contraction limits of the IBM in its U(5)–SO(6) dynamical symmetries.