The IBM description of triaxial nuclei

Abstract

Recently, interacting boson model (IBM) calculations, in the O(6) basis up to the seniority quantum number v max= 40 , were made possible thanks to the availability of the SO(5) Clebsch-Gordan (CG) coefficients, computed in floating-point arithmetic (T.A. Welsh, unpublished (2008)). In this paper we have made use of these CG coefficients to extend the IBM to situations where triaxial deformation is present. Such a description has been considered in the algebraic collective model (ACM) which is an algebraic version of the Bohr model. To describe triaxiality in the ACM a term proportional to cos23\( \gamma\) must be included in the Hamiltonian. We show that, in the IBM, this can be achieved by including a term quadratic in (\( \hat{{Q}}\) ⊗ \( \hat{{Q}}\) ⊗ \( \hat{{Q}}\))0, which is an IBM image of the term cos23\( \gamma\) . Quadrupole shape invariants are used to investigate the \( \beta\) and \( \gamma\) rigidity of the states obtained with such a Hamiltonian and a comparison with the rigid asymmetric rotor model is presented. The staggering of \( \gamma\) -band level energies, obtained in the present approach, is analyzed and compared to the ones predicted by the geometrical models and by the IBM. A comparison between the experimental and calculated staggerings in 190Os and 192Os is shown.