Triaxial shapes in the interacting vector boson model

Abstract

A new dynamical symmetry limit of the two-fluid Interacting Vector Boson Model (IVBM), defined through the chain Sp(12, R) ⊃ U (3, 3) ⊃ U * (3) ⊗ SU (1, 1) ⊃ SU * (3) ⊃ SO(3), is introduced. The SU * (3) algebra considered in the present paper closely resembles many properties of the SU * (3) limit of IBM-2, which have been shown by many authors geometrically to correspond to the rigid triaxial model. The influence of different types of perturbations on the SU * (3) energy surface, in particular the addition of a Majorana interaction and an O(6) term to the model Hamiltonian, is studied. The effect of these perturbations results in the formation of a stable triaxial minimum in the energy surface of the IVBM Hamiltonian under consideration. Using a schematic Hamiltonian which possesses a perturbed SU * (3) dynamical symmetry, the theory is applied for the calculation of the low-lying energy spectrum of the nucleus

Axial asymmetry in the IVBM

“…As it was shown in Ref. [9], this dynamical symmetry is appropriate for nuclei in which the one type of particles is particle-like and the other is holelike. For more details concerning the algebraic structure of this dynamical symmetry of the IVBM, we refer the readers to Ref.…”

“…In Ref. [9] a new dynamical symmetry limit of the twofluid Interacting Vector Boson Model (IVBM) was introduced, which seems to be appropriate for the description of deformed even-even nuclei, exhibiting triaxial features. It was shown there that the addition of Majorana interaction to the SU * (3) model Hamiltonian produces a stable triaxial minimum.…”

“…In this paper, we develop further our theoretical approach initiated in Ref. [9] by considering in more details the spectra of some even-even transitional nuclei, supposed to be axially asymmetric, in the framework of the symplectic IVBM with Sp(12, R) as a group of dynamical symmetry. We focus on the γ-band properties and show how the γ-band energies (and the corresponding energy staggering) are affected by the presence of the introduced interaction.…”

“…For more details concerning the algebraic structure of this dynamical symmetry of the IVBM, we refer the readers to Ref. [9]. All bilinear combinations of the creation and annihilation operators of the two vector bosons generate the boson representations of the non-compact symplectic group Sp(12, R):…”

“…We also introduce the following notations u † m (α = 1/2) = p † m and u † m (α = −1/2) = n † m . In terms of the p− and n−boson operators, the Weyl generators of the ladder representation of U (3, 3) are [9]…”