Transition probabilities in the U(3,3) limit of the symplectic interacting vector boson model

Abstract

The tensor properties of the algebra generators are determined in respect to the reduction chain Sp(12, R) ⊃ U (3, 3) ⊃ Up(3) ⊗ Un(3) ⊃ U * (3) ⊃ O(3), which defines one of the dynamical symmetry limits of the Interacting Vector Boson Model (IVBM). The symplectic basis according to the considered chain is thus constructed and the action of the Sp(12, R) generators as transition operators between the basis states is illustrated. The matrix elements of the U (3, 3) ladder operators in the so obtained symmetry-adapted basis are given. The U (3, 3) limit of the model is further tested on the more complicated and complex problem of reproducing the B(E2) transition probabilities between the collective states of the ground band in 104 Ru, 192 Os, 192 P t, and 194 P t isotopes, considered by many authors to be axially asymmetric. Additionally, the excitation energies of the ground and γ bands in 104 Ru are calculated. The theoretical predictions are compared with the experimental data and some other collective models which accommodate the γ−rigid or γ−soft structures. The obtained results reveal the applicability of the model for the description of the collective properties of nuclei, exhibiting axially asymmetric features.

Axial asymmetry in the IVBM

“…(For more details concerning the tensor properties of the Sp(12, R) algebra generators and the construction of the symplectic basis see Ref. [40].) In Figure 10 we compare our theoretical predictions for the interband M1 transitions bitween the states of the GSB and γ band with experiment [15] for the two nuclei 190 Os and 192 Os, respectively.…”

“…The general approach required for the calculation of the matrix elements of the transition operators defined in respect to the chain (1), as well as its application to the more complicated and complex problem of reproducing the B(E2) transition probabilities between the collective states of the ground band in some isotopes exhibiting axially asymmetric features, is given in [40]. Here, in addition to the intraband E2 transitions between the states of the GSB we consider also the E2 transitions between the states of the γ band, as well as the interband M 1 transitions between the γ and GSB in the two nuclei 190 Os and 192 Os, for which there is enough available experimental data.…”

“…Using the tensorial properties of the Sp(12, R) generators and the mapping considered above, it is easy to define the E2 transition operator between the states of the GSB and γ band as [40]:…”

“…(For more details concerning the tensor properties of the Sp(12, R) algebra generators and the construction of the symplectic basis see Ref. [40]. )…”