Triaxial rotor in the SU(3) limit of the interacting boson model

Abstract

A mapping from a triaxial rotor Hamiltonian to that of the SU(3) limit description in the interacting boson model (IBM) is established, which is achieved by the SU(3) realization of the triaxial rotor. A detailed comparison between the triaxial dynamics generated from the quadrupole-deformed rotor and those from the IBM image is made. The results indicate that the mapping can be well realized. A preliminary test for 128 Ba further confirms the finite-N effect of the mapping. It thus provides an alternative way to understand the triaxiality in the finite-N system and additional insight into understanding the SU(3) IBM theory from microscopic point of view via the SU(3) shell model. PHYSICAL REVIEW C 90, 044310 (2014) which thus generate the dynamical symmetry group of the quantum rotor [20], the semidirect product group T 5 ⊗ s SO (3) with the Lie algebra denoted as t 5 ⊕ so(3). In the body-fixed principal-axial system, one has [7-9] 044310-2

γ -soft rotor with configuration mixing in the O(6) limit of the interacting boson model

“…for g = 0. Since physical spectrum should be lower-bound, only α = α + shown in (11) is possible, which corresponds to c given in (15) and the eigen-energy provided in (12) and (16) with positive sign. Otherwise, the spectrum will become upper-bound, which is non-physical and discarded.…”

“…Otherwise, the spectrum will become upper-bound, which is non-physical and discarded. In (16), 2 ∆ 2 − g 2 is the energy of the collective 2p-2h excitation. Again, the sign of g does not affect the 2p-2h excitation energy.…”

“…A similar exponential form ofQ •Q was introduced in [26] for the symplectic no-core shell-model calculations, which justifies the IBM form used in (40) is reasonable as long as the parameter ξ ≪ 1. The third and fourth order terms X 3 and X 4 in (40) are originated from the mapping result of a triaxial rotor Hamiltonian to that of the SU(3)-limit in the IBM [15,16]. Though the quadrupole operator in the SU(3)-limit and that in the O(6)-limit are different, they are quite the same in the large-N limit.…”

“…Firstly, it will be shown that a reasonably simplified configuration mixing scheme based on the O(6)-limit of the IBM-1 is analytically solvable, which could be useful in the analysis of experimental data of γ-soft nuclei such as 194 Pt. Secondly, it is demonstrated that the rotor extension [15,16] in the O(6)-limit of the IBM seems necessary in order to produce nonzero quadrupole moments with correct sign and O(6)-limit forbidden E2 transitions. It is futher revealed that almost all low-lying levels below 2.17MeV in 194 Pt can be well described by modifying the O(6)-type quadrupole-quadrupole interaction with an exponential form.…”

Al3+- Phenanthroline Xerogel for Dual Application: Catalyst for Knoevenagel Condensation and Fluorescent Chemosensor for Azo Dyes

“…Our research focuses on development of new organic and organic-inorganic hybrid materials for diverse applications. [10À16] In present manuscript, we have synthesized new metal organic xerogel 4 (named as AlPDAX) based on Al (III) and 1,10-phenanthroline-2,9-dicarboxylic acid (1). The xerogel is evaluated as a catalyst for Knoevenagel condensation and as chemosensor for recognition of azo dyes.…”