Boson representations of symplectic algebras

Georgieva, A. I.; Ivanov, M. I.; Raychev, P. P.; Roussev, R. P.

doi:10.1007/bf00668689

Cited by 24 publications

(26 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, the problem of constructing the su q (3)⊃so q (3) decomposition is a very difficult one. Since this decomposition is needed in constructing the q-deformed versions of several collective models, including the Elliott model 241,242,243,248 , the su(3) limit of the IBM 169,179,180 , the Fermion Dynamical Symmetry Model (FDSM) 249,250 , the Interacting Vector Boson Model (IVBM) 251,252,253,254 , the nuclear vibron model for clustering 255 , as well as the su(3) limit of the vibron model 256 for diatomic molecules, we report here the state of the art in this problem: i) As far as the completely symmetric irreps of su q (3) are concerned, the problem has been solved by Van der Jeugt 257,258,259,260,261 . This suffices for our needs in the framework of the toy IBM, since only completely symmetric su q (3) irreps occur in it.…”

Section: The So Q (3) Limitmentioning

confidence: 99%

Quantum groups and their applications in nuclear physics

Bonatsos

Daskaloyannis

1999

Progress in Particle and Nuclear Physics

198

203

View full text Add to dashboard Cite

Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical tools (q-numbers, q-analysis, q-oscillators, q-algebras), the su q (2) rotator model and its extensions, the construction of deformed exactly soluble models (u(3)⊃so (3) model, Interacting Boson Model, Moszkowski model), the 3-dimensional q-deformed harmonic oscillator and its relation to the nuclear shell model, the use of deformed bosons in the description of pairing correlations, and the symmetries of the anisotropic quantum harmonic oscillator with rational ratios of frequencies, which underly the structure of superdeformed and hyperdeformed nuclei, are discussed in some detail. A brief description of similar applications to the structure of molecules and of atomic clusters, as well as an outlook are also given.

show abstract

Section: The So Q (3) Limitmentioning

confidence: 99%

Quantum groups and their applications in nuclear physics

Bonatsos

Daskaloyannis

1999

Progress in Particle and Nuclear Physics

198

203

View full text Add to dashboard Cite

show abstract

“…In all cases the effect has been seen in several nuclei and its magnitude is clearly larger than the experimental errors. In cases 1) and 3) the relative displacement of the neighbours increases in general as a function of the angular momentum I [2,7], while in case 2) (octupole bands), the relevant models [8,9,10,11,12] predict constant displacement of the odd levels with respect to the even levels as a function of I, i.e. all the odd levels are raised (or lowered) by the same amount of energy.…”

Section: Introductionmentioning

confidence: 94%

Staggering Effects in Nuclear and Molecular Spectra

Bonatsos

Karoussos

Daskaloyannis

et al. 2001

New Trends in Quantum Systems in Chemistry and Physics

Self Cite

View full text Add to dashboard Cite

It is shown that the recently observed ∆J = 2 staggering effect (i.e. the relative displacement of the levels with angular momenta J, J + 4, J + 8, . . . , relatively to the levels with angular momenta J + 2, J + 6, J + 10, . . . ) seen in superdeformed nuclear bands is also occurring in certain electronically excited rotational bands of diatomic molecules (YD, CrD, CrH, CoH), in which it is attributed to interband interactions (bandcrossings). In addition, the ∆J = 1 staggering effect (i.e. the relative displacement of the levels with even angular momentum J with respect to the levels of the same band with odd J) is studied in molecular bands free from ∆J = 2 staggering (i.e. free from interband interactions/bandcrossings). Bands of YD offer evidence for the absence of any ∆J = 1 staggering effect due to the disparity of nuclear masses, while bands of sextet electronic states of CrD demonstrate that ∆J = 1 staggering is a sensitive probe of deviations from rotational behaviour, due in this particular case to the spin-rotation and spin-spin interactions.

show abstract

“…Note that the number of bosons N is not a good quantum number along the chain (24) and hence the U (6) irrep label [N ] 6 is irrelevant and will be omitted in the further considerations. The matrix elements of U (3, 3) generators can be calculated using the fact that the Hilbert state space is the tensor product of the p− and n−boson representation spaces [N p ] 3 and [N n ] * 3 , i.e.…”

Section: Matrix Elements Of the U (3 3)mentioning

confidence: 99%

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

Ganev¹

2012

Phys. Rev. C

View full text Add to dashboard Cite

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.

show abstract

Boson representations of symplectic algebras

Cited by 24 publications

References 14 publications

Quantum groups and their applications in nuclear physics

Quantum groups and their applications in nuclear physics

Staggering Effects in Nuclear and Molecular Spectra

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

Contact Info

Product

Resources

About