An application of the three-dimensional<b><i>q</i></b>-deformed harmonic oscillator to the shell model

Raychev, P. P.; Roussev, R. P.; Iudice, N. Lo; Terziev, P. A.

doi:10.1088/0954-3899/24/10/009

Cited by 19 publications

(51 citation statements)

References 39 publications

(68 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…One can easily see that the level scheme produced by the 3-dim q-HO with spin-orbit interaction reproduces very well the level scheme of the MHO with spin-orbit interaction 275 .…”

Section: -Dimensional Q-deformed Harmonic Oscillator With Q-deformedmentioning

confidence: 53%

Quantum groups and their applications in nuclear physics

Bonatsos

Daskaloyannis

1999

Progress in Particle and Nuclear Physics

197

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

“…One can easily see that the level scheme produced by the 3-dim q-HO with spin-orbit interaction reproduces very well the level scheme of the MHO with spin-orbit interaction 275 .…”

Section: -Dimensional Q-deformed Harmonic Oscillator With Q-deformedmentioning

confidence: 53%

Quantum groups and their applications in nuclear physics

Bonatsos

Daskaloyannis

1999

Progress in Particle and Nuclear Physics

197

203

View full text Add to dashboard Cite

show abstract

“…In this space a deformed angular momentum algebra, so q (3), can be defined [6]. The Hamiltonian of the 3-dimensional q-deformed harmonic oscillator is defined so that it satisfies the following requirements:…”

Section: The 3-dimensional Q-deformed Harmonic Oscillator (3-dim Q-ho)mentioning

confidence: 99%

“…It has been proved [6] that the Hamiltonian of the 3-dimensional q-deformed harmonic oscillator satisfying the above requirements takes the form…”

Section: The 3-dimensional Q-deformed Harmonic Oscillator (3-dim Q-ho)mentioning

confidence: 99%

Deformed harmonic oscillators for metal clusters: Analytic properties and supershells

et al. 2002

View full text Add to dashboard Cite

The analytic properties of Nilsson's Modified Oscillator (MO), which was first introduced in nuclear structure, and of the recently introduced, based on quantum algebraic techniques, 3-dimensional q-deformed harmonic oscillator (3-dim q-HO) with u q (3) ⊃ so q (3) symmetry, which is known to reproduce correctly in terms of only one parameter the magic numbers of alkali clusters up to 1500 (the expected limit of validity for theories based on the filling of electronic shells), are considered. Exact expressions for the total energy of closed shells are determined and compared among them. Furthermore, the systematics of the appearance of supershells in the spectra of the two oscillators is considered, showing that the 3-dim q-HO correctly predicts the first supershell closure in alkali clusters without use of any extra parameter.

show abstract

“…Evaluation of the high temperature expansion coefficients were done by mapping onto the computation of some matrix elements for the q-deformed harmonic oscillator. Raychev et al 8 calculated the deviations from the nuclear shell model using the q-deformed three-dimensional harmonic oscillator. Bonatsos, Lewis, Raychev and Terziev 9 demonstrated that the three-dimensional q-deformed harmonic oscillator correctly predicts the first supershell closure in alkali clusters without introducing additional parmeters.…”

Section: Introductionmentioning

confidence: 99%