An application of the 3-dimensional q-deformed harmonic oscillator to the nuclear shell model

An analysis of the construction of a q-deformed version of the 3-dimensional harmonic oscillator, which is based on the application of q-deformed algebras, is presented. The results together with their applicability to the shell model are compared with the predictions of the modified harmonic oscillator.Comment: 12 pages, LaTe

Molecular Spectra from Rotationally Invariant Hamiltonians Based on the Quantum Algebra SUq(2) and Irreducible Tensor Operators under SUq(2)

The rotational invariance under the usual physical angular momentum of the SUq(2) Hamiltonian for the description of rotational molecular spectra is explicitly proved and a connection of this Hamiltonian to the formalism of Amal'sky is provided. In addition, a new Hamiltonian for rotational spectra is introduced, based on the construction of irreducible tensor operators (ITOs) under SUq(2) and use of q-deformed tensor products and q-deformed Clebsch-Gordan coefficients. The rotational invariance of this SUq(2) ITO Hamiltonian under the usual physical angular momentum is explicitly proved and a simple closed expression for its energy spectrum (the ``hyperbolic tangent formula'') is introduced. Numerical tests against an experimental rotational band of HF are provided.Comment: 27 pages, LaTe

Symmetries and staggering effects in nuclear rotational spectra

We study the fine structure of nuclear rotational spectra on the basis of both dynamical and discrete symmetry approaches. In this framework we show that the odd--even (Delta I = 1) staggering effects observed in various rotational bands carry detailed information about the collective band-mixing interactions and the collective shape properties of heavy nuclei.Comment: LaTeX, 4 pages plus 1 figure (.ps). To appear in the proceedings of the European Conference on the Structure of the Nucleus at the Dawn of the Century (Bologna, Italy, 29/5/00-3/6/00), ed. G. Bonsignori et a

Simplified boson realization of the soq(3)so_q(3) subalgebra of uq(3)u_q(3) and matrix elements of soq(3)so_q(3) quadrupole operators

A simplified boson realization of the $so_q(3)$ subalgebra of $u_q(3)$ is constructed. A simplified form of the corresponding $so_q(3)$ basis states is obtained. The reduced matrix elements of a special second-rank tensor operator (quadrupole operator) are calculated in the $so_q(3)$ basis.Comment: 13 pages, LaTeX. Uses ioplppt.sty, iopl12.st

Rotationally Invariant Hamiltonians for Nuclear Spectra Based on Quantum Algebras

The rotational invariance under the usual physical angular momentum of the SUq(2) Hamiltonian for the description of rotational nuclear spectra is explicitly proved and a connection of this Hamiltonian to the formalisms of Amal'sky and Harris is provided. In addition, a new Hamiltonian for rotational spectra is introduced, based on the construction of irreducible tensor operators (ITO) under SUq(2) and use of q-deformed tensor products and q-deformed Clebsch-Gordan coefficients. The rotational invariance of this SUq(2) ITO Hamiltonian under the usual physical angular momentum is explicitly proved, a simple closed expression for its energy spectrum (the ``hyperbolic tangent formula'') is introduced, and its connection to the Harris formalism is established. Numerical tests in a series of Th isotopes are provided.Comment: 34 pages, LaTe

Rotations of nuclei with reflection asymmetry correlations

We propose a collective Hamiltonian which incorporates interactions capable to generate rotations in nuclei with simultaneous presence of octupole and quadrupole deformations. It is demonstrated that the model formalism could be applied to reproduce the staggering effects observed in nuclear octupole bands. On this basis we propose that the interactions involved would provide a relevant handle in the study of collective phenomena in nuclei and other quantum mechanical systems with reflection asymmetry correlations.Comment: LaTeX, 9 pages plus 3 figures given in separate .ps files. To appear in the proceedings of the International Conference on Nuclear Structure and Related Topics (Dubna, Russia, 6-10/6/2000), ed. R. Jolos, V. Voronov, et a

Sequence of Potentials Lying Between the U(5) and X(5) Symmetries

Starting from the original collective Hamiltonian of Bohr and separating the beta and gamma variables as in the X(5) model of Iachello, an exactly soluble model corresponding to a harmonic oscillator potential in the beta-variable (to be called X(5)-$\beta^2$) is constructed. Furthermore, it is proved that the potentials of the form $\beta^{2n}$ (with n being integer) provide a ``bridge'' between this new X(5)-$\beta^2$ model (occuring for n=1) and the X(5) model (corresponding to an infinite well potential in the beta-variable, materialized for n going to infinity. Parameter-free (up to overall scale factors) predictions for spectra and B(E2) transition rates are given for the potentials $\beta^2$, $\beta^4$, $\beta^6$, $\beta^8$, corresponding to E(4)/E(2) ratios of 2.646, 2.769, 2.824, and 2.852 respectively, compared to the E(4)/E(2) ratios of 2.000 for U(5) and 2.904 for X(5). Hints about nuclei showing this behaviour, as well as about potentials ``bridging'' the X(5) symmetry with SU(3) are briefly discussed.Comment: 18 pages, LaTeX, 5 postscript figure

Deformed Harmonic Oscillators for Metal Clusters: Analytic Properties and Supershells

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 Uq(3) > SOq(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.Comment: 25 pages LaTeX plus 21 postscript figure