42 research outputs found
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
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
q-Analogue of
A natural embedding for the
corresponding quantum algebras is constructed through the appropriate
comultiplication on the generators of each of the and
algebras. The above embedding is proved in their -boson realization by means
of the isomorphism between the (mn)(m)(n) algebras.Comment: 11 pages, no figures. In memory of professor R. P. Rousse
Multidimensional Isotropic and Anisotropic Q-Oscillator Models
q-oscillator models are considered in two and higher dimensions and their
symmetries are explored. New symmetries are found for both isotropic and
anisotropic cases. Applications to the spectra of triatomic molecules and
superdeformed nuclei are discussed.Comment: 12 Pages, LATEX, no figures, (Submitted to J. PHYS. A
In memoriam two distinguished participants of the Bregenz Symmetries in Science Symposia: Marcos Moshinsky and Yurii Fedorovich Smirnov
Some particular facets of the numerous works by Marcos Moshinsky and Yurii
Fedorovich Smirnov are presented in these notes. The accent is put on some of
the common interests of Yurii and Marcos in physics, theoretical chemistry, and
mathematical physics. These notes also contain some more personal memories of
Yurii Smirnov.Comment: Submitted for publication in Journal of Physics: Conference Serie
Unified description of magic numbers of metal clusters in terms of the 3-dimensional q-deformed harmonic oscillator
Magic numbers predicted by a 3-dimensional q-deformed harmonic oscillator
with Uq(3)>SOq(3) symmetry are compared to experimental data for atomic
clusters of alkali metals (Li, Na, K, Rb, Cs), noble metals (Cu, Ag, Au),
divalent metals (Zn, Cd), and trivalent metals (Al, In), as well as to
theoretical predictions of jellium models, Woods-Saxon and wine bottle
potentials, and to the classification scheme using the 3n+l pseudo quantum
number. In alkali metal clusters and noble metal clusters the 3-dimensional
q-deformed harmonic oscillator correctly predicts all experimentally observed
magic numbers up to 1500 (which is the expected limit of validity for theories
based on the filling of electronic shells), while in addition it gives
satisfactory results for the magic numbers of clusters of divalent metals and
trivalent metals, thus indicating that Uq(3), which is a nonlinear extension of
the U(3) symmetry of the spherical (3-dimensional isotropic) harmonic
oscillator, is a good candidate for being the symmetry of systems of several
metal clusters. The Taylor expansions of angular momentum dependent potentials
approximately producing the same spectrum as the 3-dimensional q-deformed
harmonic oscillator are found to be similar to the Taylor expansions of the
symmetrized Woods-Saxon and wine-bottle symmetrized Woods-Saxon potentials,
which are known to provide successful fits of the Ekardt potentials.Comment: 23 pages including 7 table
Ground-gamma band mixing and odd-even staggering in heavy deformed nuclei
It is proposed that the odd-even staggering (OES) in the - bands of
heavy deformed nuclei can be reasonably characterized by a discrete
approximation of the fourth derivative of the odd-even energy difference as a
function of angular momentum . This quantity exhibits a well developed
staggering pattern (zigzagging behavior with alternating signs) in rare earth
nuclei and actinides with long - bands (). It is shown that
the OES can be interpreted reasonably as the result of the interaction of the
band with the ground band in the framework of a Vector Boson Model
with SU(3) dynamical symmetry. The model energy expression reproduces
successfully the staggering pattern in all considered nuclei up to .
The general behavior of the OES effect in rotational regions is studied in
terms of the ground-- band-mixing interaction, showing that strong OES
effect occurs in regions with strong ground-- band-mixing interaction.
The approach used allows a detailed comparison of the OES in bands
with the other kinds of staggering effects in nuclei and diatomic molecules.Comment: 25 pages, 11 postscript figure
Delta I = 2 staggering in rotational bands of diatomic molecules as a manifestation of interband interactions
It is shown that the recently observed Delta I = 2 staggering seen in
superdeformed nuclear bands is also occurring in certain electronically excited
rotational bands of diatomic molecules. In the case of diatomic molecules the
effect is attributed to interband interactions (bandcrossings).Comment: LaTeX, 9 pages plus 24 figures given in separate .ps file