716 research outputs found
Energy Systematics of Low-lying Collective States within the Framework of the Interacting Vector Boson Model
In a new application of the algebraic Interacting Vector Boson Model (IVBM),
we exploit the reduction of its Sp(12,R) dynamical symmetry group to Sp(4,R) x
SO(3), which defines basis states with fixed values of the angular momentum L.
The relationship of the latter to $U(6) \subset U(3)x U(2), which is the
rotational limit of the model, means the energy distribution of collective
states with fixed angular momentum can be studied. Results for low-lying
spectra of rare-earth nuclei show that the energies of collective positive
parity states with L=0,2,4,6... lie on second order curves with respect to the
number of collective phonons n or vector bosons N=4n out of which the states
are built. The analysis of this behavior leads to insight regarding the common
nature of collective states, tracking vibrational as well as rotational
features.Comment: 8 pages, 5 figures, 4 table
Collective states of the odd-mass nuclei within the framework of the Interacting Vector Boson Model
A supersymmetric extension of the dynamical symmetry group of
the Interacting Vector Boson Model (IVBM), to the orthosymplectic group
is developed in order to incorporate fermion degrees of
freedom into the nuclear dynamics and to encompass the treatment of odd mass
nuclei. The bosonic sector of the supergroup is used to describe the complex
collective spectra of the neighboring even-even nuclei and is considered as a
core structure of the odd nucleus. The fermionic sector is represented by the
fermion spin group .
The so obtained, new exactly solvable limiting case is applied for the
description of the nuclear collective spectra of odd mass nuclei. The
theoretical predictions for different collective bands in three odd mass
nuclei, namely , and from rare earth region are
compared with the experiment. The transition probabilities for the
and between the states of the ground band are also
studied. The important role of the symplectic structure of the model for the
proper reproduction of the behavior is revealed. The obtained results
reveal the applicability of the models extension.Comment: 18 pages, 8 figure
Unified dynamical symmetries in the symplectic extension of the interacting vector boson model
The algebraic Interacting Vector Boson Model (IVBM) is extended by exploiting three new subgroup chains in the reduction of its highest symplectic dynamical symmetry group Sp(12, R) to the physical angular momentum subgroup SO(3). The corresponding exactly solvable limiting cases are applied to achieve a description of complex nuclear collective spectra of even-even nuclei in the rare earth and actinide regions up to states of very high angular momentum. First we exploit two reductions in which collective modes can be mixed, and obtain successful descriptions of both positive and negative parity band conflgurations. The structure of band-head conflgurations, whose importance is established in the flrst two limits, is examined in a third reduction, that also provides important links between the subgroups of the other limits. © 2008 IOP Publishing Ltd
Six-dimensional Davidson potential as a dynamical symmetry of the symplectic Interacting Vector Boson Model
A six-dimensional Davidson potential, introduced within the framework of the
Interacting Vector Boson Model (IVBM), is used to describe nuclei that exhibit
transitional spectra between the purely rotational and vibrational limits of
the theory. The results are shown to relate to a new dynamical symmetry that
starts with the reduction. Exact
solutions for the eigenstates of the model Hamiltonian in the basis defined by
a convenient subgroup chain of SO(6) are obtained. A comparison of the
theoretical results with experimental data for heavy nuclei with transitional
spectra illustrates the applicability of the theory.Comment: 9 pages, 4 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
Symplectic dynamical symmetries in algebraic models of nuclear structure
Based on a generalized reduction scheme for boson representations of symplectic algebras of the type Sp(4k,R), we consider the symplectic extension of a boson realization of compact unitary algebras for the k 1, k 3 and k 6 cases, which have relevance in nuclear structure theory. First we review an application of the k 1 case for the creation of a Sp(4, R) classification scheme, which is used for obtaining a generalized phenomenological description of important nuclear characteristics in terms of the classification quantum numbers for large sets of nuclei. Then for the k 3 and k 6 cases we outline some of the new possibilities that appear in the symplectic extensions of the Interacting Vector Boson Model (IVBM) and the Interacting Boson Model (IBM-2), respectively. The examples presented are used to describe the collective modes of the nuclear spectra in individual nuclei as well as in sequences of nuclei. © Published under licence by IOP Publishing Ltd
Deformations of the fermion realization of the sp(4) algebra and its subalgebras
With a view towards future applications in nuclear physics, the fermion
realization of the compact symplectic sp(4) algebra and its q-deformed versions
are investigated. Three important reduction chains of the sp(4) algebra are
explored in both the classical and deformed cases. The deformed realizations
are based on distinct deformations of the fermion creation and annihilation
operators. For the primary reduction, the su(2) sub-structure can be
interpreted as either the spin, isospin or angular momentum algebra, whereas
for the other two reductions su(2) can be associated with pairing between
fermions of the same type or pairing between two distinct fermion types. Each
reduction provides for a complete classification of the basis states. The
deformed induced u(2) representations are reducible in the action spaces of
sp(4) and are decomposed into irreducible representations.Comment: 28 pages, LaTeX 12pt article styl
Staggering effects in nuclear and molecular spectra
It is shown that the recently observed Delta 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 Delta 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 Delta J = 2 staggering (i.e. free from
interband interactions/bandcrossings). Bands of YD offer evidence for the
absence of any Delta J = 1 staggering effect due to the disparity of nuclear
masses, while bands of sextet electronic states of CrD demonstrate that Delta 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.Comment: LaTeX, 16 pages plus 30 figures given in separate .ps files. To
appear in the proceedings of the 4th European Workshop on Quantum Systems in
Chemistry and Physics (Marly-le-Roi, France, 1999), ed. J. Maruani et al.
(Kluwer, Dordrecht
New Description of the Doublet Bands in Doubly Odd Nuclei
The experimentally observed doublet bands in some odd-odd
nuclei are analyzed within the orthosymplectic extension of the Interacting
Vector Boson Model (IVBM). A new, purely collective interpretation of these
bands is given on the basis of the obtained boson-fermion dynamical symmetry of
the model. It is illustrated by its application to three odd-odd nuclei from
the region, namely , and . The
theoretical predictions for the energy levels of the doublet bands as well as
and transition probabilities between the states of the yrast band in
the last two nuclei are compared with experiment and the results of other
theoretical approaches. The obtained results reveal the applicability of the
orthosymplectic extension of the IVBM.Comment: 15 pages, 13 figure
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