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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
Deformations of the Boson Representation and its Subalgebras
The boson representation of the sp(4,R) algebra and two distinct deformations
of it, are considered, as well as the compact and noncompact subalgebras of
each. The initial as well as the deformed representations act in the same Fock
space.
One of the deformed representation is based on the standard q-deformation of
the boson creation and annihilation operators. The subalgebras of sp(4,R)
(compact u(2) and three representations of the noncompact u(1,1) are also
deformed and are contained in this deformed algebra. They are reducible in the
action spaces of sp(4,R) and decompose into irreducible representations.
The other deformed representation, is realized by means of a transformation
of the q-deformed bosons into q-tensors (spinor-like) with respect to the
standard deformed su(2). All of its generators are deformed and have
expressions in terms of tensor products of spinor-like operators. In this case,
an other deformation of su(2) appears in a natural way as a subalgebra and can
be interpreted as a deformation of the angular momentum algebra so(3). Its
representation is reducible and decomposes into irreducible ones that yields a
complete description of the same
Analytic Formulae for the Matrix Elements of the Transition Operators in the Symplectic Extension of the Interacting Vector Boson Model
The tensor properties of all the generators of Sp(12,R) - the group of
dynamical symmetry of the Interacting Vector Boson Model (IVBM), are given with
respect to the reduction chain Sp(12,R) U(6) U(3) x U(2)
O(3) x U(1). Matrix elements of the basic building blocks of the
model are evaluated in symmetry adapted basis along the considered chain. As a
result of this, the analytic form of the matrix elements of any operator in the
enveloping algebra of the Sp(12,R), defining a certain transition operator, can
be calculated. The procedure allows further applications of the symplectic IVBM
for the description of transition probabilities between nuclear collective
states.Comment: 6 page
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
On the uniformly continuity of the solution map for two dimensional wave maps
The aim of this paper is to analyse the properties of the solution map to the Cauchy problem for the wave map equation with a source term, when the target is the hyperboloid that is embedded in . The initial data are in . We prove that the solution map is not uniformly continuous
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