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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
Simultaneous Description of Even-Even, Odd-Mass and Odd-Odd Nuclear Spectra
The orthosymplectic extension of the Interacting Vector Boson Model (IVBM) is
used for the simultaneous description of the spectra of different families of
neighboring heavy nuclei. The structure of even-even nuclei is used as a core
on which the collective excitations of the neighboring odd-mass and odd-odd
nuclei are built on. Hence, the spectra of the odd-mass and odd-odd nuclei
arise as a result of the consequent and self-consistent coupling of the fermion
degrees of freedom of the odd particles, specified by the fermion sector
, to the boson core which states
belong to an irreducible representation.
The theoretical predictions for different low-lying collective bands with
positive and negative parity for two sets of neighboring nuclei with distinct
collective properties are compared with experiment and IBM/IBFM/IBFFM
predictions. The obtained results reveal the applicability of the used
dynamical symmetry of the model.Comment: 6 pages, 1 figure, A talk given at the 7th International Conference
of the Balkan Physical Union, September 9-13, 2009, Alexandropoulos, Greec
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