77 research outputs found

### Axial asymmetry in the IVBM

The dynamical symmetry limit of the two-fluid Interacting Vector Boson Model
(IVBM), defined through the chain $Sp(12,R) \supset U(3,3) \supset U_{p}(3)
\otimes \overline{U_{n}(3)} \supset SU^{\ast}(3) \supset SO(3)$, is considered
and applied for the description of nuclear collective spectra exhibiting
axially asymmetric features. The effect of the introduction of a Majorana
interaction to the $SU^{\ast}(3)$ model Hamiltonian on the $\gamma$-band
energies is studied. The theoretical predictions are compared with the
experimental data for $^{192}Os$, $^{190}Os$, and $^{112}Ru$ isotopes. It is
shown that by taking into account the full symplectic structures in the
considered dynamical symmetry of the IVBM, the proper description of the energy
spectra and the $\gamma$-band energy staggering of the nuclei under
considerations can be achieved. The obtained results show that the potential
energy surfaces for the following two nuclei $^{192}Os$ and $^{112}Ru$, possess
almost $\gamma$-flat potentials with very shallow triaxial minima, suggesting a
more complex and intermediate situation between $\gamma$-rigid and
$\gamma$-unstable structures. Additionally, the absolute $B(E2)$ intraband
transition probabilities between the states of the ground state band and
$\gamma$ band, as well as the $B(M1)$ interband transition probabilities
between the states of the ground and $\gamma$ bands for the two nuclei
$^{192}Os$ and $^{190}Os$ are calculated and compared with experiment and for
the $B(E2)$ values with the predictions of some other collective models
incorporating the $\gamma$-rigid or $\gamma$-unstable structures. The obtained
results agree well with the experimental data and reveal the relevance of the
used dynamical symmetry of IVBM in the description of nuclei exhibiting axially
asymmetric features in their spectra.Comment: 10 pages, 10 figures. arXiv admin note: text overlap with
arXiv:1402.174

### 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
$SO^{F}(2\Omega)\subset OSp(2\Omega/12,R)$, to the boson core which states
belong to an $Sp^{B}(12,R)$ 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

### Microscopic shell-model counterpart of the Bohr-Mottelson model

In the present paper we demonstrate that there exists a fully microscopic
shell-model counterpart of the Bohr-Mottelson model by embedding the latter in
the microscopic shell-model theory of atomic nucleus within the framework of
the recently proposed fully microscopic proton-neutron symplectic model (PNSM).
For this purpose, another shell-model coupling scheme of the PNSM is considered
in which the basis states are classified by the algebraic structure $SU(1,1)
\otimes SO(6)$. It is shown that the configuration space of the PNSM contains a
six-dimensional subspace that is closely related to the configuration space of
the generalized quadrupole-monopole Bohr-Mottelson model and its dynamics
splits into radial and orbital motions. The group $SO(6)$ acting in this space,
in contrast, e.g., to popular IBM, contains an $SU(3)$ subgroup which allows to
introduce microscopic shell-model counterparts of the exactly solvable limits
of the Bohr-Mottelson model that closely parallel the relationship of the
original Wilets-Jean and rotor models. The Wilets-Jean-type dynamics in the
present approach, in contrast to the original collective model formulation, is
governed by the microscopic shell-model intrinsic structure of the symplectic
bandhead which defines the relevant Pauli allowed $SO(6)$, and hence $SU(3)$,
subrepresentations. The original Wilets-Jean dynamics of the generalized
Bohr-Mottelson model is recovered for the case of closed-shell nuclei, for
which the symplectic bandhead structure is trivially reduced to the scalar or
equivalent to it irreducible representation.Comment: 12 pages, no figure

### 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) $\supset$ U(6) $\supset$ U(3) x U(2)
$\supset$ 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

### Triaxial Shapes in the Interacting Vector Boson Model

A new dynamical symmetry limit of the two-fluid Interacting Vector Boson
Model (IVBM), defined through the chain $Sp(12,R) \supset U(3,3) \supset
U^{\ast}(3) \otimes SU(1,1) \supset SU^{\ast}(3) \supset SO(3)$, is introduced.
The $SU^{\ast}(3)$ algebra considered in the present paper closely resembles
many properties of the $SU^{\ast}(3)$ limit of IBM-2, which have been shown by
many authors geometrically to correspond to the rigid triaxial model. The
influence of different types of perturbations on the $SU^{\ast}(3)$ energy
surface, in particular the addition of a Majorana interaction and an O(6) term
to the model Hamiltonian, is studied. The effect of these perturbations results
in the formation of a stable triaxial minimum in the energy surface of the IVBM
Hamiltonian under consideration. Using a schematic Hamiltonian which possesses
a perturbed $SU^{\ast}(3)$ dynamical symmetry, the theory is applied for the
calculation of the low-lying energy spectrum of the nucleus $^{192}$Os. The
theoretical results obtained agree reasonably with the experimental data and
show a very shallow triaxial minimum in the energy surface for the ground state
in $^{192}$Os, suggesting that the newly proposed dynamical symmetry might be
appropriate for the description of the collective properties of different
nuclei, exhibiting triaxial features.Comment: 10 pages, 9 figure

### Phase Structure of the Interacting Vector Boson Model

The two-fluid Interacting Vector Boson Model (IVBM) with the U(6) as a
dynamical group possesses a rich algebraic structure of physical interesting
subgroups that define its distinct exactly solvable dynamical limits. The
classical images corresponding to different dynamical symmetries are obtained
by means of the coherent state method. The phase structure of the IVBM is
investigated and the following basic phase shapes, connected to a specific
geometric configurations of the ground state, are determined: spherical,
$U_{p}(3)\otimes U_{n}(3)$, $\gamma-$unstable, O(6), and axially deformed
shape, $SU(3)\otimes U_{T}(2)$. The ground state quantum phase transitions
between different phase shapes, corresponding to the different dynamical
symmetries and mixed symmetry case, are investigated.Comment: 9 pages, 10 figure

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