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

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

Collective states of the odd-mass nuclei within the framework of the Interacting Vector Boson Model

A supersymmetric extension of the dynamical symmetry group $Sp^{B}(12,R)$ of the Interacting Vector Boson Model (IVBM), to the orthosymplectic group $OSp(2\Omega/12,R)$ 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 $SO^{F}(2\Omega)\supset SU^{F}(2)$. 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 $^{157}Gd$, $^{173}Yb$ and $^{163}Dy$ from rare earth region are compared with the experiment. The $B(E2)$ transition probabilities for the $^{157}Gd$ and $^{163}Dy$ 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 $B(E2)$ behavior is revealed. The obtained results reveal the applicability of the models extension.Comment: 18 pages, 8 figure

New Description of the Doublet Bands in Doubly Odd Nuclei

The experimentally observed $\Delta I = 1$ 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 $A\sim 130$ region, namely $^{126}Pr$, $^{134}Pr$ and $^{132}La$. The theoretical predictions for the energy levels of the doublet bands as well as $E2$ and $M1$ 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

Structure of the doublet bands in doubly odd nuclei: The case of 128Cs^{128}Cs

The structure of the $\Delta J = 1$ doublet bands in $^{128}Cs$ is investigated within the framework of the Interacting Vector Boson Fermion Model (IVBFM). A new, purely collective interpretation of these bands is given on the basis of the used boson-fermion dynamical symmetry of the model. The energy levels of the doublet bands as well as the absolute $B(E2)$ and $B(M1)$ transition probabilities between the states of both yrast and yrare bands are described quite well. The observed odd-even staggering of both $B(M1)$ and $B(E2)$ values is reproduced by the introduction of an appropriate interaction term of quadrupole type, which produces such a staggering effect in the transition strengths. The calculations show that the appearance of doublet bands in certain odd-odd nuclei could be a consequence of the realization of a larger dynamical symmetry based on the non-compact supersymmetry group $OSp(2\Omega /12, R)$.Comment: 12 pages, 8 figure

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

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