H. G. Ganev

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

The structure of the {Delta}J=1 doublet bands in {sup 128}Cs is investigated within the framework of the interacting vector boson-fermion model. 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 noncompact supersymmetry group OSp(2{Omega}/12,R).

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{approx}130 region, namely {sup 126}Pr, {sup 134}Pr, and {sup 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.

Description of mixed-mode dynamics within the symplectic extension of the Interacting Vector Boson Model

In the algebraic Interacting Vector Boson Model (IVBM) it is assumed that the nuclear dynamics can be described by means of two types of vector “quasiparticles,” which are also characterized by another quantum number—a “T-spin” (an analogue to the F-spin). The non-compact symplectic group Sp(12, R) appears as the group of dynamical symmetry for the problem of two interacting vector bosons. The symplectic structure allows the change in the number of phonons, needed to build the collective states, that results in larger model spaces, which can accommodate the more complex structural effects as observed in the contemporary experiment. The applications of the IVBM are extended by exploiting three new subgroup chains in the reduction of 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. The first reduction that we exploit is one that extends the rotational limit of the number preserving version of the model; namely, Sp(12, R) ⊃ U(6) ⊃ U(2) ⊗ SU(3). Another limit of the symplectic IVBM, Sp(12, R) ⊃ Sp(2, R) ⊗ SO(6), contains in a natural way the 6-dimensional Davidson potential. In both of these cases, because collective modes can be mixed, we obtain successful descriptions of both positive and negative parity band configurations. The structure of band-head configurations, whose importance is established in the first two limits, is also examined in a third reduction, Sp(12, R) ⊃ Sp(4, R) ⊗ SO(3). The distributions of energies that are obtained in this limit with respect to the number of bosons that build each of the states with fixed angular momentum, enables one to distinguish typical collective vibrational and rotational spectra. This algebraic chain also provides important links between the subgroups of the other limits. The symplectic extension of the IVBM permits a richer classification of the states than its unitary version and is shown to be appropriate for a description of rather diverse nuclear spectra.

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 Sps12, Rd dynamical symmetry group to Sps 4, Rd ^ SOs3d, which defines basis states with fixed values of the angular momentum L. The relationship of the latter to Us6d , Us3d ^ Us2d, 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 =4 n 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.

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.

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.

Transition probabilities in the U(6) limit of the symplectic interacting vector boson model

The tensor properties of the algebra generators and the basis are determined in respect to the reduction chain Sp(

Six-dimensional Davidson potential as a dynamical symmetry of the symplectic interacting vector boson model

12,R

Analysis of new experimental data on the {sup 160}Dy spectrum with the symplectic interacting vector boson model

) \ensuremath{\supset} U(6) \ensuremath{\supset} U(3) \ensuremath{\bigotimes} U(2) \ensuremath{\supset} O(3) \ensuremath{\bigotimes} U(1), which defines one of the dynamical symmetries of the interacting vector boson model. The action of the Sp(

Description of Mixed-Mode Dynamics within the Symplectic Extension of the Interacting

12,R