A. I. Georgieva

Deformations of the fermion realization of the sp(4) algebra and its subalgebras

With a view towards future applications in nuclear physics, the fermion realization of the compact symplectic sp(4) algebra and its q-deformed versions are investigated. Three important reduction chains of the sp(4) algebra are explored in both the classical and deformed cases. The deformed realizations are based on distinct deformations of the fermion creation and annihilation operators. For the primary reduction, the su(2) substructure can be interpreted as either the spin, isospin or angular momentum algebra, whereas for the other two reductions su(2) can be associated with pairing between fermions of the same type or pairing between two distinct fermion types. Each reduction provides for a complete classification of the basis states. The deformed induced u(2) representations are reducible in the action spaces of sp(4) and are decomposed into irreducible representations.

Staggering behavior of 0^+ state energies in the Sp(4) pairing model

We explore, within the framework of an algebraic sp(4) shell model, discrete approximations to various derivatives of the energies of the lowest isovector-paired 0^+ states of atomic nuclei in the 40 <A < 100 mass range. The results show that the symplectic model can be used to successfully interpret fine structure effects driven by the proton-neutron (pn) and like-particle isovector pairing interactions as well as interactions with higher J multipolarity. A finite energy difference technique is used to investigate two-proton and two-neutron separation energies, observed irregularities found around the N=Z region, and the like-particle and pn isovector pairing gaps. A prominent staggering behavior is observed between groups of even-even and odd-odd nuclides. An oscillation, in addition to that associated with changes in isospin values, that tracks with alternating seniority quantum numbers related to the isovector pairing interaction is also found.

q-Deformation of symplectic dynamical symmetries in algebraic models of nuclear structure

With a view toward further nuclear structure applications of approaches based on quantum-deformed (or q-deformed) algebras, introduced to the authors by Yu.F. Smirnov, we construct a q analog of a boson realization of the symplectic noncompact sp(4, R) algebra together with a q analog of a fermion realization of the symplectic compact sp(4) algebra. The first study, on the q-deformed Sp(4,R) symmetry, is applied to the development of a q analog of the two-dimensional Interacting Boson Model with q-deformed SU(3) the underpinning dynamical symmetry group. An explicit realization in terms of q-tensor operators with respect to the standard suq(2) algebra is given. The group-subgroup structure of this framework yields the physical interpretation of the generators of the groups under consideration. The second symplectic algebra, the q-deformed sp(4), is applied to studying isovector pairing correlations in atomic nuclei. A specific q deformation of the sp(4) algebra is realized in terms of q deformed fermion creation and annihilation operators of the shell model. The generators of the algebra close on four distinct realizations of the uq(2) subalgebra. These reductions, which correspond to different types of pairing interactions, yield a complete classification of the basis states. An analysis of the role of the q deformation is based on a comparison of the results for energies of the lowest isovector-paired 0+ states in the deformed and nondeformed cases.

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.

Deformations of the boson sp(4,R) representation and its subalgebras

The boson representation of sp(4,R) algebra and two distinct deformations of it, spq(4,R) and spt(4,R), 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, , which is reducible into two irreducible representations acting in the subspaces + and - of . The deformed representation of spq(4,R) is based on the standard q-deformation of the boson creation and annihilation operators. The subalgebras of sp(4,R) (compact u(2) and noncompact u?(1,1) with ? = 0,?) are also deformed and their deformed representations are contained in spq(4,R). They are reducible in the + and - spaces and decompose into irreducible representations. In this way a full description of the irreducible unitary representations of uq(2) of the deformed ladder series uq0(1,1) and of two deformed discrete series uq?(1,1) are obtained. The other deformed representation, spt(4,R), is realized by means of a transformation of the q-deformed bosons into q-tensors (spinor-like) with respect to the suq(2) operators. All of its generators are deformed and have expressions in terms of tensor products of spinor-like operators. In this case, a deformed sut(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 in is reducible and decomposes into irreducible ones that yields a complete description of the same. The basis states in +, which require two quantum labels, are expressed in terms of three of the generators of the sp(4,R) algebra and are labelled by three linked integer parameters.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.

A MAPPING CONSTRUCTION FOR THE Q-DEFORMED SO(3) U(3) EMBEDDING

Anticipating subsequent applications in nuclear structure theory, a first construction of a Dyson mapping for a q-deformed u(3) algebra, relevant to this field, is presented. To achieve this, a q-deformed algebra is initially considered, realized in terms of tensor operators with respect to the standard and containing a q-deformed so(3) angular momentum algebra. The desired mapping is then realized in terms of two boson-type conjugated tensor operators of first rank. A key problem is to determine the commutation relations between them. Our construction is based on the requirement that subsets of the commutation relations of the original so(3) algebra is preserved. As a result the images of the so(3)-subalgebra of close the same commutation relations as the initial subalgebra of the angular momentum. In addition a q-deformed u(3) algebra, containing the so(3)-subalgebra of the images, is obtained. Its generators are the q-deformed components of a quadrupole operator, together with the images of the so(3)-subalgebra. In the limiting case the reduction , crucial to nuclear structure physics, is recovered.

Dynamical symmetries in contemporary nuclear structure applications

In terms of group theory—the language of symmetries, the concept of spontaneous symmetry breaking is represented in terms of chains of group-subgroup structures that define the dynamical symmetry of the system under consideration. This framework enables exact analytic solutions of the associated eigenvalue problems.

Description of Mixed‐mode Dynamics with Symplectic Interacting Vector Boson Model

The symplectic extension to Sp(12, R) of the unitary dynamical symmetry U(6)⊃U(3)⊗U(2)⊃O(3)⊗U(1) of the Interacting Vector Boson Model /IVBM/, that has been used for a description of only—well deformed even‐even nuclei is shown to also provide for the larger possibility of a description of mixed‐mode dynamics in this particular limit. This is due to the introduction of the dependence on the total number of the two kinds of bosons in the model Hamiltonian, as well as in the basis states from which they are built and than mapped onto the experimentally observed collective bands in nuclear spectra. Another advantage of the proposed model is the introduced algebraic definition of opposite parity states, which allows the description of bands of positive and negative parity. The larger limits of applications are demonstrated with examples of various types of heavy nuclei ranging from nearly spherical trough transitional to well deformed ones and for a the description of the key collective bands, starting from t...

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(

EXACTLY SOLVABLE PAIRING MODELS

12,R