Partial dynamical symmetries

Leviatan, A.

doi:10.1016/j.ppnp.2010.08.001

Cited by 75 publications

(97 citation statements)

References 146 publications

(454 reference statements)

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“…The concept of PDS [8] is a generalization of that of a dynamical symmetry (DS) [9] where the conditions of the latter (solvability of the complete spectrum, existence of exact quantum numbers for all eigenstates, and predetermined structure of the eigenfunctions) are relaxed and apply to only part of the eigenstates and/or of the quantum numbers. PDSs have been identified in various dynamical systems involving bosons and fermions (for a review, see Ref.…”

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confidence: 99%

Partial dynamical symmetry as a selection criterion for many-body interactions

2013

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We propose the use of partial dynamical symmetry (PDS) as a selection criterion for higher-order terms in situations when a prescribed symmetry is obeyed by some states and is strongly broken in others. The procedure is demonstrated in a first systematic classification of many-body interactions with SU(3) PDS that can improve the description of deformed nuclei. As an example, the triaxial features of the nucleus 156 Gd are analyzed. Many-body forces play an important role in quantum many-body systems [1]. They appear either at a fundamental level or as effective interactions which arise due to restriction of degrees of freedom and truncation of model spaces. A known example is the structure of light nuclei, where two-nucleon interactions are insufficient to achieve an accurate description and higher-order interactions between the nucleons must be included [2]. Given the difficulty in constraining the nature of such higher-order terms from experiments, one is faced with the problem of their determination. One way, currently the subject of active research [3], is to determine them from chiral effective field theory applied to quantum chromodynamics. This establishes a hierarchy of inter-nucleon interactions according to their order. In light-medium nuclei, these interactions serve as input for ab-initio methods (e.g., the no-core shell model (NCSM) [4]) to generate, by means of similarity transformations, A-body effective Hamiltonians in computational tractable model spaces.The situation is more complex in heavy nuclei, where ab-initio methods are limited by the enormous increase in size of the model spaces required to accommodate correlated collective motion of many nucleons. One possible approach to circumvent this problem, is to augment the NCSM method through a symplectic symmetry-adapted choice of basis [5]. A second approach is to employ energy density functionals and incorporate beyond mean-field effects by mapping to collective Hamiltonians [6], e.g., the interacting boson model (IBM) [7]. In both approaches the Hilbert spaces are based on particular dynamical algebras which lead to a dramatic reduction of the basis dimension. Nevertheless, even with such simplification, the number of possible interactions in the effective Hamiltonians grows rapidly with their order, and a selection criterion is called for. In this Rapid Communication, we suggest a method to select possible higher-order terms which is based on the idea of partial dynamical symmetry (PDS).The concept of PDS [8] is a generalization of that of a dynamical symmetry (DS) [9] where the conditions of the latter (solvability of the complete spectrum, existence of exact quantum numbers for all eigenstates, and predetermined structure of the eigenfunctions) are relaxed and apply to only part of the eigenstates and/or of the quantum numbers. PDSs have been identified in various dynamical systems involving bosons and fermions (for a review, see Ref.[8]). They play a role in diverse phenomena including nuclear and molecular spectroscopy [10][11][12], q...

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Partial dynamical symmetry as a selection criterion for many-body interactions

2013

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“…The essential idea is to relax the stringent conditions of complete solvability, so that only part of the eigenspectrum retains all the DS quantum numbers. Various types of bosonic and fermionic PDS are known to be relevant to nuclear spectroscopy [4][5][6][7][8][9][10][11][12][13]. In the present contribution we demonstrate the relevance of PDS to the odd-even staggering in the γ-band of 156 Gd [13].…”

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“…This effect can be visualized by plotting the quantity [3] One is thus confronted with the need to select suitable higher-order terms that can break the DS in the γ-band but preserve it in the ground and β bands. These are precisely the defining properties of a partial dynamical symmetry (PDS) [4]. The essential idea is to relax the stringent conditions of complete solvability, so that only part of the eigenspectrum retains all the DS quantum numbers.…”

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Partial dynamical symmetry and odd-even staggering in deformed nuclei

Leviatan

2015

EPJ Web of Conferences

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Abstract. Partial dynamical symmetry (PDS) is shown to be relevant for describing the odd-even staggering in the γ-band of 156 Gd while retaining solvability and good SU(3) symmetry for the ground and β bands. Several classes of interacting boson model Hamiltonians with SU(3) PDS are surveyed.A convenient starting point for describing axiallydeformed nuclei is the SU(3) limit of the interacting boson model (IBM) [1]. The latter limit corresponds to the chain of nested algebraswhere below each algebra the associated labels of irreducible representations (irreps) are given, and K is a multiplicity label. The eigenstates |[N](λ, μ)K, L are obtained with a Hamiltonian with SU(3) DS which has the formThe quadratic and cubic Casimir operators of SU(3) arê. The monopole (s) and quadrupole (d) bosons represent valence nucleon pairs whose total number N is conserved.Ĥ DS is completely solvable with eigenenergieswhere f 2 (λ, μ) = λ 2 +(λ+μ)(μ+3) and f 3 (λ, μ) = (λ−μ)(2λ+μ+ 3)(λ+2μ+3). The spectrum resembles that of a quadrupole axially-deformed rotor with eigenstates arranged in SU(3) multiplets and K corresponds geometrically to the projection of the angular momentum on the symmetry axis. The lowest SU(3) irrep (2N, 0) contains the ground band g(K = 0), while (2N − 4, 2) encompasses the β(K = 0) and γ(K = 2) bands. The in-band rotational spectrum is that of a rigid rotor with characteristic L(L + 1) splitting for all K-bands. A comparison with the experimental spectrum and E2 rates of 156 Gd is shown in Figs. 1-2 γ-band is quite poor. The latter display an odd-even staggering with pronounced deviations from a rigid-rotor pattern, indicative of a triaxial behavior. This effect can be visualized by plotting the quantity [3] Article available at

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“…The Hamiltonian of SU(3)-DS is composed of a linear combination of the Casimir operators of the SU(3) and O(3) groups. A twobody SU(3)-PDS Hamiltonian in the framework of IBM has the form [12] …”

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Description of 160Dy nucleus by partial dynamical SU(3) symmetry

Fouladi

Jafarizadeh²,

Fouladi

et al. 2013

Open Physics

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Abstract:We considered the characteristic features of SU(3) partial dynamical symmetry in the interacting boson model framework to show the relevance of such intermediate symmetry structure in the nuclear spectroscopy of the 160 Dy nucleus. The predictions of SU(3)-PDS for the energy spectrum and the transition probabilities were compared with the most recent experimental data and an acceptable degree of agreement was achieved. PACS

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Partial dynamical symmetries

Cited by 75 publications

References 146 publications

Partial dynamical symmetry as a selection criterion for many-body interactions

Partial dynamical symmetry as a selection criterion for many-body interactions

Partial dynamical symmetry and odd-even staggering in deformed nuclei

Description of 160Dy nucleus by partial dynamical SU(3) symmetry

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