Higher-rank discrete symmetries in the IBM I. Octahedral shapes: General Hamiltonian

Isacker, P. Van; Bouldjedri, A.; Zerguine, S.

doi:10.1016/j.nuclphysa.2015.03.003

Cited by 9 publications

(30 citation statements)

References 33 publications

(80 reference statements)

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“…The coefficients a 3µ and b 3µ have the interpretation of the shape variables appearing in the expansion (1). In contrast to the geometric model of Bohr and Mottelson [18] where deformation is associated with the entire nucleus, in the IBM it is generated by the valence nucleons only.…”

Section: The Sf Interacting Boson Modelmentioning

confidence: 99%

“…This paper is a continuation of Refs. [1,2], henceforth referred to as I and II, as part of a series concerning nuclear shapes with a higher-rank discrete symmetry in the framework of the interacting boson model (IBM) and its possible extensions [3]. In I and II we considered the case of hexadecapole deformation giving rise to shapes with octahedral symmetry and their manifestation in the sdg-IBM.…”

Section: Introductionmentioning

confidence: 99%

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Higher-rank discrete symmetries in the IBM. III Tetrahedral shapes

Van Isacker,

Bouldjedri,

Zerguine

2020

Preprint

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In the context of the sf -IBM, the interacting boson model with s and f bosons, the conditions are derived for a rotationally invariant and parity-conserving Hamiltonian with up to two-body interactions to have a minimum with tetrahedral shape in its classical limit. A degenerate minimum that includes a shape with tetrahedral symmetry can be obtained in the classical limit of a Hamiltonian that is transitional between the two limits of the model, U f (7) and SO sf (8). The conditions for the existence of such a minimum are derived. The system can be driven towards an isolated minimum with tetrahedral shape through a modification of two-body interactions between the f bosons. General comments are made on the observational consequences of the occurrence of shapes with a higher-rank discrete symmetry in the context of algebraic models.

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Section: The Sf Interacting Boson Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Higher-rank discrete symmetries in the IBM. III Tetrahedral shapes

Van Isacker,

Bouldjedri,

Zerguine

2020

Preprint

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“…This paper is the second in the series initiated with Ref. [1], henceforth referred to as I. The overall purpose of this series is the study of nuclear shapes with a higher-rank discrete symmetry, in particular of the tetrahedral or octahedral type, in the framework of a variety of interacting boson models.…”

Section: Introductionmentioning

confidence: 99%

Higher-rank discrete symmetries in the IBM. II Octahedral shapes: Dynamical symmetries

Bouldjedri

Zerguine

Isacker

2020

Preprint

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The symmetries of the sdg-IBM, the interacting boson model with s, d and g bosons, are studied as regards the occurrence of shapes with octahedral symmetry. It is shown that no sdg-IBM Hamiltonian with a dynamical symmetry displays in its classical limit an isolated minimum with octahedral shape. However, a degenerate minimum that includes a shape with octahedral symmetry can be obtained from a Hamiltonian that is transitional between two limits, U g (9) ⊗ U d (5) and SO sg (10) ⊗ U d (5), and the conditions for its existence are derived. An isolated minimum with octahedral shape, either an octahedron or a cube, may arise through a modification of two-body interactions between the g bosons. Comments on the observational consequences of this construction are made.

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“…It is the aim of this contribution to discuss the ACM for two-, three-and four-body clusters, and study possible applications in α-cluster nuclei, like 8 Be, 12 C and 16 O. In these applications, it is important to take into account the permutation symmetry between the identical α clusters.…”

Section: Introductionmentioning

confidence: 99%

Geometrical symmetries of nuclear systems: ${{ \mathcal D }}_{3h}$ and ${{ \mathcal T }}_{d}$ symmetries in light nuclei

Bijker¹

2016

Phys. Scr.

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Abstract. The role of discrete (or point-group) symmetries in α-cluster nuclei is discussed in the framework of the algebraic cluster model which describes the relative motion of the α-particles. Particular attention is paid to the discrete symmetry of the geometric arrangement of the α-particles, and the consequences for the structure of the corresponding rotational bands. The method is applied to study cluster states in the nuclei 12 C and 16 O. The observed level sequences can be understood in a simple way as a consequence of the underlying discrete symmetry that characterizes the geometrical configuration of the α-particles, i.e. an equilateral triangle with D 3h symmetry for 12 C, and a tetrahedron with T d symmetry for 16 O. The structure of rotational bands provides a fingerprint of the underlying geometrical configuration of α-particles.

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Higher-rank discrete symmetries in the IBM I. Octahedral shapes: General Hamiltonian

Abstract: In the context of the interacting boson model with s, d and g bosons, the conditions for obtaining an intrinsic shape with octahedral symmetry are derived for a general Hamiltonian with up to two-body interactions.

Cited by 9 publications

References 33 publications

Higher-rank discrete symmetries in the IBM. III Tetrahedral shapes

Higher-rank discrete symmetries in the IBM. III Tetrahedral shapes

Higher-rank discrete symmetries in the IBM. II Octahedral shapes: Dynamical symmetries

Geometrical symmetries of nuclear systems: ${{ \mathcal D }}_{3h}$ and ${{ \mathcal T }}_{d}$ symmetries in light nuclei

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