Geometrical symmetries of nuclear systems: \mathcal D _3h and \mathcal T _d symmetries in light nuclei

2016/06/03 by R. Bijker, Roelof Bijker · 2 citations
Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Cluster (spacecraft) #Discrete symmetry #Equilateral triangle #Geometry #Homogeneous space #Mathematical physics #Mathematics #Nuclear physics research studies #Physics #Quantum Chromodynamics and Particle Interactions #Rotational symmetry #Simple (philosophy) #Symmetry (geometry) #Tetrahedral symmetry #Tetrahedron #Theoretical physics #nucl-ex #nucl-th

paper · pdf · doi:10.1088/0031-8949/91/7/073005

published as Phys. Scr. 91 (2016) 073005 (24pp) · 27 pages, 20 figures, 3 tables. Invited comment, Physica Scripta, Focus Issue of Nuclear Structure: Celebrating the 75 Nobel Prize

arxiv created 2016/06/03 · openalex publication_date 2016/06/09 · arxiv updated 2016/06/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

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

Citations

• On the "Magic Numbers" in Nuclear Structure
• On the Consequences of the Symmetry of the Nuclear Hamiltonian on the Spectroscopy of Nuclei
• The Hoyle state in 12 C
• Properties of a generalized pseudo-spin system: Application of the time dependent mean field method to and SU(4) invariant hamiltonian
• Cluster states in nuclei as representations of aU(ν+1)group
• Viewpoint: Rotations of the Hoyle State in Carbon-12
• Algebraic Models of Hadron Structure
• �ber den Bau der Atomkerne. I
• Classical Electrodynamics

Cited by

• The Algebraic Cluster Model: Structure of 16O
• Discrete symmetries in the cluster shell model

Related

• On the symmetries of the 12C nucleus
• Geometrical analysis of the algebraic cluster model
• alpha-cluster correlations and symmetry breaking in light nuclei
• The Algebraic Cluster Model: Structure of 16O
• Spectrum and electromagnetic properties of ²⁴Mg in the Geometric α-cluster Model with D_4h symmetry at leading order