Geometrical symmetries of nuclear systems: D(3h) and T(d) symmetries in light nuclei

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.

27 pages, 20 figures, 3 tables. Invited comment, Physica Scripta, Focus Issue of Nuclear Structure: Celebrating the 75 Nobel Prize

References in corpus (4)

• Structure and rotations of the Hoyle state
• Evidence for Triangular D_3h Symmetry in 12C
• Evidence for tetrahedral symmetry in 16O
• Higher-rank discrete symmetries in the IBM. I Octahedral shapes: general Hamiltonian

Cited by in corpus (8)

• Alpha particle clusters and their condensation in nuclear systems
• The Algebraic Cluster Model: Structure of 16O
• Cluster structure of light nuclei
• Angular momentum and parity projected multidimensionally constrained relativistic Hartree-Bogoliubov model
• Discrete symmetries in the cluster shell model
• First order Coriolis-coupling for rotational spectrum of a tetrahedrally-deformed core plus one-particle system
• Odd-mass nuclei in the cluster shell model
• Triangular symmetry in cluster nuclei