Discrete symmetries in the cluster shell model

Abstract

The role of discrete (or point-group) symmetries is discussed in the framework of the Cluster Shell Model which describes the splitting of single-particle levels in the deformed field of cluster potentials. We discuss the classification of the eigenstates for the cases of a triangular and tetrahedral configuration of alpha-particles in terms of the irreducible representations of the double point groups D'(3h) and T'(d), respectively, and show how the discrete symmetry of a given eigenstate can be determined. Finally, we derive the Coriolis coupling for each one of these geometrical configurations.

13 pages, 5 figures, 4 tables, to be published in EPJ-ST on "Symmetries in Atomic Nuclei. New Perspectives"

References in corpus (7)

• Evidence for Triangular D_3h Symmetry in 12C
• Evidence for tetrahedral symmetry in 16O
• Alpha particle clusters and their condensation in nuclear systems
• Cluster structure of light nuclei
• Evidence for Triangular D'(3h) Symmetry in 13C
• Higher-rank discrete symmetries in the IBM. I Octahedral shapes: general Hamiltonian
• First order Coriolis-coupling for rotational spectrum of a tetrahedrally-deformed core plus one-particle system

Cited by in corpus (2)

• Cluster structure of 21Ne and 21Na
• Signatures of $\alpha$-clustering in ${}^{12}$C and ${}^{13}$C