Eur. Phys. J. Special Topics 229, 2353–2366 (2020)
https://doi.org/10.1140/epjst/e2020-000006-0

Regular Article

Discrete symmetries in the cluster shell model

Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A.P. 70-543, 04510 México D.F., Mexico

^a e-mail: bijker@nucleares.unam.mx

Received: 18 January 2020
Accepted: 28 August 2020
Published online: 23 October 2020

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 α-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.