In this contribution, we present the cluster shell model which is analogous to the Nilsson model, but for cluster potentials. Special attention is paid to the consequences of the discrete symmetries of three α-particles in an equilateral triangle configuration. This configuration is characterized by a special structure of the rotational bands which can be used as a fingerprint of the underlying geometric configuration. The cluster shell model is applied to the nucleus 13 C.
In this contribution, we present evidence for the occurrence of triangular symmetry in cluster nuclei. We discuss the structure of rotational bands for 3α and 3α +1 configurations with triangular D
3h
symmetry by exploiting the double group
D
3
h
′
and study the application to 12 C and 13C. The structure of rotational bands can be used as a fingerprint of the underlying geometric configuration of α particles.
In analogy with the Nilsson model, we calculate the splitting of spherical singleparticle levels in a deformed field, but for cluster potentials. We study applications to alphacluster nuclei with two, three and four alpha particles, in which the deformation corresponds to the relative distance between the alpha particles. The splitting of the single-particle levels is studied for the cases of a dumbbell, equilateral triangle and a regular tetrahedron. The observed patterns may be used to gain insight into how the single-particle levels evolve with deformation.
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