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In this contribution, we present evidence for the occurrence of triangular symmetry in cluster nuclei. We discuss the structure of rotational bands for 3-alpha and 3-alpha+1 configurations with triangular D(3h) symmetry by exploiting the double group D(3h), and study the application to 12C and 13C. The structure of rotational bands can be used as a fingerprint of the underlying geometric configuration of alpha-particles.
We derive the rotation-vibration spectrum of a 3alpha+1 neutron (proton) configuration with triangular D(3h) symmetry by exploiting the properties of the double group D(3h), and show evidence for this symmetry to occur in the rotation-vibration spect
It is shown that the rotational band structure of the cluster states in 12C and 16O can be understood in terms of the underlying discrete symmetry that characterizes the geometrical configuration of the alpha-particles, i.e. an equilateral triangle f
We review recent studies of the cluster structure of light nuclei within the framework of the algebraic cluster model (ACM) for nuclei composed of k alpha-particles and within the framework of the cluster shell model (CSM) for nuclei composed of k al
After recapitulating the procedure to find the bands and the states occurring in the $mathcal{D}_{3h}$ alpha-cluster model of $^{12}$C in which the clusters are placed at the vertexes of an equilateral triangle, we obtain the selection rules for elec
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 alpha-particles in an equilateral triangle