Geometric symmetries in light nuclei

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. This document is composed of an abstract and the slides of the presentation. (author)