Discrete and continuous symmetries in α-cluster nuclei

Abstract

I discuss some properties of the algebraic cluster model which is based on the introduction of a spectrum generating algebra for the relative motion of the clusters. Particular attention is paid to the permutation symmetry of identical clusters. As an example, it is shown how the method can be used to study α-cluster configurations in 12C and 16O with point group symmetries, D3h and Td, respectively.