Spectra of Phases of Clusterized Nuclei

In the theoretical understanding of nuclear structure, different models play a crucial role due to the complications of the quantum mechanical many-body problem. One of the fundamental models is the cluster model, based on the molecular picture. We investigate here the possible phases of nuclear clusterization in a quantitative way. In particular, the semimicroscopic algebraic cluster model is applied, in which the phases are defined by the dynamical symmetry limits. We construct detailed spectra corresponding to the shell-like, rigid-molecule-like and weak-coupled phases, and compare them. Special attention is focused on the role of the Pauli principle. The spectra of the limiting cases show dramatic differences, and only one of them harmonizes with this basic natural law. The experimentally observed ${}^{12}$C + $\alpha$ spectrum is considered for the discussion.