On the intersection of the shell, collective and cluster models of atomic nuclei I: Multi-shell excitations

The relation of the shell, collective and cluster models of the atomic nuclei is discussed from the viewpoint of symmetries. In the fifties the U(3) symmetry was found as their common part for a single shell problem. For multi major-shell excitations, considered here, the U(3)$\otimes$U(3) dynamical symmetry turns out to be their intersection.