On the shell model connection of the cluster model

Complete text of publication follows. The interrelation of basic nuclear structure models is a longstanding problem. The connection between the spherical shell model and the quadrupole collective model has been studied extensively, and symmetry considerations proved to be especially useful in this respect. A collective band was interpreted in the shell model language long ago as a set of states (of the valence nucleons) with a specific SU(3) symmetry. Furthermore, the energies of these rotational states are obtained to a good approximation as eigenvalues of an SU(3) dynamically symmetric shell model Hamiltonian. On the other hand the relation of the shell model and cluster model is less well explored. The connection of the harmonic oscillator (i.e. SU(3)) bases of the two approaches is known, but it was established only for the unrealistic harmonic oscillator interactions. Here we investigate the question: Can an SU(3) dynamically symmetric interaction provide a similar connection between the spherical shell model and the cluster model, like the one between the shell and collective models? In other words: whether or not the energy of the states of the cluster bands, defined by a specific SU(3) symmetries, can be obtained from a shell model Hamiltonian (with SU(3) dynamical symmetry). We carried out calculations within the framework of the semimicroscopic algebraic cluster model, in which not only the cluster model space is obtained from the full shell model space by an SU(3) symmetry-dictated truncation, but SU(3) dynamically symmetric interactions are also applied. Actually, Hamiltonians of this kind proved to be successful in describing the gross features of cluster states in a wide energy range. The novel feature of the present work is that we apply exclusively shell model interactions. The energies obtained from such a Hamiltonian for several bands of the (12C, 14C, 16O, 20Ne, 40Ca) + α systems turn out to be in good agreement with the experimental values. The present results show that te simple and transparent SU(3) connection between the spherical shell model and the cluster model is valid not only for the harmonic oscillator interactions, but for much more general (SU(3) dynamically symmetric) Hamiltonians as well, which result in realistic energy spectra. Via the shell model, the cluster picture is connected to the quadrupole collective model, too. (author)