Simplified modeling of cluster-shell competition in carbon isotopes

We study the cluster-shell competition in carbon isotopes. Two parameters are introduced for the ¹²C core to characterize the transition from a cluster state to a shell-model state as a measure of the cluster-shell competition: one expresses the relative distance between {α} clusters and the other does the dissolution of one of the {α} clusters. We show the energy curves as functions of these parameters. The calculation is performed by combining the simplified modeling of cluster-shell competition for the ¹²C core and AMD triple-S. As the neutron number increases, the α-α distance becomes smaller; on the contrary, the dissolution of {α} clusters is enhanced. The origins of the anomalously small $B(E2)$ value of ¹⁶C are discussed from cluster-shell competition point of view, and the appearance of pure cluster state around the 10 MeV region is suggested.