Linear chain structure of three alpha clusters in 13C

We investigate a linear chain configuration of three clusters with a neutron 13 C. To characterize this configuration, an operator P is introduced, which is the sum of parity inversion operators for each proton. The staes with positives expectation values for this operator are found to form a rotational band structure, and the moment of inertia agrees well with the experimentally suggested value. Allowing a small bending angle stabilizes the linear chain configuration of three clusters with a valence neutron, which is a hyper deformed stat