Using a new local cluster potential, cluster structures around double shell closures have been investigated. The calculations of spectra including electromagnetic transitions are in reasonable agreement with experimental data. Besides the nuclei, ${}^{20}$Ne, ${}^{44}$Ti, ${}^{60}$Zn, and ${}^{212}$Po, which have been intensively analyzed by cluster models, we have also studied two other good candidates, ${}^{52}$Ti and ${}^{136}$Te, for $\alpha$-cluster structure in neutron-rich regions. In ${}^{136}$Te, the unexpectedly small $B(E2;0^{+}\to 2^{+})$ would be due to the cluster characteristic. The new cluster potential without any readjustment of the parameter values has been also applied to the investigations of possible ${}^6$He-cluster structure in nuclei, ${}^{22}$Ne, ${}^{46}$Ti, ${}^{54}$Ti, ${}^{62}$Zn, and ${}^{138}$Te, which have the same doubly magic cores as the $\alpha$-cluster nuclei above. Similarly good results can be obtained, compared with experimental data. It is an advantage that the new cluster potential suits the different types of cluster structures with a set of fixed parameters which do not need any readjustment for different cluster-core structures.

• Received 27 October 2012

DOI:https://doi.org/10.1103/PhysRevC.87.014311