One of the cluster behaviors observed in light nuclei such as 20 Ne and 44 Ti is the presence of an alpha particle rotating around a double magic number core. In this work, a theoretical method is used for investigation of rotational spectra of two-particle cluster states. To this end, Deng-Fan potential in addition to Hellman potential is used as the core and cluster potential. Next, given the Wildermuth condition, and proper quantum numbers describing the relative motion of the alpha particle and core, the rotational levels of 20 Ne and 44 Ti isotopes are calculated. Our studies show that the results are in good agreement with the available data.

In this paper, clustering energy was investigated in light alpha-conjugate nuclei considering cluster-cluster interaction instead of nucleon-nucleon interaction and using phenomenological non-microscopic method. The observed energy levels were calculated from rotational band of ⁸Be, ¹²C and ¹⁶O isotopes. The results showed that these isotopes, in their cluster state, have a non-spherical structure.

12C isotope composing 3[Formula: see text] cluster was investigated in this study. Therefore, 12C can be considered as a 3-body system. For studying the interactions in 3[Formula: see text] clusters, a central potential was applied. Jacobi relative coordinates were also employed and center of mass motion was removed. In this paper, the Klein–Gordon (K–G) equation was solved using Nikiforov–Uvarov potential. At the end, the energy spectrum and wave function of isotope 12C were determined and the results were compared with the experimental data which showed good coincidence reflecting the success of our model in prediction.

According to the experimental results, even–even light nuclei have cluster structures at some excited states. To study nuclei having two identical clusters we used a two-center potential well model. We calculated the energy levels by solving the Schrödinger equation and evaluating the effect of spin–orbit coupling in cylindrical coordinates. Finally, the results of calculations were applied for the 8Be isotope.