The structure of light nuclei is considered using the $\alpha$ cluster model. On the basis of $\alpha$ clusters, the model structures of the nuclei ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$ and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ are proposed as composed of three particles. The bound state problems for these nuclei are solved using separable potentials, where the Faddeev equations are given. Three different types of the nonlocal separable potentials are used, i.e., potentials of the Yamaguchi, Gaussian, and Tabakin forms. The Gaussian and Tabakin potentials contain both attraction and repulsion. Solving the Faddeev equations, numerical calculations are performed for the resulting integral equations. The present theoretically calculated values of binding energies for these nuclei are in good agreement with the experimental data. The very close agreement between theoretical and experimental values of the binding energies indicates that the repulsive forces of the nuclear potential are very important and should be taken into account.

[NUCLEAR STRUCTURE ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$; three-body model. Calculated binding energies.]

• Received 22 March 1977

DOI:https://doi.org/10.1103/PhysRevC.17.341