Abstract
A three-alpha model calculation of the 12C nucleus by the Faddeev equation is carried out with a rank-4 separable alpha-alpha potential which takes the Pauli principle into account. We obtained almost all of the low-lying energy levels of the 12C nucleus. Probability distributions of the alpha particle in these states are illustrated by using the Hebach-Henneberg technique. The charge density, the electron-scattering form factor in the elastic channel and the quadrupole moment [ B( E2)] are also investigated. Effects of the three-body (cluster) force which originates from nucleon exchanges over the three-clusters are investigated in terms of phenomenological symmetric and semi-symmetric polarized three-body forces which have been discussed by Portilho-Agrello-Coon. It was found that the symmetric one can reproduce the low-lying energy levels of the 12C nucleus in the correct order; however, the use of a polarized three-body force is inconvenient. It is stressed that the inclusion of a three-body (cluster) force is very important to reproduce the experimental data.
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