We propose a three-body potential among alpha particles based on a single ${\alpha }^{*}$ excitation and adjust its parameters so that the experimental binding energy and charge radius of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ in the $3-\alpha$ model is obtained. With this potential we calculate the elastic and the $0_1^{+}$→$0_2^{+}$ inelastic form factor and reduced transition probabilities. The three-body potential in conjunction with an Ali-Bodmer two-body potential yields a satisfactory fit to the $0_1^{+}$→$0_2^{+}$ inelastic form factor and a very good agreement with the measured reduced transition probability.

NUCLEAR STRUCTURE $3-\alpha$ model of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, three-body potential among alpha particles, elastic and inelastic form factors of electron scattering, reduced transition probabilities.

• Received 29 November 1982

DOI:https://doi.org/10.1103/PhysRevC.27.2923