Three-body potential among alpha particles

Abstract

We propose a three-body potential among alpha particles based on a single ${\ensuremath{\alpha}}^{*}$ excitation and adjust its parameters so that the experimental binding energy and charge radius of $^{12}\mathrm{C}$ in the $3\ensuremath{-}\ensuremath{\alpha}$ model is obtained. With this potential we calculate the elastic and the ${0}_{1}^{+}$\ensuremath{\rightarrow}${0}_{2}^{+}$ 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 ${0}_{1}^{+}$\ensuremath{\rightarrow}${0}_{2}^{+}$ inelastic form factor and a very good agreement with the measured reduced transition probability.NUCLEAR STRUCTURE $3\ensuremath{-}\ensuremath{\alpha}$ model of $^{12}\mathrm{C}$, three-body potential among alpha particles, elastic and inelastic form factors of electron scattering, reduced transition probabilities.