The bound state of three $\alpha$ particles is considered. For the $\alpha$-cluster model, we consider the Coulomb Green's function in the nucleus ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. The calculated binding energy of the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ nucleus is consistent with previous calculations.

• Received 30 June 1970

DOI:https://doi.org/10.1103/PhysRevC.4.302