When ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ is treated as a bound system of three $\alpha$ particles interacting through the Ali-Bodmer $\alpha -\alpha$ force, as modified by Vallieres et al., we find using the Faddeev technique no 0+ excited state below the two-body threshold. When the $\alpha -\alpha$ force is made more attractive, a 0+ excited state eventually appears. It is not an Efimov state.

NUCLEAR STRUCTURE ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, examining 0+ excited state for Efimov characteristics through $\alpha -\alpha$ force.

• Received 21 April 1977

DOI:https://doi.org/10.1103/PhysRevC.18.1534