The pole approximation that Narodetskii introduced into the theory of four-particle scattering is here applied to ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, which is assumed to be composed of four structureless α particles. The binding energy of the excited $0^{+}$ state of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ was calculated by using an Irving variational wave functions for the ground state of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and taking both Yukawa and exponential $\alpha \alpha$ potentials. In the light of earlier theoretical results on ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, comparing the present results with experiment suggests that at least for calculation of the bound states, the $\alpha$-particle model of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ is reasonable.

• Received 13 March 1972

DOI:https://doi.org/10.1103/PhysRevC.6.677