We apply the Faddeev equations with separable potentials for the decay of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}_{}^{*}{}_{}{}^{} (J^{\pi }=1^{+}; 12.71 \mathrm{MeV})$ [formed in the reaction ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}({}_{}{}^3{}_{}{}^{}\mathrm{He},\alpha ){}_{}{}^{12}{}_{}{}^{}\mathrm{C}_{}^{*}{}_{}{}^{}$] via ${}_{}{}^8{}_{}{}^{}\mathrm{Be}$ ($2^{+}$; 2.9 MeV) into three $\alpha$ particles. The $\alpha$-particle energy spectrum is calculated. No effect of unitarity constraints (rescattering) is observed in the energy spectrum.

NUCLEAR REACTIONS ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}({}_{}{}^3{}_{}{}^{}\mathrm{He},\alpha ){}_{}{}^{12}{}_{}{}^{}\mathrm{C}_{}^{*}{}_{}{}^{}\to 3\alpha$, calculated $\alpha$-particle energy spectrum.

• Received 9 May 1977

DOI:https://doi.org/10.1103/PhysRevC.16.529