A measurement has been made of the branching ratio, $\frac{{\Gamma }_{\mathrm{rad}}}{\Gamma }$, for electromagnetic transitions from the 7.65-MeV state of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. This ratio is of particular interest in that the rate of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ synthesis in stellar helium burning is proportional to ${\Gamma }_{\mathrm{rad}}$. The 7.65-MeV state was excited by inelastic scattering of 24-MeV $\alpha$ particles on ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, and electromagnetic transitions were identified by detecting coincidences between the inelastic $\alpha$ particles and the associated ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ ions remaining after $\gamma$-ray or electron-pair emission. It was found that $\frac{{\Gamma }_{\mathrm{rad}}}{\Gamma }=(4.2\mathrm{}\pm 0.2)\times {10}^{-4\mathrm{}}$, which may be compared to the previous best value of (2.9±0.3)×${10}^{-4\mathrm{}}$. The new result, combined with available information on the width and branching ratio for electron-pair emission, leads to a radiative width ${\Gamma }_{\mathrm{rad}}={\Gamma }_{\gamma }+{\Gamma }_{e^{\pm }}=(3.9\mathrm{}\pm 1.2)$ meV.

[NUCLEAR STRUCTURE ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, 7.65-MeV state; measured $\frac{{\Gamma }_{\mathrm{rad}}}{\Gamma }$. Helium burning.]

• Received 10 September 1973

DOI:https://doi.org/10.1103/PhysRevC.9.69