The branching ratio $\frac{{\Gamma }_{\mathrm{rad}}}{\Gamma }$ for the electromagnetic decay of the 7.655 MeV second excited state of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ has been measured by detecting the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(0.0 MeV) recoils in coincidence with $\alpha$ particles from the ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}({}_{}{}^3{}_{}{}^{}\mathrm{He}, {\alpha }_2){}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ (7.655 MeV) reaction at $E_{{}_{}{}^3{}_{}{}^{}\mathrm{He}}=4.00\mathrm{}$ MeV. Coincidence events were identified by means of time-of-flight, energy, and kinematic constraints. Thus, of all the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ nuclei formed in the second excited state, only those decaying to the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ ground state by either $\gamma$-ray or positron-electron pair emission were selected. Hence the experiment provides a direct measurement of $\frac{{\Gamma }_{\mathrm{rad}}}{\Gamma }$, where ${\Gamma }_{\mathrm{rad}}={\Gamma }_{\gamma }+{\Gamma }_{e\pm }$, and gives $\frac{{\Gamma }_{\mathrm{rad}}}{\Gamma }=(4.15\mathrm{}\pm 0.34)\times {10}^{-4\mathrm{}}$, which is in good agreement with other recent measurements, and suggests that the previously accepted value of $\frac{{\Gamma }_{\mathrm{rad}}}{\Gamma }=(2.9\mathrm{}\pm 0.3)\times {10}^{-4\mathrm{}}$ may be too low. The significance of this result is discussed with respect to helium burning rates in stars.

NUCLEAR REACTIONS ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}({}_{}{}^3{}_{}{}^{}\mathrm{He}, \alpha )$, $E=4.0\mathrm{}$ MeV; measured $\alpha$-${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ coin. ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ level deduced $\frac{{\Gamma }_{\mathrm{rad}}}{\Gamma }$. Enriched target.

• Received 13 May 1975

DOI:https://doi.org/10.1103/PhysRevC.12.1158