Background: The radiative branching ratio of the Hoyle state is crucial to estimate the triple-$\alpha$ reaction rate in stellar environments at medium temperatures of $T=0.1$ to 2 GK. Knowledge of the $\gamma$-decay channel is critical as this is the dominant radiative decay channel for the Hoyle state. A recent study by Kibédi et al. [Phys. Rev. Lett. 125, 182701 (2020)] has challenged our understanding of this astrophysically significant branching ratio and its constraints.

Purpose: The main purpose was to perform a new measurement of the $\gamma$-decay branching ratio of the Hoyle state to deduce the radiative branching ratio of the Hoyle state. An additional objective was to independently verify aspects of the aforementioned measurement conducted by Kibédi et al. [Phys. Rev. Lett. 125, 182701 (2020)].

Method: For the primary experiment of this work the Hoyle state was populated by the ${}^{12}\mathrm{C}(p,p^{\prime })$ reaction at 10.8 MeV at the Oslo Cyclotron Laboratory. The $\gamma$-decay branching ratio was deduced through triple-coincidence events, each consisting of a proton-ejectile energy corresponding to population of the $0_2^{+}$ Hoyle state, and the subsequent cascade of 3.21 and 4.44 MeV $\gamma$ rays. To verify the analysis, a surrogate $\gamma$-ray cascade from the $0_2^{+}$ state in ${}^{28}\mathrm{Si}$ was also studied. Following the same methodology, an independent analysis of the 2014 data published by Kibédi et al. [Phys. Rev. Lett. 125, 182701 (2020)] was carried out.

Results: From the main experiment of this work, a $\gamma$-decay branching ratio of the Hoyle state was determined as ${\mathrm{\Gamma }}_{\gamma }^{7.65}/{\mathrm{\Gamma }}^{7.65}=4.0\left(3\right)\times {10}^{-4}$, yielding a radiative branching ratio of ${\mathrm{\Gamma }}_{\text{rad}}/\mathrm{\Gamma }=4.1\left(4\right)\times {10}^{-4}$. The independent reanalysis of the 2014 experiment published by Kibédi et al. [Phys. Rev. Lett. 125, 182701 (2020)] in this work yielded ${\mathrm{\Gamma }}_{\gamma }^{7.65}/{\mathrm{\Gamma }}^{7.65}=4.5\left(6\right)\times {10}^{-4}$, with a corresponding radiative branching ratio of ${\mathrm{\Gamma }}_{\text{rad}}/\mathrm{\Gamma }=4.6\left(6\right)\times {10}^{-4}$.

Conclusions: The radiative branching ratio of the Hoyle state reported in this work is in excellent agreement with several recent studies, as well as the previously adopted ENSDF average of ${\mathrm{\Gamma }}_{\text{rad}}/\mathrm{\Gamma }=4.16\left(11\right)\times {10}^{-4}$. In this work, several issues were found in the analysis of Kibédi et al. [Phys. Rev. Lett. 125, 182701 (2020)], with the corrected values no longer being discrepant with the ENSDF average.

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• Hydrostatic stellar nucleosynthesis
• Nuclear reaction rates
• Nuclear reactions
• Nuclear structure & decays
• Radiative capture
• 6 ≤ A ≤ 19