A saga on the ${\hat{I}}^3$-decay branching ratio of the Hoyle state

Abstract

The radiative branching ratio of the Hoyle state is crucial to estimate the triple-$\hat{I}\pm$ reaction rate in stellar environments at medium temperatures of $T=0.1$ to 2 GK. Knowledge of the ${\hat{I}}^3$-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. The main purpose was to perform a new measurement of the ${\hat{I}}^3$-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 measurement conducted by Kibédi et al. For the primary experiment of this work the Hoyle state was populated by the ${}^{12}\text{C}(p,p^{\prime })$ reaction at 10.8 MeV at the Oslo Cyclotron Laboratory. The ${\hat{I}}^3$-decay branching ratio was deduced through triple-coincidence events between a proton populating the Hoyle state and the subsequent ${\hat{I}}^3$-ray cascade. An independent analysis of the 2014 data published by Kibédi et al. has been carried out. From the main experiment of this work, a ${\hat{I}}^3$-decay branching ratio of the Hoyle state was determined as $Γ_γ^{7.65}/Γ^{7.65}=4.0(3)\times 10^{-4}$, yielding a radiative branching ratio of $\hat{I}{“}_{\text{rad}}/\hat{I}“=4.1(4)\times 10^{-4}$. The reanalysis of the 2014 experiment in this work yielded $Γ_γ^{7.65}/Γ^{7.65}=4.5(6)\times 10^{-4}$, with a radiative branching ratio of $\hat{I}{“}_{\text{rad}}/\hat{I}“=4.6(6)\times 10^{-4}$. The measurements of the radiative branching ratio of the Hoyle state in this work is in excellent agreement with several recent studies, as well as the previously adopted ENSDF average of $\hat{I}{“}_{\text{rad}}/\hat{I}“=4.16(11)\times 10^{-4}$.