Radiative decay branching ratio of the Hoyle state

The triple-alpha process is a vital reaction in nuclear astrophysics, characterized by two consecutive reactions ($2\alpha\leftrightarrows{^{8}\rm{Be}}(\alpha,\gamma){^{12}\rm{C}}$) that drive carbon formation. The second reaction occurs through the Hoyle state, a 7.65 MeV excited state in ${^{12}\rm{C}}$ with $J^{\pi}=0^{+}$.The rate of the process depends on the radiative width, which can be determined by measuring the branching ratio for electromagnetic decay. Recent measurements by Kib\'edi, \textit{et al.} conflicted with the adopted value and resulted in a significant increase of nearly 50\% in this branching ratio, directly affecting the triple-alpha reaction. This work aims to utilize charged-particle spectroscopy with magnetic selection as a means to accurately measure the total radiative branching ratio ($\Gamma_{\rm{rad}}/\Gamma$) of the Hoyle state in $^{12}{\rm C}$. The Hoyle state in $^{12}{\rm C}$ was populated via $^{12}\rm{C}(\alpha, \alpha')^{12}\rm{C^{*}}$ inelastic scattering. The scattered $\alpha$-particles were detected using a $\Delta$E-E telescope, while the recoiled $^{12}{\rm C}$ ions were identified in a magnetic spectrometer. A radiative branching ratio value of $\Gamma_{\rm{rad}}/\Gamma\times10^{4}=4.0\pm0.3({\rm stat.})\pm0.16({\rm syst.})$ was obtained. The radiative branching ratio for the Hoyle state obtained in this work is in agreement with the original adopted value. Our result suggests that the proton-$\gamma$-$\gamma$ spectroscopy result reported by Kib\'edi \textit{et al.} may be excluded.