Radiative decay branching ratio of the Hoyle state

Background: 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 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. Purpose: 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 $^{12}{\rm C}$. Methods: 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. Results: A radiative branching ratio value of $\Gamma_{\rm{rad}}/\Gamma\times10^{4}=4.0\pm0.3({\rm stat.})\pm0.16({\rm syst.})$ was obtained. Conclusions: 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 et al. may be excluded.