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Stellar carbon synthesis occurs exclusively via the $3\alpha$ process, inwhich three $\alpha$ particles fuse to form $^{12}$C in the excited Hoylestate, followed by electromagnetic decay to the ground state. The Hoyle stateis above the $\alpha$ threshold, and the rate of stellar carbon productiondepends on the radiative width of this state. The radiative width cannot bemeasured directly, and must instead be deduced by combining three separatelymeasured quantities. One of these quantities is the $E0$ decay branching ratioof the Hoyle state, and the current $10$\% uncertainty on the radiative widthstems mainly from the uncertainty on this ratio. The $E0$ branching ratio wasdeduced from a series of pair conversion measurements of the $E0$ and $E2$transitions depopulating the $0^+_2$ Hoyle state and $2^+_1$ state in $^{12}$C,respectively. The excited states were populated by the $^{12}$C$(p,p^\prime)$reaction at 10.5 MeV beam energy, and the pairs were detected with theelectron-positron pair spectrometer, Super-e, at the Australian NationalUniversity. The deduced branching ratio required knowledge of the protonpopulation of the two states, as well as the alignment of the $2^+_1$ state inthe reaction. For this purpose, proton scattering and $\gamma$-ray angulardistribution experiments were also performed. An $E0$ branching ratio of$\Gamma^{E0}_{\pi}/\Gamma=8.2(5)\times10^{-6}$ was deduced in the current work,and an adopted value of $\Gamma^{E0}_{\pi}/\Gamma=7.6(4)\times10^{-6}$ isrecommended based on a weighted average of previous literature values and thenew result. The new recommended value for the $E0$ branching ratio is about 14%larger than the previous adopted value of$\Gamma^{E0}_{\pi}/\Gamma=6.7(6)\times10^{-6}$, while the uncertainty has beenreduced from 9% to 5%.

Improved precision on the experimental E0 decay branching ratio of the Hoyle state