Angular distributions for the ${}^{12}\mathrm{C}(p,p^{\prime }){}^{12}\mathrm{C}^{*}\left(7.65\mathrm{MeV}\right)$ reaction populating the Hoyle state have been measured at incident proton energies between 10.8 and 18.0 MeV. It extends the available experimental cross section data in the intermediate energy region and suggests a small resonance around 12.0 MeV. The measured cross sections along with the available data were used to evaluate the proton-induced deexcitation rates of the Hoyle state. The resulting enhancement factors for the triple-$\alpha$ reaction rate are found to differ substantially throughout the calculated temperature range, $0.1–10.0$ GK, and can be as much as $22\%$ higher than the previous estimate that relied on sparse experimental data. The observed deviation highlights the sensitivity of the enhancement to the underlying inelastic scattering cross sections. Further, the experimental data provides more reliable constraints for modeling ${}^{12}\mathrm{C}$ production in hot and dense stellar environments, especially in proton-rich astrophysical environments.

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• H & He induced nuclear reactions
• Inelastic scattering reactions
• Nuclear astrophysics
• Nuclear reaction rates
• Nuclear reactions
• 6 ≤ A ≤ 19