The astrophysical $S^{*}\left(E\right)$ factor for the ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ reaction within the Gamow window ($E_G=1.5\pm 0.3$ MeV) plays a pivotal role in modeling stellar carbon burning and explosive nucleosynthesis scenarios. However, direct measurements—or even simple extrapolations—at these energies are severely hindered by Coulomb suppression and the possible presence of narrow resonances. To address this challenge, we performed an indirect measurement of the ${}^{12}\mathrm{C}({}^{16}\mathrm{O},\alpha \mathit{p}){}^{23}\mathrm{Na}$ reaction at the HI-13 Tandem Accelerator, employing ${}^{16}\mathrm{O}=({}^{12}\mathrm{C}\oplus \alpha )$ as the Trojan horse nucleus. A key innovation of this Trojan horse method (THM) study is the implementation of a copper beam-stopper foil, which enabled the detection of spectator particles near $0^{\circ }$ –the angular region where their yield is maximized under quasi-free kinematics. The $S^{*}\left(E\right)$ factor for the ${}^{12}\mathrm{C}({}^{12}\mathrm{C},\mathit{p}){}^{23}\mathrm{Na}$ reaction in the astrophysically relevant energy range was extracted using the THM formalism based on the distorted-wave Born approximation (DWBA). Our results confirm the presence of resonant structures within the Gamow window around 1.5 MeV in both the $p_0$ and $p_1$ proton channels. No evidence of a hindrance effect is observed in the measured energy range. Without considering the resonance details, the overall trend of our results is qualitatively in reasonable agreement with the THM-Tumino2018 and TTIK2025 data, but differs significantly from the trend of the Modified-THM-Muk2019 data.

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• Nuclear astrophysics
• 20 ≤ A ≤ 38
• Cluster models
• Few-body systems
• Nuclear data analysis & compilation
• Nuclear reactions