Indirect Measurement of the ${\mathrm{S}}^{\ast }(\mathrm{E})$ Factor for ${}^{12}\mathrm{C}({}^{12}\mathrm{C},p){}^{23}\mathrm{Na}$ at Gamow Energies via the Trojan Horse Method with Near-0 degree Spectator Detection

Abstract

The astrophysical S*(E) factor for the 12C+12C reaction within the Gamow window 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 12C(16O,ap)23Na reaction at the HI-13 Tandem Accelerator, employing 16O=(12C+a) 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, the angular region where their yield is maximized under quasi-free kinematics. The S*(E) factor for the 12C(12C,p)23Na reaction in the astrophysically relevant energy range was extracted using the THM formalism based on the DWBA. Our results confirm the presence of resonant structures within the Gamow window around 1.5 MeV in both the p0 and p1 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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