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The 12C+12C fusion reaction at deep subbarrier energies is important for understanding the carbon burning process in massive star and explosive binary systems. However, its reaction rates are very difficult to measure directly or evaluate by simple extrapolation due to the extremely small cross sections and complex resonance structures near the Gamow window. In this work, we use one of its exit channels, i.e. 23Na+p to populate the excited states of the compound nucleus 24Mg via the conventional thick-target inverse kinematics method. By applying γ-charged particle coincidence, we have obtained excitation functions for the proton and α emission channels, respectively, and derived the resonance parameters through a simultaneous multi-channel R-matrix analysis. It is clear that a series of discrete resonances exist in the most relevant excitation energy region of 24Mg. The astrophysical S-factor of the 12C+12C fusion reaction is evaluated by adopting a systematic reduced width for the entrance channel. In particular, branching ratios of the dominant four decay channels are estimated across the entire Gamow window of the 12C+12C fusion reactions. Significant fluctuations are shown that may have strong impacts on the final outcome of the carbon burning process.

We present a precise measurement of the asymptotic normalization coefficient (ANC) for the ^16 O ground state (GS) through the ^12 C( ^11 B, ^7 Li) ^16 O transfer reaction using the Quadrupole‐3‐Dipole (Q3D) magnetic spectrograph. The present work sheds light on the existing discrepancy of more than 2 orders of magnitude between the previously reported GS ANC values. This ANC is believed to have a strong effect on the ^12 C( α , γ ) ^16 O reaction rate by constraining the external capture to the ^16 O ground state, which can interfere with the high-energy tail of the 2 ^+ subthreshold state. Based on the new ANC, we determine the astrophysical S -factor and the stellar rate of the ^12 C( α , γ ) ^16 O reaction. An increase of up to 21% in the total reaction rate is found within the temperature range of astrophysical relevance compared with the previous recommendation of a recent review. Finally, we evaluate the impact of our new rate on the pair-instability mass gap for black holes (BH) by evolving massive helium core stars using the MESA stellar evolution code. The updated ^12 C( α , γ ) ^16 O reaction rate decreases the lower and upper edges of the BH gap about 12% and 5%, respectively.