The ${}^{13}\mathrm{C}(\alpha ,n){}^{16}\mathrm{O}$ reaction is the main neutron source for the slow-neutron-capture process in asymptotic giant branch stars and for the intermediate process. Direct measurements at astrophysical energies in above-ground laboratories are hindered by the extremely small cross sections and vast cosmic-ray-induced background. We performed the first consistent direct measurement in the range of $E_{\mathrm{c}.\mathrm{m}.}=0.24$ to 1.9 MeV using the accelerators at the China Jinping Underground Laboratory and Sichuan University. Our measurement covers almost the entire intermediate process Gamow window in which the large uncertainty of the previous experiments has been reduced from 60% down to 15%, eliminates the large systematic uncertainty in the extrapolation arising from the inconsistency of existing datasets, and provides a more reliable reaction rate for the studies of the slow-neutron-capture and intermediate processes along with the first direct determination of the alpha strength for the near-threshold state.

We present a precise measurement of the asymptotic normalization coefficient (ANC) for the ¹⁶O ground state (GS) through the ¹²C(¹¹B, ⁷Li)¹⁶O 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 ¹²C(α, γ)¹⁶O reaction rate by constraining the external capture to the ¹⁶O 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 ¹²C(α, γ)¹⁶O 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 ¹²C(α, γ)¹⁶O reaction rate decreases the lower and upper edges of the BH gap about 12% and 5%, respectively.

The ${}^{12}\mathrm{C}(\alpha ,\gamma ){}^{16}\mathrm{O}$ reaction is one of the most crucial reactions in nuclear astrophysics. The $E2$ external capture to the ${}^{16}\mathrm{O}$ ground state (GS) has not been emphasized in previous analyses but may make a significant contribution to the ${}^{12}\mathrm{C}(\alpha ,\gamma ){}^{16}\mathrm{O}$ cross section depending on the value of the GS asymptotic normalization coefficient (ANC). In the present work, we determine this ANC to be $337\pm 45{\mathrm{fm}}^{-1/2}$ through the ${}^{12}\mathrm{C}({}^{11}\mathrm{B},{}^7\mathrm{Li}){}^{16}\mathrm{O}$ reaction using a high-precision magnetic spectrograph. This sheds light on the existing large discrepancy of more than 2 orders of magnitude between the previously reported ANC values. Based on the new ANC, we experimentally constrain the GS external capture and show that through interference with the high energy tail of the $2^{+}$ subthreshold state, a substantial enhancement in the GS $S_{E2}(300)$ factor can be obtained ($70\pm 7\mathrm{keV}\mathrm{b}$) compared to that of a recent review (45 keV b), resulting in an increase of the total $S$ factor from 140 to 162 keV b, which is now in good agreement with the value obtained by reproducing supernova nucleosynthesis calculations with the solar-system abundances. This work emphasizes that the external capture contribution for the ground state transition cannot be neglected in future analyses of the ${}^{12}\mathrm{C}(\alpha ,\gamma ){}^{16}\mathrm{O}$ reaction.