The ${}^{12}\mathrm{C}(\alpha ,\gamma ){}^{16}\mathrm{O}$ reaction plays a key role in the evolution of stars with masses of $M>0.55M_{\odot }$. The cross-section of the ${}^{12}\mathrm{C}(\alpha ,\gamma ){}^{16}\mathrm{O}$ reaction within the Gamow window ($E_{\text{c.m.}}=300\mathrm{keV}, T_9=0.2$) is extremely small (about ${10}^{-17}$ barn), which makes the direct measurement in a ground-based laboratory with existing techniques unfeasible. Up until now, the cross-sections at lower energies can only be extrapolated from the data at higher energies. However, two subthreshold resonances, located at $E_x=7.117\mathrm{MeV}$ and $E_x=6.917\mathrm{MeV}$, make this extrapolation more complicated. In this work, the 6.917 MeV subthreshold resonance in the ${}^{12}\mathrm{C}(\alpha ,\gamma ){}^{16}\mathrm{O}$ reaction was investigated via the ${}^{12}\mathrm{C}({}^{11}\mathrm{B},{}^7\mathrm{Li}){}^{16}\mathrm{O}$ reaction. The experiment was performed using the Q3D magnetic spectrograph at the HI-13 tandem accelerator. We measured the angular distribution of the ${}^{12}\mathrm{C}({}^{11}\mathrm{B},{}^7\mathrm{Li}){}^{16}\mathrm{O}$ transfer reaction leading to the 6.917 MeV state. Based on the finite-range distorted wave Born approximation (FRDWBA) and coupled-reaction-channel (CRC) analysis, we derived the asymptotic normalization coefficient (ANC) of the 6.917 MeV level in ${}^{16}\mathrm{O}$ to be ($1.10\pm 0.29$) $\times {10}^{10}{\mathrm{fm}}^{-1}$, with which the reduced $\alpha$ width was computed to be $18.0\pm 4.7\mathrm{keV}$ at the channel radius of 6.5 fm. Finally, we calculated the astrophysical $S_{E2}\left(300\right)$ factor of the ground-state transitions to be 46.2 $\pm$ 7.7 keV b. The result for the astrophysical $S_{E2}\left(300\right)$ factor confirms the values obtained in various direct and indirect measurements and presents an independent examination of the most important data in nuclear astrophysics.

• Received 26 April 2017
• Revised 13 November 2018

DOI:https://doi.org/10.1103/PhysRevC.99.025805