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The ${}^{12}\mathrm{C}(\alpha,\gamma){}^{16}\mathrm{O}$ reaction plays a keyrole in the evolution of stars with masses of $M >$ 0.55 $M_\odot$. Thecross-section of the ${}^{12}\mathrm{C}(\alpha,\gamma){}^{16}\mathrm{O}$reaction within the Gamow window ($E_\textrm{c.m.}$ = 300 keV, $T_\textrm9$ =0.2) is extremely small (about $10^{-17}$ barn), which makes the directmeasurement in a ground-based laboratory with existing techniques unfeasible.Up until now, the cross-sections at lower energies can only be extrapolatedfrom the data at higher energies. However, two subthreshold resonances, locatedat $E_x$ = 7.117 MeV and $E_x$ = 6.917 MeV, make this extrapolation morecomplicated. In this work, the 6.917 MeV subthreshold resonance in the${}^{12}\mathrm{C}(\alpha,\gamma){}^{16}\mathrm{O}$ reaction was investigatedvia the${}^{12}\mathrm{C}({}^{11}\mathrm{B},{}^{7}\mathrm{Li}){}^{16}\mathrm{O}$reaction. The experiment was performed using the Q3D magnetic spectrograph atthe 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 FRDWBA analysis,we derived the asymptotic normalization coefficient (ANC) of the 6.917 MeVlevel in $^{16}$O to be (1.10 $\pm$ 0.29) $\times 10^{10}$ fm$^{-1}$, withwhich the reduced $\alpha$ width was computed to be $18.0\pm4.7$ keV at thechannel radius of 6.5 fm. Finally, we calculated the astrophysical$S_{E2}(300)$ factor of the ground-state transitions to be 46.2 $\pm$ 7.7 keVb. The result for the astrophysical $S_{E2}(300)$ factor confirms the valuesobtained in various direct and indirect measurements and presents anindependent examination of the most important data in nuclear astrophysics.

physical review. c

Astrophysical $S_{E2}$ factor of the  ${}^{12}\mathrm{C}(\alpha,\gamma){}^{16}\mathrm{O}$ reaction through the  ${}^{12}\mathrm{C}({}^{11}\mathrm{B},{}^{7}\mathrm{Li}){}^{16}\mathrm{O}$  transfer reaction