New determination of the astrophysical $S_{E1}$ factor of the ${}_{12}C(\alpha ,\gamma ){}_{16}O$ reaction via the ${}_{12}C({}_{11}B,{}_7\mathrm{Li}){}_{16}O$ transfer reaction

The ${}_{12}C(\alpha ,\gamma ){}_{16}O$ reaction substantially influences the abundance ratios of the main isotopes of carbon and oxygen and hence has been regarded as the holy grail in nuclear astrophysics. Its importance lies in the fact that it significantly affects the yield of key elements and that it plays a crucial role in the study of the mass gap of black holes. This reaction's cross section is greatly influenced by the subthreshold state 7.117-MeV $1^{-}$ of ${}_{16}O$, which is challenging to determine. To study such states the $\alpha$-cluster transfer reaction can be helpful. In this work, the angular distribution of the ${}_{12}C({}_{11}B,{}_7\mathrm{Li}){}_{16}O$ reaction was measured, leading to the 7.117-MeV $1^{-}$ state at $E_{{}_{11}B}\left(\mathrm{lab}\right)=50$ MeV. By using the finite-range distorted-wave Born approximation and coupled-reaction-channel analysis, we obtained the asymptotic normalization coefficient (ANC) to be $(2.54\pm 0.40)\times {10}^{28}$ ${\mathrm{fm}}^{-1}$ and the reduced $\alpha$ width to be $4.92\pm 0.77$ keV at a channel radius of 6.5 fm. Then, by using the $R$-matrix code azure, we calculated the astrophysical $S$ factor of the ${}_{12}C(\alpha ,\gamma ){}_{16}O$ reaction and found that the astrophysical $S_{E1}$ (300) factor of the ground-state transitions is $55.3\pm 9.0$ keV b. This value is lower than what was found in previous works, indicating that the $S$ factor is highly sensitive to the ANC.