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

The C-12(alpha, gamma)O-16 reaction plays a key role in the evolution of stars with masses of M > 0.55 M-circle dot. The cross-section of the C-12(alpha, gamma)O-16 reaction within the Gamow window (E-c.m. = 300 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 MeV and E-x = 6.917 MeV, make this extrapolation more complicated. In this work, the 6.917 MeV subthreshold resonance in the C-12(alpha, gamma)O-16 reaction was investigated via the C-12(B-11,Li- 7)O-16 reaction. The experiment was performed using the Q3D magnetic spectrograph at the HI-13 tandem accelerator. We measured the angular distribution of the C-12(B-11,Li- 7)O-16 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 O-16 to be (1.10 +/- 0.29) x 10(10) fm(-1), with which the reduced alpha width was computed to be 18.0 +/- 4.7 keV at the channel radius of 6.5 fm. Finally, we calculated the astrophysical S-E2(300) factor of the ground-state transitions to be 46.2 +/- 7.7 keV b. The result for the astrophysical S-E2(300) factor confirms the values obtained in various direct and indirect measurements and presents an independent examination of the most important data in nuclear astrophysics.