Indirect study of the12C(α,γ)16O reaction via the12C(7Li, t)16O transfer reaction

The ${}^{12}$C($\ensuremath{\alpha}$,$\ensuremath{\gamma}$)${}^{16}$O reaction plays a crucial role in stellar evolution. The rate of this reaction determines directly the ${}^{12}$C-to-${}^{16}$O abundance ratio at the end of the helium burning phase of stars and consequently has a big effect on the subsequent nucleosynthesis and even on the evolution of massive stars. However, despite many experimental studies, the low-energy cross section of ${}^{12}$C($\ensuremath{\alpha}$,$\ensuremath{\gamma}$)${}^{16}$O remains uncertain. The extrapolation of the measured cross sections to stellar energies ($E\ensuremath{\sim}300$ keV) is made particularly difficult by the presence of the 2${}^{+}$ (${E}_{x}=6.92$ MeV) and 1${}^{\ensuremath{-}}$ (${E}_{x}=7.12$ MeV)subthreshold states of ${}^{16}$O. To further investigate the contribution of these two subthreshold resonances to the ${}^{12}$C($\ensuremath{\alpha}$,$\ensuremath{\gamma}$)${}^{16}$O cross section, we determine their $\ensuremath{\alpha}$-reduced widths via a measurement of the transfer reaction ${}^{12}$C(${}^{7}$Li, $t$)${}^{16}$O at two incident energies, 28 and 34 MeV. The uncertainties on the determined $\ensuremath{\alpha}$-spectroscopic factors and the $\ensuremath{\alpha}$-reduced widths were reduced thanks to a detailed distorted-wave Born approximation analysis of the transfer angular distributions measured at the two incident energies. The $R$-matrix calculations of ${}^{12}$C($\ensuremath{\alpha}$,$\ensuremath{\gamma}$)${}^{16}$O cross section using our obtained $\ensuremath{\alpha}$-reduced widths for the 2${}^{+}$ and 1${}^{\ensuremath{-}}$ subthreshold resonances lead to an $E1$ $S$ factor at 300 keV of $100\ifmmode\pm\else\textpm\fi{}28$ keV b, which is consistent with values obtained in most of the direct and indirect measurements as well as the NACRE collaboration compilation while the result for the $E2$ component ${S}_{E2}\phantom{\rule{0.28em}{0ex}}(300\phantom{\rule{4.pt}{0ex}}\text{keV})=50\ifmmode\pm\else\textpm\fi{}19$ keV b disagrees with the NACRE adopted value.