Sub-CoulombαTransfers onC12and theC12(α,γ)O16SFactor

The ${}^{12}\mathrm{C}(\alpha ,\gamma {)}^{16}\mathrm{O}$ reaction is crucial for the understanding of He burning in massive stars, but the low-energy cross section is highly uncertain. To address this problem we have measured at sub-Coulomb energies total cross sections for the ${}^{12}\mathrm{C}{(}^6\mathrm{Li},d{)}^{16}\mathrm{O}$ and ${}^{12}\mathrm{C}{(}^7\mathrm{Li},t{)}^{16}\mathrm{O}$ reactions to the bound $2^{+}$ and $1^{-}$ states of ${}^{16}\mathrm{O}$. The data are analyzed to obtain the reduced $\alpha$ widths of these states. Together with capture and phase-shift data, these results provide for a more accurate determination of the low-energy $12\mathrm{C}(\alpha ,\gamma {)}^{16}\mathrm{O}$ $S$ factor: $S_{E1\mathrm{}}\left(0.3\mathrm{MeV}\right)=101\mathrm{}\pm 17\mathrm{keV}\mathrm{b}$ and $S_{E2\mathrm{}}\left(0.3\mathrm{MeV}\right){=42\mathrm{}}_{-23\mathrm{}}^{+16\mathrm{}}\mathrm{keV}\mathrm{b}$ for the $E1\mathrm{}$ and $E2\mathrm{}$ multipole components of the reaction.