Astrophysical Reaction Rate for the Neutron-Generator Reaction ${}^{13}\mathrm{C}(\alpha ,n){}^{16}\mathrm{O}$ in Asymptotic Giant Branch Stars

The reaction ${}^{13}\mathrm{C}(\alpha ,n)$ is considered to be the main source of neutrons for the $s$ process in asymptotic giant branch stars. At low energies, the cross section is dominated by the $1/2^{+}$ 6.356 MeV subthreshold resonance in ${}^{17}\mathrm{O}$ whose contribution at stellar temperatures is uncertain by a factor of 10. In this work, we performed the most precise determination of the low-energy astrophysical $S$ factor using the indirect asymptotic normalization (ANC) technique. The $\alpha$-particle ANC for the subthreshold state has been measured using the sub-Coulomb $\alpha$-transfer reaction $({}^6\mathrm{Li},d)$. Using the determined ANC, we calculated $S(0)$, which turns out to be an order of magnitude smaller than in the nuclear astrophysics compilation of reaction rates.

Figure 1

Spectrum of deuterons from the ${}^6\mathrm{Li}({}^{13}\mathrm{C},d)$ reaction, at 6° with the 8.5 MeV ${}^{13}\mathrm{C}$ beam. The inset shows the level scheme of ${}^{17}\mathrm{O}$ [11]. The solid line is a Gaussian fit.

Figure 2

Angular distribution of the ${}^{13}\mathrm{C}({}^6\mathrm{Li},d){}^{17}\mathrm{O}(1/2^{+})$ reaction. Data taken at 8.5 MeV of ${}^{13}\mathrm{C}$ are shown as diamonds and 8.0 MeV data as boxes. The dashed and solid lines are DWBA calculations at ${}^{13}\mathrm{C}$ energies 8.31 and 7.81 MeV, respectively (see text).

Figure 3

$S$ factor of the ${}^{13}\mathrm{C}(\alpha ,n)$ reaction. The experimental data, corrected for electron screening, are from Refs. 4, 19. The best fit, obtained with a $0.4\times {10}^6\mathrm{MeV}\times b$ nonresonance contribution, is shown as the solid curve. The contribution of the $1/2^{+}$ state is shown as the dashed curve. The dashed-dotted curves represent a 28% uncertainty band due to the uncertainty in the $1/2^{+}S(0)$ factor. The dotted curves were calculated using a 0.2 and $0.6\times {10}^6\mathrm{MeV}\times b$ nonresonance contribution with $1/2^{+}S(0)$ factor of 1.8 and $3.2\times {10}^6\mathrm{MeV}\times b$, respectively, and represent the overall uncertainty band.

Figure 4

Rate of the ${}^{13}\mathrm{C}(\alpha ,n)$ reaction. The dashed-dotted curve is from Ref. 3; the solid curve is the rate obtained in this work. The yellow (light) band in the inset represents uncertainties from Ref. 3; new uncertainties are shown in red (dark).