Measurement of the ${}^{13}\mathrm{C}(\alpha ,n_0){}^{16}\mathrm{O}$ Differential Cross Section from 0.8 to 6.5 MeV

The cross section of the ${}^{13}\mathrm{C}(\alpha ,n){}^{16}\mathrm{O}$ reaction is needed for nuclear astrophysics and applications to a precision of 10% or better, yet inconsistencies among 50 years of experimental studies currently lead to an uncertainty of $\approx 15\%$. Using a state-of-the-art neutron detection array, we have performed a high resolution differential cross section study covering a broad energy range. These measurements result in a dramatic improvement in the extrapolation of the cross section to stellar energies potentially reducing the uncertainty to $\approx 5\%$ and resolving long standing discrepancies in higher energy data.

Figure 1

The differential cross sections of the present work for the ${}^{13}\mathrm{C}(\alpha ,n_0){}^{16}\mathrm{O}$ reaction, where different angles of measurement have been scaled by the indicated multiplicative factor.

Figure 2

Comparison of the present measurements with those of Refs. [35, 49, 50, 51, 52] and the $R$-matrix cross section from the ENDF/B VIII.0 evaluation [12] at ${\theta }_{\mathrm{lab}}=0°$ and two example angular distributions from this work.

Figure 3

Comparison of the present ${}^{13}\mathrm{C}(\alpha ,n_0){}^{16}\mathrm{O}$ data and that of Refs. [9, 52] to the ${}^{13}\mathrm{C}(\alpha ,n){}^{16}\mathrm{O}$ data of Brandenburg et al. [53]. The data above $E_{\alpha }\approx 5\mathrm{MeV}$ indicate strong contributions from excited state transitions.

Figure 4

$S$ factor for the ${}^{13}\mathrm{C}(\alpha ,n){}^{16}\mathrm{O}$ reaction at low energies. The shaded gray region indicates the uncertainty estimated by deBoer et al. [61]. The red region represents the 16% and 84% confidence limits obtained from the brick analysis with the present data. The percentages following each data set indicate the systematic uncertainty of that work. The data have been scaled according to the normalization factors obtained from the fit as given in the Supplemental Material [33]. The arrow indicates the Gamow energy range for $T=0.2\mathrm{GK}$.