Measurements of the ${}^{13}\mathrm{C}(\alpha ,n){}^{16}\mathrm{O}$ cross section up to $E_{\alpha }=8$ MeV

We present results from direct measurements of the total ${}^{13}\mathrm{C}(\alpha ,n){}^{16}\mathrm{O}$ cross section over laboratory energies $E_{\alpha }=2.9$–8.0 MeV, performed with the ${}^3{\mathrm{HeBF}}_3$ giant barrel neutron detector at the Edwards Accelerator Laboratory. The cross sections reported in this work are considerably lower than prior direct measurements for $E_{\alpha }>5$ MeV, in agreement with prior corrections based on Hauser-Feshbach estimates. However, applying branching ratios based on Hauser-Feshbach estimates to our data would not reproduce existing direct measurements for partial decay channels. This indicates both the promise and limitations of Hauser-Feshbach for branching ratio estimates of $(\alpha ,n)$ reactions on light nuclides. The ${}^{13}\mathrm{C}(\alpha ,n)$ thick-target yields inferred from this work for $E_{\alpha }>6$ MeV are significantly larger than those currently employed in estimates of dark matter and neutrino detector backgrounds.

Figure 1

${}^{13}\mathrm{C}(\alpha ,n)$ total cross section results from this work compared to direct measurements of Refs. [10, 11, 12]. The results of Ref. [11] have been multiplied by $\times 0.8$ as suggested by their note added in the proof. The data of Ref. [12] have also been adjusted as suggested by Ref. [15]. The upper panel shows the entire energy range measured in this work, while the lower panels show selected energy ranges. Uncertainties for this work are dominated by a correlated systematic uncertainty of 16%.

Figure 2

${}^{13}\mathrm{C}(\alpha ,n)$ total cross section results from this work compared to direct measurements of Ref. [12], the adjusted data of Ref. [12] suggested by Ref. [15], the $(\alpha ,n_0)$ results from Ref. [2], and the $(\alpha ,n_0)$ results obtained by applying the $n_0$ branching calculated in Ref. [15] to the total cross section reported in this work (“approx $n_0$”). Results are also shown for $(\alpha ,n_0)$ when applying reciprocity (using EXFOR [30]) to the ${}^{16}\mathrm{O}(n,\alpha )$ data of Refs. [17, 18]. Uncertainties for this work are dominated by a correlated systematic uncertainty of 16%.

Figure 3

${}^{\mathrm{nat}}\mathrm{C}(\alpha ,n)$ thick-target yields, assuming a carbon target with natural abundances [this energy range is below the ${}^{12}\mathrm{C}(\alpha ,n)$ threshold.], calculated using our cross section data for $E_{\alpha }>5$ MeV and the data of Ref. [12] below (HeBGB), where the bands of each represent their total uncertainties, compared to yields resulting from the evaluated cross section of Ref. [20] (JENDL/AN 2005), as well as measured ${}^{\mathrm{nat}}\mathrm{C}(\alpha ,n)$ thick-target yields from Ref. [38]. The ${}^{232}\mathrm{Th}$ and ${}^{238}\mathrm{U}$ decay series $E_{\alpha }$ with decay branches greater than 1% are also shown by the $\times$ and $+$, respectively.