Uncertainty of the astrophysical ${}^{17,18}\mathrm{O}(\alpha ,n){}^{20,21}\mathrm{Ne}$ reaction rates and the applicability of the statistical model for nuclei with $A\lesssim 20$

Background: The $(\alpha ,n)$, and $(\alpha ,\gamma )$ reactions on ${}^{17,18}\mathrm{O}$ have significant impact on the neutron balance in the astrophysical $s$ process. In this scenario stellar reaction rates are required for relatively low temperatures below $T_9\lesssim 1$.

Purpose: The uncertainties of the ${}^{17,18}\mathrm{O}(\alpha ,n){}^{20,21}\mathrm{Ne}$ reactions are investigated. Statistical model calculations are performed to study the applicability of this model for relatively light nuclei in extension to a recent review for the $20\le A\le 50$ mass range.

Method: The available experimental data for the ${}^{17,18}\mathrm{O}(\alpha ,n){}^{20,21}\mathrm{Ne}$ reactions are compared with statistical model calculations. Additionally, the reverse ${}^{20}\mathrm{Ne}(n,\alpha ){}^{17}\mathrm{O}$ reaction is investigated, and similar studies for the ${}^{17}\mathrm{F}$ mirror nucleus are provided.

Results: It is found that, on average, the available experimental data for ${}^{17}\mathrm{O}$ and ${}^{18}\mathrm{O}$ are well described within the statistical model, resulting in reliable reaction rates above $T_9\gtrsim 1.5$ from these calculations. However, significant experimental uncertainties are identified for the ${}^{17}\mathrm{O}(\alpha ,n_0){}^{20}\mathrm{Ne}$ (ground state) channel.

Conclusions: The statistical model is able to predict astrophysical reaction rates for temperatures above 1 GK with uncertainties of less than a factor of two for the nuclei under study. An experimental discrepancy for the ${}^{17}\mathrm{O}(\alpha ,n){}^{20}\mathrm{Ne}$ reaction needs to be resolved.

Figure 1

Total ${}^{18}\mathrm{O}(\alpha ,n){}^{21}\mathrm{Ne}$ $S$ factor from neutron counting experiments [19, 20, 22, 36] and partial $(\alpha ,n_0)$ and $(\alpha ,n_1)$ cross section measurements [29] in comparison to talys calculations. The $(\alpha ,n_0)$ and $(\alpha ,n_1)$ data are scaled by factors of ${10}^{-2}$ and ${10}^{-4}$ for better visibility. For further discussion see text.

Figure 2

Total ${}^{17}\mathrm{O}(\alpha ,n){}^{20}\mathrm{Ne}$ $S$ factor from neutron counting experiments [19, 20, 22] and partial $(\alpha ,n_0)$ and $(\alpha ,n_1)$ cross section measurements [29] in comparison with talys calculations [total $(\alpha ,n)$ shown by full black line; $(\alpha ,n_0)$ shown by golden dotted line; $(\alpha ,n_1)$ shown by light green dashed line]. Further total $(\alpha ,n)$ data are measured by detection of the ${}^{20}\mathrm{Ne}$ recoil nucleus in inverse kinematics [24]. The $(\alpha ,n_0)$ and $(\alpha ,n_1)$ data are scaled by factors of ${10}^{-2}$ and ${10}^{-4}$ for better visibility. For further discussion see text.

Figure 3

Same as Fig. 2 for low energies. Above the opening of the $n_1$ channel at $E_{\alpha }=1293$ keV ($E_{\mathrm{c}.\mathrm{m}.}=1047$ keV), the Best data for the $n_0$ channel exceed the Bair and the Denker data and are also significantly above the talys prediction (golden dotted line). Below the $n_1$ threshold, the experimental data sets roughly agree. Note that, contrary to Fig. 2, the $(\alpha ,n_0)$ and $(\alpha ,n_1)$ data are not scaled. For further discussion see text.

Figure 4

Experimental cross section of the ${}^{20}\mathrm{Ne}(n,\alpha ){}^{17}\mathrm{O}$ reaction [25, 26, 27, 28] in comparison to a statistical model calculation. Because of the dominating ${\alpha }_0$ channel, the $(n,\alpha )$ data provide an additional constraint for the ${}^{17}\mathrm{O}(\alpha ,n_0){}^{20}\mathrm{Ne}$ cross section.

Figure 5

Same as Fig. 2 for the overlap region between the Best data for the $(\alpha ,n_0)$ channel and the converted $(n,\alpha )$ data of Johnson et al. [25] and Bell et al. [26]. The $(\alpha ,n_0)$ data are in significant disagreement with the $(n,\alpha )$ data. The talys calculation reproduces the average trend of the $(n,\alpha )$ data. For further discussion see text.

Figure 6

Experimental cross section of the ${}^{20}\mathrm{Ne}(p,\alpha ){}^{17}\mathrm{F}$ reaction [30] in comparison with a statistical model calculation. Similar to the ${}^{20}\mathrm{Ne}(n,\alpha ){}^{17}\mathrm{O}$ reaction, because of the dominating ${\alpha }_0$ channel the $(p,\alpha )$ data provide an additional constraint for the ${}^{17}\mathrm{F}(\alpha ,p_0){}^{20}\mathrm{Ne}$ cross section.

Figure 7

Reaction rate $N_A\langle \sigma v\rangle$ of the ${}^{18}\mathrm{O}(\alpha ,n){}^{21}\mathrm{Ne}$ reaction from the NACRE compilation, from the experimental resonance properties by Best et al. [29], and from the statistical model calculations using talys. The upper part (a) shows the rates $N_A\langle \sigma v\rangle$; the lower part (b) shows the rates normalized to the NACRE fit, including horizontal arrows which indicate the approximate validity of the different rates. For further discussion see text.

Figure 8

Reaction rate $N_A\langle \sigma v\rangle$ of the ${}^{17}\mathrm{O}(\alpha ,n){}^{20}\mathrm{Ne}$ reaction from the NACRE compilation, from the experimental resonance properties by Best et al. [23], and from the statistical model calculations using talys. The upper part (a) shows the rates $N_A\langle \sigma v\rangle$; the lower part (b) shows the rates normalized to the NACRE fit, including horizontal arrows which indicate the approximate validity of the different rates. For further discussion see text.

Figure 9

Ratio between the calculated $(\alpha ,n)$ cross sections, normalized to the standard potential of McFadden and Satchler [10], using different $\alpha$-nucleus potentials for (a) ${}^{18}\mathrm{O}$ and (b) ${}^{17}\mathrm{O}$. The calculated cross sections do not vary by more than a factor of two.