Uncertainty of the astrophysical ${}^{17,18}$O($\alpha$,n)${}^{20,21}$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 ${}^{17,18}$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 ${}^{17,18}$O($\alpha$,n)${}^{20,21}$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 ${}^{17,18}$O($\alpha$,n)${}^{20,21}$Ne reactions are compared to statistical model calculations. Additionally, the reverse ${}^{20}$Ne(n,$\alpha$)${}^{17}$O reaction is investigated, and similar studies for the ${}^{17}$F mirror nucleus are provided. Results: It is found that on average the available experimental data for ${}^{17}$O and ${}^{18}$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 ${}^{17}$O($\alpha$,n${}_0$)${}^{20}$Ne(g.s.) 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 ${}^{17}$O($\alpha$,n)${}^{20}$Ne reaction needs to be resolved.