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Background: The ($\alpha$,n) and ($\alpha$,$\gamma$) reactions on $^{17,18}$Ohave significant impact on the neutron balance in the astrophysical$s$-process. In this scenario stellar reaction rates are required forrelatively low temperatures below $T_9 \lesssim 1$.  Purpose: The uncertainties of the $^{17,18}$O($\alpha$,n)$^{20,21}$Nereactions are investigated. Statistical model calculations are performed tostudy the applicability of this model for relatively light nuclei in extensionto 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 modelcalculations. Additionally, the reverse $^{20}$Ne(n,$\alpha$)$^{17}$O reactionis investigated, and similar studies for the $^{17}$F mirror nucleus areprovided.  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 thesecalculations. However, significant experimental uncertainties are identifiedfor the $^{17}$O($\alpha$,n$_0$)$^{20}$Ne(g.s.) channel.  Conclusions: The statistical model is able to predict astrophysical reactionrates for temperatures above 1 GK with uncertainties of less than a factor oftwo for the nuclei under study. An experimental discrepancy for the$^{17}$O($\alpha$,n)$^{20}$Ne reaction needs to be resolved.

physical review. c

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