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

TL;DR

This study assesses the uncertainties in astrophysical reaction rates for $^{17,18}$O($ extalpha$,n)$^{20,21}$Ne and evaluates the statistical model's applicability for light nuclei, finding it reliable above 1 GK with some experimental discrepancies.

Contribution

It provides a comprehensive comparison of experimental data with statistical model calculations for light nuclei, extending the model's validation to nuclei with mass number less than 20.

Findings

Statistical model describes experimental data well above 1.5 GK.

Reaction rates are reliable within a factor of two above 1 GK.

Experimental uncertainties and discrepancies need further investigation.

Abstract

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.