\begin{document}$ S_{n} $\end{document}) of a neutron-rich nucleus is proportional to the difference between the proton radii of mirror nuclei (\begin{document}$ R_{p}^{\rm mir} $\end{document}). This indicates that \begin{document}$ S_{n} $\end{document} may be deduced from \begin{document}$ R_{p}^{\rm mir} $\end{document}. Compared with the results of the Skyrme-Hartree-Fock model, pairing effects are found to enhance the correlation for most mirror pairs, whereas deformation effects may weaken the correlation. Furthermore, the correlation between \begin{document}$ S_{n} $\end{document} and \begin{document}$ R_{p}^{\rm mir} $\end{document} is studied for isotones with \begin{document}$ N=20 $\end{document} and \begin{document}$ N=28 $\end{document}, which reveals a stronger linear correlation with increasing \begin{document}$ |N-Z| $\end{document}. This result demonstrates that it is possible to extract the neutron-skin thickness of an unstable nucleus from the proton radii difference of the mirror nuclei of its isotones."> Investigation of the relationship between mirror proton radii and neutron-skin thickness -
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