\begin{document}$ S_{2n} $\end{document} and root mean square (rms) radii agree with the experimental data. It is shown that there is a halo structure in extremely neutron-rich \begin{document}$ ^{164-180} $\end{document}Te and \begin{document}$ ^{164-182} $\end{document}Xe, as well as a thick neutron skin in extremely neutron-rich Pd and Cd isotopes. From the numbers of neutrons (\begin{document}$ N_{_\lambda} $\end{document}) and (\begin{document}$ N_{_0} $\end{document}) occupying the levels above the Fermi surface and zero-potential energy level, it was found that pairing correlations play an important role in the formation of halo phenomena. These findings are further supported by investigating \begin{document}$ S_{2n} $\end{document}, rms radii, occupation probabilities, contributions of single-particle levels to the neutron rms radii, and density distributions. The neutron rms radii increased sharply, evidently deviating from the traditional rule \begin{document}$ r\propto N^{1/3} $\end{document}, and the density distributions were very diffuse. Finally, the contributions of different single-particle levels to the total neutron density and wavefunction are discussed. It was found that the sudden increase in the neutron rms radii and diffuse density distributions mainly arise from the resonant levels with a lower orbital angular momentum near the continuum threshold."> Systematic research on the ground state properties of medium-mass neutron-rich nuclei -
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