The possible exotic nuclear properties in the neutron-rich Ca, Ni, Zr, and Sn isotopes are examined with the continuum Skyrme Hartree–Fock–Bogoliubov theory in the framework of the Green’s function method. The pairing correlation, the couplings with the continuum, and the blocking effects for the unpaired nucleon in odd-A nuclei are properly treated. The Skyrme interaction SLy4 is adopted for the ph channel and the density-dependent δ\documentclass[12pt]{minimal}
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\begin{document}$$\delta$$\end{document} interaction is adopted for the pp channel, which well reproduce the experimental two-neutron separation energies S2n\documentclass[12pt]{minimal}
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\begin{document}$$S_\textrm{2n}$$\end{document} and one-neutron separation energies Sn\documentclass[12pt]{minimal}
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\begin{document}$$S_\textrm{n}$$\end{document}. It is found that the criterion Sn>0\documentclass[12pt]{minimal}
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\begin{document}$$S_\textrm{n}>0$$\end{document} predicts a neutron drip line with neutron numbers much smaller than those for S2n>0\documentclass[12pt]{minimal}
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\begin{document}$$S_\textrm{2n}>0$$\end{document}. Owing to the unpaired odd neutron, the neutron pairing energies -Epair\documentclass[12pt]{minimal}
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\begin{document}$$-E_\textrm{pair}$$\end{document} in odd-A nuclei are much lower than those in the neighboring even–even nuclei. By investigating the single-particle structures, the possible halo structures in the neutron-rich Ca, Ni, and Sn isotopes are predicted, where sharp increases in the root-mean-square (rms) radii with significant deviations from the traditional r∝A1/3\documentclass[12pt]{minimal}
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\begin{document}$$r\varpropto A^{1/3}$$\end{document} rule and diffuse spatial density distributions are observed. Analyzing the contributions of various partial waves to the total neutron density ρlj(r)/ρ(r)\documentclass[12pt]{minimal}
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\begin{document}$$\rho _{lj}(r)/\rho (r)$$\end{document} reveals that the orbitals located around the Fermi surface—particularly those with small angular momenta—significantly affect the extended nuclear density and large rms radii. The number of neutrons Nλ\documentclass[12pt]{minimal}
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\begin{document}$$N_{\lambda }$$\end{document} (N0\documentclass[12pt]{minimal}
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\begin{document}$$N_0$$\end{document}) occupying above the Fermi surface λn\documentclass[12pt]{minimal}
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\begin{document}$$\lambda _\text{n}$$\end{document} (continuum threshold) is discussed, whose evolution as a function of the mass number A in each isotope is consistent with that of the pairing energy, supporting the key role of the pairing correlation in halo phenomena.
