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The possible exotic nuclear properties in the neutron-rich Ca, Ni, Zr, and Snisotopes are explored with the continuum Skyrme Hartree-Fock-Bogoliubov theoryformulated with the Green's function method. The available experimentaltwo-neutron separation energies $S_{\rm 2n}$ and one-neutron separationenergies $S_{\rm n}$ are well reproduced. Much shorter drip lines predicted by$S_{\rm n}$ are obtained compared with those by $S_{\rm 2n}$. The systematicstudies of the neutron pairing energies $-E_{\rm pair}$ shown that values ofthe odd-$A$ nuclei are much smaller in comparison with those of the neighboringeven-even nuclei due to the absent contribution of pairing energy by theunpaired odd neutron. By investigating the single-particle structures, the rmsradii and the density distributions, the possible halo structures in theneutron-rich Ca, Ni, and Sn isotopes are predicted, in which the sharpincreases of rms radii with significant deviations from the traditional$r\varpropto A^{1/3}$ rule and very diffuse spatial distributions in densitiesare observed. By analyzing the contributions of different partial waves to thetotal neutron density $\rho_{lj}(r)/\rho(r)$, the orbitals locating around theFermi surface especially those with low angular momenta are found the mainreason causing the extended nuclear density and large rms radii. Finally, thenumbers of the neutrons $N_{\lambda}$~($N_0$) occupied above the Fermi surface$\lambda_n$~(in the continuum) are discussed, the behaviors of which arebasically consistent with those of pairing energy, supporting the key role ofthe pairing correlations in the halo phenomena.

Continuum Skyrme Hartree-Fock-Bogoliubov theory with Green's function method for neutron-rich Ca, Ni, Zr, Sn isotopes