To study exotic odd nuclear systems, the self-consistent continuum Skyrme-Hartree-Fock-Bogoliubov theory formulated with Green's function technique is extended to include blocking effects with the equal filling approximation. Detailed formulas are presented. By comparing with box-discretized calculations, the great advantages of the Green's function method in describing the extended density distributions, resonant states, and the couplings with the continuum in exotic nuclei are shown. Taking the neutron-rich odd nucleus ${}^{159}\mathrm{Sn}$ as an example, the halo structure is investigated by blocking the lowest quasiparticle state. We find that it is mainly the weakly bound states near the Fermi surface that contribute a lot to the extended density distributions at large coordinate space. Finally, taking the neutron-rich Sn isotopes with mass numbers $A=122\text{–}178$ as examples, the halo structures are studied systematically. The small two-neutron separation energy and the low Fermi energy in a long mass range after the shell $N=82$ offer a good environment for the emergence of the halo structure. The neutron rms radius in ${}^{133}\mathrm{Sn}$ and the heavier isotopes display a steep increase with $A$ and deviate from the traditional rule of $r\propto A^{1/3}$. Correspondingly, the densities for those nuclei are very extended. Besides, the odd-even staggering of neutron radius $r_{\mathrm{rms}}$ is observed in the mass region $A=151\text{–}165$, due to the occupations of the odd neutrons on the low $p$ orbits.

• Received 8 January 2019

DOI:https://doi.org/10.1103/PhysRevC.99.054316