The impact of the Lipkin–Nogami (LN) method on a giant halo is investigated within the relativistic continuum Hartree–Bogoliubov (RCHB) theory. The ground-state properties of Ca isotopes obtained from RCHB and RCHB+LN calculations are presented. The results show that the LN correction does not change the range of Ca isotopes with a giant halo. Taking ⁶⁶Ca as an example, the neutron density distribution with LN correction is found to be slightly more diffused, which can be illustrated by the enlargement of the root mean square radius and the enhancement of the relative contribution in neutron $3s_{1/2}$ level.

The role of near neutron-drip-line nuclei in the rapid neutron-capture process ($r$-process) is studied with the classical $r$-process model. Simulations under different astrophysical conditions ($T$, $n_n$) show that $r$-process paths approach the neutron-drip line under low-temperature and high-neutron-density conditions. A sensitivity study reveals that variations in the nuclear masses of these exotic nuclei lead to obvious abundance variations in the $A=110-125$, $A=175-185$, $A=200-205$ and superheavy regions. By contrast, the $r$-process rare-earth peak and the $A=130,195$ peaks remain largely unaffected. The nuclei that obviously impact $r$-process abundances are mainly distributed in the region of $25\leq Z\leq 90$ and $50\leq N\leq 180$, with the nuclei around neutron magic numbers found to be particularly important for the $r$-process, even in the near-neutron-drip-line region.