  We have investigated the nuclear shell effects at N=126 in the region of the
third peak of the r-process nucleosynthesis within the framework of the
relativistic mean-field theory using the Lagrangian model NL-SV1 with the
vector self-coupling of omega-meson. Our study encompasses even-even nuclei
with N=110-140 in the isotopic chains of Hf (Z=72) down to Ba (Z=56). It is
shown that the nuclear shell effects at N=126 remain strong even as one moves
far away from the line of the beta-stability. As the neutron drip line
approaches N=126, nuclei exhibit vanishingly small neutron separation energy.
However, going beyond the neutron drip line, we observe an interesting feature
in that some nuclei near N ~ 132-134 for the isotopic chains of Z=62-68 show
enhanced neutron separation energy. This is especially pronounced for the
isotopes of Gd (Z=64) and Dy (Z=66). These nuclei exhibit the phenomenon of
stability beyond the neutron drip line. Our analysis of the single-particle
spectrum shows that this is engendered by the deformation assumed by these
nuclei with the consequence that the neutron single-particle spectrum is pushed
down in energy, thus leading to enhanced stability beyond the drip line.
