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 \sim 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 .