The shell structure of nuclei beyond $N=126$ relevant to the third peak at $A\approx 195$ in $r$-process nuclear abundances in investigated. Within the framework of the relativistic Hartree-Bogoliubov theory in deformed space, a comparative study of the response of nuclei with three different model Lagrangians, NL-SV1, SVI-2, and NL3, is made. Ground-state properties of even-even nuclei in the isotopic chains of $Z=58–72$ in the highly neutron-rich region are investigated. A comparison of binding energies with mass formulas shows that in the extreme region of the $r$-process path, the RMF model SVI-2 without nonlinearities of $\sigma$ and $\omega$ mesons shows an excellent agreement with the mass formula HFB-24. It is shown that in all the above Lagrangian models, in the neutron rich region between the shell closures $N=126$ and $N=184$, there is a preponderance of nuclides exhibiting coexistence of well-deformed prolate and oblate shapes in the ground state. A prolate ground state is shown to evolve smoothly to a coexisting oblate ground state via a near degeneracy with successive addition of neutrons. Induced by an onset of deformation for $N\ge 130$, nuclei approaching the $r$-process path are shown to exhibit enhanced stability in many isotopic chains $(Z>60)$. This has the effect of shifting the expected neutron drip line significantly farther into the neutron-rich region especially for the higher $Z$ chains. Consequences of the enhanced stability, the shape co-existence and degeneracy of shapes in nuclei on the $r$-process nucleosynthesis are discussed.

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• Nuclear structure & decays
• Quantum field theory
• r process
• 150 ≤ A ≤ 189
• 90 ≤ A ≤ 149
• Nuclear density functional theory