  We have investigated nuclear shell effects across the magic number N=126 in
the region of the r-process path. Microscopic calculations have been performed
using the relativistic Hartree-Bogoliubov approach within the framework of the
RMF theory for isotopic chains of rare-earth nuclei in the r-process region.
The Lagrangian model NL-SV1 with the inclusion of the vector self-coupling of
omega meson has been employed. The RMF results show that the shell effects at
N=126 remain strong and exhibit only a slight reduction in the strength in
going from the r-process path to the neutron drip line. This is in striking
contrast to a systematic weakening of the shell effects at N=82 in the
r-process region predicted earlier in the similar approach. In comparison the
shell effects with microscopic-macroscopic mass formulae show a near constancy
of shell gaps leading to strong shell effects in the region of r-process path
to the drip line. A recent analysis of solar-system r-process abundances in a
prompt supernova explosion model using various mass formulae including the
recently introduced mass tables based upon HFB approach shows that whilst mass
formulae with weak shell effects at N=126 give rise to a spread and an
overproduction of nuclides near the third abundance peak at A~190, mass tables
with droplet models showing stronger shell effects are able to reproduce the
abundance features near the third peak appropriately. In comparison, several
analyses of the second r-process peak at A~130 have required weakened shell
effects at N=82. Our predictions in the RMF theory with NL-SV1, which exhibit
weaker shell effects at N=82 and stronger one at N=126 in the r-process region,
support the conjecture that a different nature of the shell effects at the
magic numbers may be at play in r-process nucleosynthesis of heavy nuclei.
