  Background: Recent experiments on beta-delayed fission in the mercury-lead
region and the discovery of asym- metric fission in 180 Hg [1] have stimulated
theoretical interest in the mechanism of fission in heavy nuclei. Purpose: We
study fission modes and fusion valleys in 180 Hg and 198 Hg to reveal the role
of shell effects in pre-scission region and explain the experimentally observed
fragment mass asymmetry and its variation with A. Methods: We use the
self-consistent nuclear density functional theory employing Skyrme and Gogny
energy density functionals. Results: The potential energy surfaces in
multi-dimensional space of collective coordinates, including elongation,
triaxiality, reflection-asymmetry, and necking, are calculated for 180 Hg and
198 Hg. The asymmetric fission valleys - well separated from fusion valleys
associated with nearly spherical fragments - are found in in both cases. The
density distributions at scission configurations are studied and related to the
experimentally observed mass splits. Conclusions: The energy density
functionals SkM\ast and D1S give a very consistent description of the fission
process in 180 Hg and 198 Hg. We predict a transition from asymmetric fission
in 180 Hg towards more symmetric distribution of fission fragments in 198 Hg.
For 180 Hg, both models yield 100 Ru/80 Kr as the most probable split. For 198
Hg, the most likely split is 108 Ru/90 Kr in HFB-D1S and 110 Ru/88 Kr in
HFB-SkM\ast.
