Background: Recent experiments on $\beta$-delayed fission in the mercury-lead region and the discovery of asymmetric fission in ${}^{180}$Hg [A. N. Andreyev et al., Phys. Rev. Lett. 105, 252502 (2010)] 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 the prescission 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 multidimensional 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 both cases. The density distributions at scission configurations are studied and related to the experimentally observed mass splits.

Conclusions: The energy density functionals SkM${}^{*}$ 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 toward a 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${}^{*}$.

• Received 24 May 2012

DOI:https://doi.org/10.1103/PhysRevC.86.024601