Fission modes of mercury isotopes

Background: Recent experiments on $\ensuremath{\beta}$-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${}^{*}$.

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