Suppression of genuine tripartition in heavy nuclei: A self-consistent perspective

TL;DR

This study uses a self-consistent microscopic approach to analyze ternary fission in heavy nuclei, revealing that such processes are strongly suppressed compared to binary decay channels, with probabilities estimated around 10^{-8} to 10^{-11}.

Contribution

It introduces a self-consistent Hartree-Fock plus BCS method to study ternary fission, highlighting the dynamic suppression of genuine tripartition in heavy nuclei.

Findings

Ternary fission modes are only visible under strong constraints on the middle fragment's mass.

Ternary fission probability is extremely low, around 10^{-8} to 10^{-11}.

Binary decay dominates over ternary fission in heavy nuclei.

Abstract

We investigate the ternary fissions of $^{252}$Cf (spontaneous) and $^{236}$U (neutron-induced) into medium-mass fragments, as reported by the Dubna group, using the Hartree-Fock plus BCS method with the SLy6 Skyrme interaction. Compared to microscopic-macroscopic methods used so far, this self-consistent approach provides a greater flexibility of nuclear shapes. Our working hypothesis is that the shape evolution proceeds while the system is still mononuclear. The results show that a ternary fission valley emerges for intermediate elongations of the middle fragment, only when its mass is strongly constrained. This ternary mode is dynamically suppressed by the competition with the dominant binary decay channel. This suggests that a description based solely on quantum tunneling through the energy barrier is insufficient to evaluate its probability. To quantify this suppression, we apply a simple Langevin-type model of overdamped motion with constant damping and temperature, supplemented by a basic estimate of quantum tunneling where relevant. Under assumptions expected to yield an upper bound, we find the probability of ternary fission per binary decay to be on the order of $10^{-8}-10^{-9}$ for $^{252}$Cf and $10^{-10}-10^{-11}$ for $^{236}$U.