Spontaneous ternary fission into medium-mass fragments is investigated within the self-consistent Hartree-Fock-plus-BCS method using the SLy6 Skyrme interaction with delta pairing. This work complements our previous study in the actinide region by extending it to two superheavy systems: ${}^{296}\mathrm{Lv}$ for its anticipated collinear tripartition involving two tin fragments, and ${}^{288}120$, examined in various equatorial (triangularlike) partitions that may emerge from the predicted superoblate shape of its second minimum. In the collinear case of ${}^{296}\mathrm{Lv}$, the calculated energy surfaces reveal no additional energy barrier associated with the chosen ternary channel. We quantify its dynamical suppression from the competition with the predominant binary decay by applying a simple Langevin-type model of overdamped motion with constant damping and temperature. Under assumptions designed to yield an upper bound, we find the tripartition probability per binary decay to be of the order of ${10}^{-6}$, larger than the corresponding predictions for actinides within the same approach. In the case of ${}^{288}120$, we compute the energy maps for several $A_1+2\times A_2$ symmetric triangular configurations. The resulting barrier heights, above 10 MeV, although lower than in simplified approaches, remain large enough to suppress these ternary modes.

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• Fission
• Nuclear fragmentation
• Nuclear reactions