Ternary fission of a heavy nuclear system within a three-center shell model

Background: Since more than 40 years of theoretical and experimental studies of true ternary fission, one is still quite far from its understanding. The true ternary fission channel, being strongly suppressed by the macroscopic properties of the potential energy, may, however, be present with a significant probability due to shell effects.Purpose: Development of a model for the multidimensional potential energy suitable for analysis of the nucleus-nucleus collisions with the possibility of ternary exit channel. Study of the potential possibility of fission of actinides into three heavy fragments.Method: The asymmetric three-center shell model of deformed nucleus is developed in this paper. The model can be applied for analysis of ternary as well as binary fission processes.Results: The potential energy surfaces for few ternary combinations in the fission channel are calculated for the $^{252}\mathrm{Cf}$ nucleus. Their properties are discussed.Conclusions: The potential energy structures are compared with the experimental observations. It was found that the potential energy has pronounced valleys favorable for ternary fission with formation of doubly magic tin as one of the fragments and two other lighter fragments. The positions of the found fission valleys are in a good agreement with the experimental data.

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