Theoretical study of the almost sequential mechanism of true ternary fission

We consider the collinear ternary fission which is a sequential ternary decay with a very short time between the ruptures of two necks connecting the middle cluster of the ternary nuclear system and outer fragments. In particular, we consider the case where the Coulomb field of the first massive fragment separated during the first step of the fission produces a lower pre-scission barrier in the second step of the residual part of the ternary system. In this case, we obtain a probability of about ${10}^{\ensuremath{-}3}$ per binary fission for the yield of massive clusters such as $^{70}\mathrm{Ni},^{80\ensuremath{-}82}\mathrm{Ge},^{86}\mathrm{Se}$, and $^{94}\mathrm{Kr}$ in the ternary fission of $^{252}\mathrm{Cf}$. These products appear together with the clusters having mass numbers of $A=132\char21{}140$. The results show that the yield of a heavy cluster such as $^{68\ensuremath{-}70}\mathrm{Ni}$ would be followed by a product of $A=138\char21{}148$ with a large probability as observed in the experimental data obtained with the FOBOS spectrometer at the Joint Institute for Nuclear Research. The third product is not observed. The landscape of the potential-energy surface shows that the configuration of the $\mathrm{Ni}+\mathrm{Ca}+\mathrm{Sn}$ decay channel is lower by about 12 MeV than that of the $\mathrm{Ca}+\mathrm{Ni}+\mathrm{Sn}$ channel. This leads to the fact that the yield of $\mathrm{Ni}$ and $\mathrm{Sn}$ is large. The analysis on the dependence of the velocity of the middle fragment on mass numbers of the outer products leads to the conclusion that, in the collinear tripartition channel of $^{252}\mathrm{Cf}$, the middle cluster has a very small velocity, which does not allow it to be found in experiments.