Cluster description of cold (neutronless) α ternary fission of ${}^{252}\mathrm{Cf}$

A coplanar three body cluster model (two deformed fragments and an α particle) similar to the model used for the description of cold binary fission was employed for the description of cold (neutronless) α accompanied fission of ${}^{252}\mathrm{Cf}.$ No preformation factors were considered. The three body potential was computed with the help of a double folding potential generated by the M3Y-NN effective interaction and realistic fragment ground state deformations. From the minimum action principle, the α particle trajectory equations, the corresponding ternary barriers, and an approximate WKB expression for the barrier penetrability are obtained. The relative cold ternary yields were calculated as the ratio of the penetrability of a given ternary fragmentation and the sum of the penetrabilities of all possible cold ternary fragmentations. Different scenarios were considered depending on the trajectories of the fragments. It was shown that two regions of cold fragmentation exist, a deformed one corresponding to large fragment deformations and a spherical one around ${}^{132}\mathrm{Sn},$ similarly to the case of the cold binary fission of ${}^{252}\mathrm{Cf}.$ We have shown that for the scenario corresponding to the Lagrange point, where all forces acting on the α particle are in equilibrium, the cold α ternary yields of ${}^{252}\mathrm{Cf}$ are strongly correlated with the cold binary yields of the daughter nucleus ${}^{248}\mathrm{Cm}$ into the same heavy fragments. For all other scenarios only the spherical splittings are favored. We concluded that due to the present available experimental data on cold α ternary yields only the Lagrange scenario could describe the cold α ternary fission of ${}^{252}\mathrm{Cf}.$