LAUSR

We investigate the preformation probability of the light particle that formed in the preliminary stage of the ternary fission process of the $^{252}\mathrm{Cf}$ nucleus. Considering the equatorial cluster tripartition kinematics, the relative yields of the ternary fission channels with $^{4,6}\mathrm{He}, ^{10}\mathrm{Be}$ and $^{14}\mathrm{C}$ as light third nucleus, are calculated. We use the Wentzel-Kramers-Brillouin approximation to calculate the penetrability of the different nuclei involved in the ternary fission process, based on microscopic Skyrme potentials. The obtained results indicate the optimum total excitation energy of the heavy nuclei produced in the $\ensuremath{\alpha}$ ternary fission channels to be within the range of 3--4 MeV. The estimated $\ensuremath{\alpha}$-preformation probability corresponding to this range is comparable with that estimated for the spontaneous $\ensuremath{\alpha}$ decays of the participating heavy nuclei. While the extracted preformation probability at excitation energy less than its indicated optimum values exhibits unphysical large values, the calculations based on the higher excitation energies indicate extremely small values. In the ternary fission process, the preformation probability of the emitted light particles heavier than the $\ensuremath{\alpha}$ particle exponentially decreases with increasing its mass number. A phenomenological expression is suggested based on the obtained results to estimate the preformation probability of an emitted cluster of a given mass number.