Ternary fission analysis of Fm242,258 nuclei using equatorial and collinear cluster tripartition configurations

The quantum mechanical fragmentation theory--based three cluster model is employed to investigate the ground-state ternary fission of two Fm isotopes nuclei having atomic mass ${A}_{P}=242$ and 258. The mass asymmetry coordinate and the relative separation among the decaying fragments play a crucial role for the estimation of the fragmentation structure and related barrier penetration process. First, the choice of third fragment (${A}_{3}$) is fixed by minimizing the probable ${A}_{3}$ fragments having different proton neutron configurations. Further, the fission fragment combinations (${A}_{1}+{A}_{2}+{A}_{3}$) are identified for the fixed third fragments by selecting the channel of lower ternary fragmentation potential and higher relative fission yield. Two type of tripartition of radioactive nuclei are considered such as equatorial cluster tripartition (ECT) and collinear cluster tripartition (CCT). A comparative analysis of ternary fragmentation potential and relative fission yield within ECT and CCT geometrical arrangement is carried out for different choices of third fragment, i.e., ${A}_{3}=1$ to ${A}_{P}$/3. The choice of most probable fragments suggest that the proton and neutron magic shell closures play essential role in the ternary mass division. Finally, a relative analysis of binary and ternary fragmentation is worked out for better insight of dynamics involved.