Ternary-fragmentation-driving potential energies of Cf252

Abstract

Within the framework of a simple macroscopic model, the ternary-fragmentation-driving potential energies of $^{252}\mathrm{Cf}$ are studied. In this work, all possible ternary-fragment combinations of $^{252}\mathrm{Cf}$ are generated by the use of atomic mass evaluation-2016 (AME2016) data and these combinations are minimized by using a two-dimensional minimization approach. This minimization process can be done in two ways: (i) with respect to proton numbers (${Z}_{1}$, ${Z}_{2}$, ${Z}_{3}$) and (ii) with respect to neutron numbers (${N}_{1}$, ${N}_{2}$, ${N}_{3}$) of the ternary fragments. In this paper, the driving potential energies for the ternary breakup of $^{252}\mathrm{Cf}$ are presented for both the spherical and deformed as well as the proton-minimized and neutron-minimized ternary fragments. From the proton-minimized spherical ternary fragments, we have obtained different possible ternary configurations with a minimum driving potential, in particular, the experimental expectation of Sn + Ni + Ca ternary fragmentation. However, the neutron-minimized ternary fragments exhibit a driving potential minimum in the true-ternary-fission (TTF) region as well. Further, the $Q$-value energy systematics of the neutron-minimized ternary fragments show larger values for the TTF fragments. From this, we have concluded that the TTF region fragments with the least driving potential and high $Q$ values have a strong possibility in the ternary fragmentation of $^{252}\mathrm{Cf}$. Further, the role of ground-state deformations (${\ensuremath{\beta}}_{2}$, ${\ensuremath{\beta}}_{3}$, ${\ensuremath{\beta}}_{4}$, and ${\ensuremath{\beta}}_{6}$) in the ternary breakup of $^{252}\mathrm{Cf}$ is also studied. The deformed ternary fragmentation, which involves ${Z}_{3}=12--19$ fragments, possesses the driving potential minimum due to the larger oblate deformations. We also found that the ground-state deformations, particularly ${\ensuremath{\beta}}_{2}$, strongly influence the driving potential energies and play a major role in determining the most probable fragment combinations in the ternary breakup of $^{252}\mathrm{Cf}$.