The phenomenon of spontaneous fission, which includes both binary and ternary decay modes, is observed within heavy and superheavy nuclei. Extensive efforts have been made to investigate the binary and ternary decay patterns exhibited by various nuclei belonging to the heavy-mass region. In this context, our study systematically examines the ground-state binary and ternary decay mechanisms of the ${}^{252}\mathrm{Cf}$ nucleus. To accomplish this, we have used the quantum mechanical fragmentation theory approach. It is known that the orientation angles of the decaying fragments play an important role in mass distribution. Therefore, in the present work probable orientation (both optimum and fixed) effects with deformations (up to quadrupole ${\beta }_2$) of nuclei participating in the fragmentation process are taken into account. Further, the fission fragments for binary ($A_1+A_2$) and for ternary ($A_1+A_2+A_3$) decay processes are identified by selecting channels of local minima in the fragmentation potential, with the third fragment $A_3$ being ${}^4\mathrm{He}$ for the ternary fission. The inclusion of hot-compact/(${90}^{\circ }-{90}^{\circ }$)/($0^{\circ }-{90}^{\circ }$)/(${90}^{\circ }-0^{\circ }$) orientations leads to the emergence of symmetric fission fragments, where shell effects are found to play the key role, whereas the cold-elongated/($0^{\circ }-0^{\circ }$) leads to the participation of highly deformed nuclei with large mass asymmetry. In addition to this, two types of tripartition of the radioactive nucleus are considered: equatorial cluster tripartition and collinear cluster tripartition. Both configurations are studied by considering $A_3$ = ${}^{30}\mathrm{Mg}$ and ${}^{48}\mathrm{Ca}$ as fixed fragments. The most probable fragments in the exit channel $\left[{}^{72}\mathrm{Ni}\right(Z=\mathbf{28}, N=44$) $+ {}^{132}\mathrm{Sn}(Z=$ 50, $N=$ 82)$+{}^{48}\mathrm{Ca}(Z=\mathbf{20}, N=\mathbf{28}$)] indicate that the deformations and the proton/neutron shell closure play a vital role in the spontaneous fission analysis of binary and ternary channels. The calculated results are aligned with available experimental data. In addition to this, relative yield for different ternary combinations is calculated for the ${}^{252}\mathrm{Cf}$ nucleus.

• Received 10 January 2024
• Revised 28 February 2024
• Accepted 15 April 2024

DOI:https://doi.org/10.1103/PhysRevC.109.054607