Excitation-energy-dependent potential energy surfaces in the ternary breakup of Cf252

Abstract

We study the excitation energy-dependent potential-energy surfaces (PESs) for both the spherical and deformed fragments from the ternary fragmentation (TF) of $^{252}\mathrm{Cf}$ at four different excitation energies of the fissioning parent nuclei. A two-dimensional minimization approach with respect to the charge numbers (${Z}_{1}, {Z}_{2}$, and ${Z}_{3}$) of the fragments has been used to minimize all possible ternary combinations, which are generated from the atomic-mass-evaluation (AME2016) data [Chin. Phys. C 41, 030003 (2017)]. To calculate the energy-dependent TF-PES, we used the temperature-dependent binding energies (TDBE), which are calculated as follows: the temperature-dependent ($T$-dependent) macroscopic liquid-drop model (LDM) energy proper due to Krappe's formula [Phys. Rev. C 59, 2640 (1999)] and the microscopic shell correction energies due to the analytical estimates of Myers and Swiatecki [Nucl. Phys. 81, 1 (1966)]. Furthermore, the shell correction energies and the nuclear deformations are also made $T$-dependent. In this study, the $T$-dependent total interaction potential between the ternary fragments is calculated for the fragments in a collinear geometry with the lightest fragment ${A}_{3}$ being in the middle of the two main fission fragments ${A}_{1}$ and ${A}_{2}$. From the TF-PES results with the use of spherical-shell corrections, a strong energy maximum in the PES is obtained around ${Z}_{3}=2$ with the ${Z}_{1}=50$ region due to the closed-shell effects of doubly magic nuclei. In addition to this, we also obtained some other significant energy maxima around the magic and/or semimagic numbers of nuclei. These energy maxima extend further with increasing excitation energy of the fissioning parent nuclei. We also found that the true-ternary-fragmentation (TTF) fragments are reasonably favored at high excitation energies. Furthermore, the effects of $T$-dependent deformations and the $T$-dependent deformed-shell corrections in the TF-PES of $^{252}\mathrm{Cf}$ are also studied. From the TF-PES results of deformed ternary fragments, we obtained the energy maximum around ${Z}_{3}=16$ region, which may be due to the larger ${\ensuremath{\beta}}_{2}$ deformation values. Furthermore, we also studied the ternary fragmentation yields and neutron emission from the excited fragments in the $^{10}\mathrm{Be}$-accompanied spontaneous ternary fission of $^{252}\mathrm{Cf}$ and compared our calculated results with the available experimental data.