Dependence of total kinetic energy of fission fragments on the excitation energy of fissioning systems

We elucidated the reason why the average total kinetic energy (TKE) of fission fragments decreases when the excitation energy of the fissioning systems increase as indicated by experimental data for the neutron-induced fission events. To explore this problem, we used a method based on the four-dimensional Langevin equations we have developed. We have calculated the TKE of fission fragments for fissioning systems ${}^{236}\mathrm{U}^{*}$ and ${}^{240}\mathrm{Pu}^{*}$ excited above respective fission barriers, and compared the results with experimental data for n $+$ ${}^{235}\mathrm{U}$ and n $+$ ${}^{239}\mathrm{Pu}$ reactions, respectively. From the Langevin-model analysis, we have found that the shape of the abundant heavy fragments changes from almost spherical for low excitation domain to highly prolate shape for high excitation energy, while that of the light fragments does not change noticeably. The change of the “shape” of the heavy fragments causes an increase of a distance between the charge centers of the nascent fragments just after scission as excitation energy increases. Accordingly, the Coulomb repulsion between the two fragments decreases with an increase of the excitation energy, which causes the decrease of the average TKE. In this manner, we found that the change of the shape of the heavy fragment as a function of the excitation energy is the key issue for the TKE of fission fragments to decrease as the excitation energy of the fissioning nuclei increases. In other words, washing out of the shell effects, which affect the shape of the heavy fragments is the key reason for the decreasing energy dependence of the average TKE of the fission fragments.

Figure 1

The mass distribution of fission fragments originated from the compound nuclei ${}^{236}\mathrm{U}^{*}$ (left) and ${}^{240}\mathrm{Pu}^{*}$ (right). The histograms are the results of present 4D Langevin calculation for excitation energy of 7 MeV, while the open circles are evaluated values of independent fission yields, namely post-neutron yields, given in JENDL/FPY-2011 [23] for thermal-neutron induced reactions on ${}^{235}\mathrm{U}$ and ${}^{239}\mathrm{Pu}$. In addition, the $+$ symbols are values given by Okumura et al. [4] and Schillebeeckx et al. [24] for thermal-neutron induced pre-neutron emission yields on ${}^{235}\mathrm{U}$ and ${}^{239}\mathrm{Pu}$, respectively.

Figure 2

Average TKE (total kinetic energy) of fission fragments for fissioning systems of ${}^{236}\mathrm{U}^{*}$ and ${}^{240}\mathrm{Pu}^{*}$. Two panels are the overall (left) and enlarged (right) views. The scale of the vertical axis is common in these panels. The solid lines with error bars denote our calculation, while symbols are experimental data [5, 6, 7]. Note that we omit the multichance fission effects while the experimental data above several MeV include its effects.

Figure 3

Shapes of fission fragments of ${}^{236}\mathrm{U}^{*}$ and ${}^{240}\mathrm{Pu}^{*}$ just after scission for excitation energies of 7 MeV (solid lines) and 27 MeV (dash lines).

Figure 4

Quadrupole moment ($Q_{20}$) of fission fragments just after scission for the ${}^{236}\mathrm{U}^{*}$ (left panel) and ${}^{240}\mathrm{Pu}^{*}$ (right panel) fissioning systems at excitation energy of 10 MeV. In each panel, the solid histogram shows average of $Q_{20}$ for each fission fragment mass number, namely, $\langle Q_{20}\left(A\right)\rangle$. The scatter plot shows relative occurrence frequency of $Q_{20}$ by each fission event.

Figure 5

Dependence of the $\langle Q_{20}\left(A\right)\rangle$ of fission fragments originated from ${}^{236}\mathrm{U}^{*}$ (left panel) and ${}^{240}\mathrm{Pu}^{*}$ (right panel) for excitation energies $E_x=7-57$ MeV. Note that the above results reflect only first chance fission.

Figure 6

Dependence of the average octupole moment $\langle Q_{30}\left(A\right)\rangle$ of the fission fragments from ${}^{236}\mathrm{U}^{*}$ (left panel) and ${}^{240}\mathrm{Pu}^{*}$ (right panel) for excitation energies at $E_x=7-57$ MeV. Note that the above results reflect only first chance fission.

Figure 7

Distance between the center of mass $d_{cm}$ of the nascent fragments just after scission for ${}^{236}\mathrm{U}^{*}$ (solid line) and ${}^{240}\mathrm{Pu}^{*}$ (broken line) fissioning systems. Note that the above results reflect only first chance fission.

Figure 8

Schematic diagrams of shape of fission fragments just after scission for low excitation energy (upper) and high excitation energy (lower). In each case, the shape of the light fission nucleus (on the left) is prolate. On the other hand, the heavy fission fragments (on the right) is nearly sphere at low excitation energy, which turns out to be prolate at high excitation energy. Therefore, the distance between the centers of mass $d_{cm}$ between nascent fragments just after scission is larger at high excitation energy than at low excitation energy, causing average TKE to decrease to higher excitation energy.