Kinetic energy of fission fragments within a dynamical model

TL;DR

This paper investigates the kinetic energy partitioning of fission fragments in actinides using a three-dimensional Langevin dynamics model with a three-center (two-center) parametrization. It explicitly includes pre-scission kinetic energy (PKE) alongside the Coulomb energy at scission to compute fragment kinetic energies for $^{239}\mathrm{Pu}$ (via thermal-neutron fission) and $^{258}\mathrm{Fm}$, reproducing experimental trends in fission-fragment mass distributions and total/fragment kinetic energies. The results show that light fragments have nearly constant FKE around $\sim$100 MeV while heavy fragments decrease linearly with mass; PKE contributes about $2$–$4\%$ of the total kinetic energy, depending on the system, with Coulomb energy dominating. The evolution of PKE reveals it is generated near scission and correlates with the scission deformation parameter $\delta$, offering a dynamical mechanism for energy partitioning that complements FFMD and TKE measurements and informs prompt-neutron spectrum evaluations.

Abstract

Kinetic energy of individual fission fragment for actinide nuclei is, for example, important for evaluating the prompt-neutron spectrum in the laboratory system. It is experimentally known that kinetic energy for each fragment is constant at about 100 MeV for light fragments and that for heavy fragments decreases linearly with mass number. Most of the theoretical studies carried out so far attempted to calculate the total kinetic energy of both fragments, i.e. sum of the energies of two fragments, but the kinetic energy of each fragment was not analyzed in detail as far as we recognize. We have calculated them in thermal-neutron induced fission of $^{239}\mathrm{Pu}$ with a dynamical model using Langevin equations within a three-dimensional two-center parametrization. Also fission of $^{258}\mathrm{Fm}$ was investigated. It is calculated from the Coulomb energy at the scission point and the pre-scission kinetic energy. It is found that the pre-scission kinetic energy has about 2-4% contribution in the kinetic energy. The calculated results reproduce the trend of the experimental data.

Figures (7)

• Figure 1: (a) FFMD and (b) TKE distribution for $^{240}\mathrm{Pu}$ in $E^{*}=6.53\MeV$. The calculated results are shown by black lines. The experimental data of $^{239}\mathrm{Pu}(n_{\mathrm{th}}, f)$Nishio1995-wvWagemans1984-db are shown by red and orange symbols ($\textsf{Y}, \triangledown$).
• Figure 2: Calculated fission-fragment distributions on (a) mass-TKE and (b) mass-FKE for $^{240}\mathrm{Pu}$ at excitation energy of 6.53. A purple triangle in (a) is the Q-value. The calculated average TKE and average FKE are shown by solid lines in (c) and (d), respectively. The red and orange symbols ($\textsf{Y}, \triangledown$) are the experimental data of $^{239}\mathrm{Pu}(n_{\mathrm{th}}, f)$Nishio1995-wvWagemans1996-sx.
• Figure 3: Fission fragment (a) mass-TCE, (b) mass-PKE, (c) mass-FCE, and (d) mass-FPKE distributions for $^{240}\mathrm{Pu}$ at excitation energy of 6.53MeV. The averages of each distribution are shown as open circles.
• Figure 4: Calculated distributions of (a) FFMD, (b) TKE, (c) mass-TKE, and (d) mass-FKE for $^{258}\mathrm{Fm}$ from $E^{*}=7\MeV$. The FFMD and TKE of the present calculation are shown by black histograms and the experimental data of $^{258}\mathrm{Fm}(\text{sf})$Hulet1989-kp is shown by green histograms. A purple triangle in (c) is the Q-value with the addition of the excitation energy. In the panels of (c) and (d), the average value for each fragment is shown by black open circles.
• Figure 5: Same as \ref{['fig:masstce_masspke']} but for $^{258}\mathrm{Fm}$ at $E^{*}=7.0\MeV$.