Excitation energy of fission fragments within nuclear time-dependent density functional theory

TL;DR

This study assesses the predictive power of time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory for fission fragment properties, focusing on excitation energy and total kinetic energy (TKE). By implementing a new AxialHOHFB solver and performing hundreds of trajectories for Pu-240, the authors demonstrate that TDHFB can reproduce the experimental TKE for the most probable fragmentations but substantially underestimates it for symmetric and highly asymmetric splits, with results largely insensitive to the Skyrme functional parameterization. They show that TKE is effectively constant after scission and quantify fragment excitation energies, finding generally reliable values only near the most probable region; broad discrepancies with energy-sharing models (e.g., CGMF) suggest limitations of mean-field dynamics. The paper highlights the need for beyond-mean-field approaches or finite-range interactions to capture the full energy partitioning in fission and discusses the implications for nuclear data and reactor applications.

Abstract

The number and properties of the neutrons and photons emitted in nuclear fission are directly related to the excitation energy of the fission fragments when they are formed at scission. Though not observable experimentally because of the extremely short time scales, the excitation energy of fission fragments can be predicted by microscopic theory based on time-dependent density functional theory (TDDFT). Initial results on the value of the total kinetic energy of fission reactions were very promising, but could not probe all possible fragmentations. In this work, we perform large-scale TDDFT calculations in $^{240}$Pu enabled by the development of a new TDDFT solver. We obtain TDDFT trajectories covering nearly all possible fragmentations. We find that the total kinetic energy is close to experimental values only for the most likely fission while it is severely underestimated at both small and large asymmetries. This conclusion seems rather independent of the parameterization of the energy functional, both in its particle-hole and particle-particle channels.

Figures (23)

• Figure 1: Harmonic oscillator basis functions $\phi_n^{(b)}(x)$ where the oscillator length $b$ is adjusted as the orders of harmonics $n$ are increased in such a way that all the basis functions are contained within an interval $[-1\,\mathrm{fm},+1\,\mathrm{fm}\,]$.
• Figure 2: Axially symmetric density profiles $\rho(x, y = 0, z)$ of the four deformed configurations of ${}^{240}$Pu listed in Table \ref{['tab:HFB_configs']} used to test the convergence of the AxialHOHFB static solver.
• Figure 3: Convergence of the total HFB energy as $\max\{n_z\}$ increases for four (a)-(d) static configurations of $^{240}$Pu shown in Fig. \ref{['fig:4configurations']}. Inset plots focus on higher values of $\max\{n_z\}$.
• Figure 4: Energy conservation and center-of-mass position for the three TDHFB trajectories shown in Fig. \ref{['fig:3trajectories']}, with increasing basis size parameter $\max\{n_z\}$. Panels (a), (b), and (c) correspond to Trajectories #1, #2, and #3, respectively. Color maps for the density profiles match those in Fig. \ref{['fig:4configurations']}.
• Figure 5: Potential energy surface of $^{240}$Pu calculated with the Skyrme SkM$^*$ EDF, overlaid with three TDHFB trajectories initialized at the same isoenergy contour 1 MeV below the saddle point energy. Points along the trajectories are separated in time by $15\,\mathrm{fm}/c$. Each trajectory is computed with increasing values of $\max\{n_z\}$. Isoenergy lines are spaced by 1 MeV.