Fission of ${}^{240}\mathrm{Pu}$ with Symmetry-Restored Density Functional Theory

Nuclear fission plays an important role in fundamental and applied science, from astrophysics to nuclear engineering, yet it remains a major challenge to nuclear theory. Theoretical methods used so far to compute fission observables rely on symmetry-breaking schemes where basic information on the number of particles, angular momentum, and parity of the fissioning nucleus is lost. In this Letter, we analyze the impact of restoring broken symmetries in the benchmark case of ${}^{240}\mathrm{Pu}$.

Figure 1

(a) Least-energy fission pathway in ${}^{240}\mathrm{Pu}$ calculated in the HFB approximation (turquoise squares); projected onto good values of particle numbers (PNP, red triangles); projected onto good values of particle numbers, angular momentum ($J=0$) and parity (PNP & AMP, blue circles); obtained by adding the rotational correction $E_{\mathrm{RC}}$ on top of the PNP values ($\mathrm{PNP}+\mathrm{RC}$, empty squares). The insets show the convergence of the PNP and PNP & AMP for the pre-scission configuration with respect to the number of gauge angles $N_{\phi }$ and the number of rotational angles $N_{\beta }$, respectively. (b) Ratio $R_{\mathrm{RC}}=(E_{\mathrm{PNP}}^{0^{+}}-E_{\mathrm{PNP}})/E_{\mathrm{PY}}$; see text for details.

Figure 2

(a) Two-dimensional symmetry-restored PES of ${}^{240}\mathrm{Pu}$ in the $(q_{20},q_{30})$ plane for the $J^{\pi }=0^{+}$ configuration. (b) Same for $J^{\pi }=1^{-}$. Both surfaces are normalized with respect to the energy of their respective ground states. (c) Difference between the symmetry-restored and the HFB surface for the $J^{\pi }=0^{+}$ configuration. (d) Same for the $J^{\pi }=1^{-}$.

Figure 3

Primary fission fragment mass distributions in ${}^{240}\mathrm{Pu}$ obtained from felix with the PES at the HFB level (blue squares) or after PNP & AMP for the $0^{+}$ (orange circles) or $1^{-}$ (green triangles) states.