Microscopic modeling of mass and charge distributions in the spontaneous fission of ${}^{240}\mathrm{Pu}$

We propose a methodology to calculate microscopically the mass and charge distributions of spontaneous fission yields. We combine the multidimensional minimization of collective action for fission with stochastic Langevin dynamics to track the relevant fission paths from the ground-state configuration up to scission. The nuclear potential energy and collective inertia governing the tunneling motion are obtained with nuclear density functional theory in the collective space of shape deformations and pairing. We obtain a quantitative agreement with experimental data and find that both the charge and mass distributions in the spontaneous fission of ${}^{240}\mathrm{Pu}$ are sensitive both to the dissipation in collective motion and to adiabatic fission characteristics.

Figure 1

Potential energy of ${}^{240}\mathrm{Pu}$ calculated along the most probable path to fission. In the classically forbidden region (marked WKB; between the inner turning point “in” and outer turning point “out”), the collective action (1) is minimized to determine the half-life. Outside the outer turning point and scission, the evolution of the system is given by stochastic Langevin dynamics.

Figure 2

Projections of the static (dashed line) and dynamic (solid line) SF paths on the potential energy contours in the two considered regions ${\mathit{q}}_{\mathrm{I}}$ and ${\mathit{q}}_{\mathrm{II}}$ of the collective space. The contours of inner and outer turning points are shown by dash-dotted lines. Ground-state and fission-isomer minima are marked by dots.

Figure 3

Variation of the pairing gap for neutrons and protons along the static and dynamic paths of Fig. 2.

Figure 4

Mass (left) and charge (right) yield distributions for the SF of ${}^{240}\mathrm{Pu}$. The experimental values [38, 39] (mirror points) are shown by solid (open) circles. Calculations with dissipative Langevin dynamics and full inertia (solid blue lines) are compared to results obtained with nondissipative dynamics and full inertia (red dashed lines) and with dissipative dynamics and a diagonal unit inertia tensor (green dashed-dotted lines). The insets shows the yields in a linear scale.

Figure 5

Mass (left) and charge (right) distributions of heavier SF yields of ${}^{240}\mathrm{Pu}$. The symbols are the same as in Fig. 4. The shaded regions are uncertainties in the distributions due to variations in $E_0$ (narrow red band), dissipation tensor (wider cyan band), and scission configuration (linear hatch pattern).