Pairing-induced speedup of nuclear spontaneous fission

Background: Collective inertia is strongly influenced at the level crossing at which the quantum system changes its microscopic configuration diabatically. Pairing correlations tend to make the large-amplitude nuclear collective motion more adiabatic by reducing the effect of these configuration changes. Competition between pairing and level crossing is thus expected to have a profound impact on spontaneous fission lifetimes.

Purpose: To elucidate the role of nucleonic pairing on spontaneous fission, we study the dynamic fission trajectories of ${}^{264}\mathrm{Fm}$ and ${}^{240}\mathrm{Pu}$ using the state-of-the-art self-consistent framework.

Methods: We employ the superfluid nuclear density functional theory with the Skyrme energy density functional ${\mathrm{SkM}}^{*}$ and a density-dependent pairing interaction. Along with shape variables, proton and neutron pairing correlations are taken as collective coordinates. The collective inertia tensor is calculated within the nonperturbative cranking approximation. The fission paths are obtained by using the least action principle in a four-dimensional collective space of shape and pairing coordinates.

Results: Pairing correlations are enhanced along the minimum-action fission path. For the symmetric fission of ${}^{264}\mathrm{Fm}$, where the effect of triaxiality on the fission barrier is large, the geometry of the fission pathway in the space of the shape degrees of freedom is weakly impacted by pairing. This is not the case for ${}^{240}\mathrm{Pu}$, where pairing fluctuations restore the axial symmetry of the dynamic fission trajectory.

Conclusions: The minimum-action fission path is strongly impacted by nucleonic pairing. In some cases, the dynamical coupling between shape and pairing degrees of freedom can lead to a dramatic departure from the static picture. Consequently, in the dynamical description of nuclear fission, particle-particle correlations should be considered on the same footing as those associated with shape degrees of freedom.

Figure 1

Contour maps of $V$ (left; in MeV) and $|{\mathcal{M}}_C{|}^{1/3}$ (right; in ${\hslash }^2$ $\mathrm{MeV}{}^{-1}/1000)$, calculated for ${}^{264}\mathrm{Fm}$ in the $x_1\text{−}{x}_3$ plane for $x_4=0$ (top) and the $x_1\text{−}{x}_4$ plane for $x_3=0$ (bottom). Energies are plotted relatively to the ground-state value.

Figure 2

Similar to Fig. 1 except for the $x_1\text{−}{x}_2$ plane for $x_3=x_4=0$ (top) and the $x_1\text{−}{x}_3$ plane for $x_2=x_4=0$ (bottom).

Figure 3

Projections of the three-dimensional (3D; solid line) dynamic SF path for ${}^{264}\mathrm{Fm}$ (a) on the $x_1\text{−}{x}_2$ plane for $x_3=x_4=0$ and(b) on the $x_1\text{−}{x}_3$ plane for $x_2=x_4=0$, calculated using the dynamical programming method technique. The dash-dotted line shows, for comparison, the two-dimensional (2D) path computed without pairing fluctuations. The static SF path corresponding to the minimized collective potential [19] is also plotted (dotted line). Symbols on the paths denote the path lengths in units of 10. Potentials $V$ of Fig. 2 are drawn as a background reference.

Figure 4

(a) Potential $V$ (in MeV), (b) effective inertia ${\mathcal{M}}_{\mathrm{eff}}^C$ (in ${\hslash }^2$ $\mathrm{MeV}{}^{-1}/1000)$, (c) action $S$, and (d) average pairing gaps ${\Delta }_n$ and ${\Delta }_p$ (in MeV) plotted along the 2D (static pairing; dotted line) and 3D (dynamic pairing; solid line) paths. The static fission barrier is displayed for comparison in (a).

Figure 5

Similar to Fig. 3 but for ${}^{240}\mathrm{Pu}$. The static SF path is represented by the dotted line.