Dynamic versus static fission paths with realistic interactions

The properties of dynamic (least action) fission paths are analyzed and compared to the ones of the more traditional static (least energy) paths. Both the Barcelona-Catania-Paris-Madrid and Gogny D1M energy density functionals are used in the calculation of the Hartree-Fock-Bogoliubov (HFB) constrained configurations providing the potential energy and collective inertias. The action is computed as in the Wentzel-Kramers-Brillouin method. A full variational search of the least-action path over the complete variational space of HFB wave functions is cumbersome and probably unnecessary if the relevant degrees of freedom are identified. In this paper, we consider the particle number fluctuation degree of freedom that explores the amount of pairing correlations in the wave function. For a given shape, the minimum action can be up to a factor of 3 smaller than the action computed for the minimum energy state with the same shape. The impact of this reduction on the lifetimes is enormous and dramatically improves the agreement with experimental data in the few examples considered.

Figure 1

(a) HFB energy, (b) collective inertia, and (c) action represented as functions of particle number fluctuation $\Delta N^2$ for several relevant $Q_{20}$ values (given in barns). All the curves start at the $\Delta N^2$ values of the minimum energy solutions.

Figure 2

Spontaneous fission lifetimes of ${}^{234}\mathrm{U}$ obtained with different approaches as a function of the $\eta$ factor multiplying the pairing interaction strength.