Fission dynamics of compound nuclei: Pairing versus fluctuations

Energy dependence of fission observables is a key issue for wide nuclear applications. We studied real-time fission dynamics from low-energy to high excitations in the compound nucleus ${}^{240}\mathrm{Pu}$ with the time-dependent Hartree-Fock $+$ BCS approach. It is shown that the evolution time of the later phase of fission towards scission is considerably lengthened at finite temperature. As the role of dynamical pairing is vanishing at high excitations, the random transition between single-particle levels around the Fermi surface to mimic thermal fluctuations is indispensable to drive fission. The obtained fission yields and total kinetic energies with fluctuations can be divided into two asymmetric scission channels, namely, S1 and S2, which explain well experimental results and give microscopic support to the Brosa model. With increasing fluctuations, the S2 channel takes over the S1 channel and the spreading fission observables are obtained.

Figure 1

(a) TD-BCS evolutions of the number of particles in a neck of 2 fm in length at the density minimum. (b) The octupole deformation $Q_{30}$ (in units of $b=100$ ${\mathrm{fm}}^2$) of ${}^{240}\mathrm{Pu}$ with different initial temperatures $T$. TDHF results without pairing are also shown.

Figure 2

The evolutions of neutron and proton pairing energies (in MeV) within TD-BCS at different initial temperatures of $T=0$ MeV (a), 0.5 MeV (b), 1.0 MeV (c), and 1.5 MeV (d). TD-BCS results with the initial pairing field at zero temperature are also shown for $T=1.0$ MeV (e) and 1.5 MeV (f).

Figure 3

The evolutions of $Q_{30}$ and pairing energies within TD-BCS plus thermal fluctuations at temperatures of 0.9 and 1.5 MeV. Results of $T=0.9$ MeV with small scission deformations (S1 channel) are shown in thick red (gray) lines. Results without fluctuations in yellow (light gray) lines are also shown for comparison.

Figure 4

The fission pathways of ${}^{240}\mathrm{Pu}$ within TD-BCS plus thermal fluctuations in the space of quadrupole-octupole deformations ($Q_{20}$, $Q_{30}$), at temperatures of 0.75 MeV (a), 0.9 MeV (b), and 1.5 MeV (c). At $T=0.75$ and 0.9 MeV, the fission pathways without fluctuations (dashed yellow line) are also shown. Specific results of the S1 and S2 channels are also shown inside.