Formation and dynamics of fission fragments

Although the overall time scale for nuclear fission is long, suggesting a slow process, rapid shape evolution occurs in its later stages near scission. Theoretical prediction of the fission fragments and their characteristics are often based on the assumption that the internal degrees of freedom are equilibrated along the fission path. However, this adiabatic approximation may break down near scission. This is studied for the symmetric fission of ${}^{258,264}$Fm. The nonadiabatic evolution is computed using the time-dependent Hartree-Fock method, starting from an adiabatic configuration where the fragments have acquired their identity. It is shown that dynamics has an important effect on the kinetic and excitation energies of the fragments. The vibrational modes of the fragments in the post-scission evolution are also analyzed.

Figure 1

Adiabatic fission potential of ${}^{264}\mathrm{Fm}\to {}^{132}\mathrm{Sn}+{}^{132}$Sn (solid line) as function of the distance $R$ between the fragment centers of mass. The reference energy is chosen such that $E=0$ for $R\to \infty$. Adiabatic (purple surfaces) isodensities at half the saturation density ${\rho }_0/2=0.08$ fm${}^{-3}$ are shown at $R=7,8,\cdots ,15$ fm. Half a fragment is represented, the fission axis being vertical. TDHF isodensities are represented by dashed lines at $R=11,12,\cdots ,15$ fm. The nonlinear axis (top) relates the time $t$ with $R$ during the nonadiabatic evolution, with origin $t=0$ associated with preformation of ${}^{132}$Sn fragments.

Figure 2

Proton (a) and neutron (b) pairing energies as functions of $R$. Proton (c) and neutron (d) single-particle energies for states with positive (blue) and negative (red) parity. The green solid lines indicate the Fermi levels in the presence of pairing. These are continued by green dashed lines, which represent the Fermi levels located arbitrarily in the magic gaps.

Figure 3

Time evolution of various energies in the nonadiabatic phase (see text).

Figure 4

(a)–(d) Evolution of multipole moments in the nonadiabatic phase. (e)–(h) Fourier transforms are computed for $t>t_1=1.8$ zs (right of dashed line in top panels). The RPA strength functions of ${}^{132}$Sn are plotted with dashed lines (bottom) with arbitrary normalization.