Fission-fragment excitation energy sharing beyond scission

A simplified, though realistic, model describing two receding and accelerating fission fragments, due to their mutual Coulomb repulsion, shows that fission fragments share excitation energy well after they ceased to exchange nucleons. This mechanism leads to a lower total kinetic energy of the fission fragments, particularly if the pygmy resonances in the fission fragments are excited. Even though the emphasis here is on fission, similar arguments apply to fragments in heavy-ion reactions.

Figure 1

The evolution of the neutron and proton number differences $\mathrm{\Delta }N$ and $\mathrm{\Delta }Z$ [panel (a)], the FFs' intrinsic energies [panel (b)], and the TKE and, in the inset, the FFs' dipole moments $D$ [panel (c)] as a function of the fission fragments' separation $d_{\mathrm{sep}}$ in the case of induced fission of ${}^{236}\mathrm{U}$. The numerical results are from a work in progress [11]. In the inset of panel (a) the neutron (upper half) and proton (lower half) shapes of FFs' distributions are displayed at 22-fm separation and the colorbar stands for the neutron and proton density in the range 0.0–0.1 $\mathrm{fm}{}^{-3}$. The heavy FF is on the left and the light FF in on the right. Notice that the LFF is more elongated than the HFF.

Figure 2

An evaluation in the lowest-order perturbation theory of FFs' intrinsic energy $E_{\text{int}}\left(t\right)$ [panel (a)] and $E_{\text{TKE}}\left(t\right)$ [panel (b)] in the case of ${}^{240}\mathrm{Pu}$-induced fission as a function of the separation between the FFs and also as a function of the time after scission. The initial separation and fragment charges were chosen so that $e^2{Z}_1{Z}_2/\eta =176.2$ MeV, with $Z_h=53$ and $Z_L=41$, typical for average FF charges. The initial value of the Coulomb energy is compatible with very large elongations of the FFs at scission. The thinnest and medium thickness lines correspond to the case ${\mathit{\xi }}_{1,2}\left(0\right)=0$ when the FFs are initially charge unpolarized, and $\hslash {\omega }_k=\sqrt{k_k/{\mu }_k}=16$ and 6 MeV, respectively. The thickest lines correspond to ${\mathit{\xi }}_k\left(0\right)\ne 0$, thus to initially charge polarized FFs at scission, and $\hslash {\omega }_k=6$ MeV. The black solid, blue dashed, and red dotted lines correspond to damping $\hslash {\gamma }_1=\hslash {\gamma }_2=(2,4,6)$ MeV, respectively [see Eqs. (19) and (20)].