Figure 1

Typical time evolutions of the nucleon occupation probabilities in a TDSLDA simulation of induced fission of ${}^{236}\mathrm{U}$ started near the top of the outer fission barrier until complete fission fragment separation and for XY collision (see Ref. [40] for convention) at zero impact parameter of ${}^{238}\mathrm{U}+{}^{238}\mathrm{U}$ with 1500 MeV initial center-of-mass frame energy. The simulations were performed with the nuclear EDF SeaLL1 [41] with the lise code [42]. Scission occurs at $t\approx 2300$ fm/$c$. In collision the two final fragments are fully separated at $t>1000$ fm/$c$. The upper panel displays the short-time evolution of the cumulative nucleon occupation probability ${\sum }_k|n_k(t+\mathrm{\Delta }t)-n_k\left(t\right)|$ with $\mathrm{\Delta }t\approx 30$ $\mathrm{fm}/c$ for fission and $\mathrm{\Delta }t\approx 64$ fm/$c$ for collisions. In the inset the canonical neutron occupation probabilities ${\tilde{n}}_k\left(t\right)$, ordered by size, are displayed at the start and finish of the simulation and one can clearly see the formation of the long momentum tails. The total change in the nucleon occupation probability ${\sum }_k|n_k\left(t\right)-n_k\left(0\right)|$ as a function of time is shown in the lower panel. Note that for any $\mathrm{\Delta }t$ in the absence of pairing ${\sum }_k|n_k(t+\mathrm{\Delta }t)-n_k\left(t\right)|\equiv 0$. Here $n_k\left(t\right)={\sum }_{\sigma =\uparrow ,\downarrow }\int d\mathit{r}{\left|v_k(\mathit{r},\tau ,\sigma ,t)\right|}^2$, for either $\tau =n,p$ [see Eq. (9)].