Fission dynamics of ${}^{252}\mathbf{Cf}$

The time-dependent generator coordinate method with the gaussian overlap approximation (TDGCM+GOA) formalism is applied to describe the fission of ${}^{252}\mathrm{Cf}$. We perform analysis of fission from the initial states laying in the energetic range from the ground state to the state located 4 MeV above the fission barrier. The fission fragment mass distributions, obtained for different parity, energy of levels, and types of mixed states, are calculated and compared with experimental data. The impact of the total time of wave packet propagation on the final results is studied as well. The weak dependence of obtained mass yields on the initial conditions is shown.

Figure 1

(a) The potential energy surface of ${}^{252}\mathrm{Cf}$. The p-sl is depicted in white. (b) Density profiles corresponding to the configurations marked by dots are presented in the panel.

Figure 2

The tunneling probability $\zeta \left(t\right)$ [Eq. (7)] of ${}^{252}\mathrm{Cf}$ eigenstates ($g^{+}$—red triangles, $g^{-}$—green circles) as a function of time. The open symbols refer to the states located under fission barrier while the full ones correspond to the states laying above the barrier.

Figure 3

The energy dependence of the tunneling probability $\zeta (t=T^{\mathrm{propag}})$ [Eq. (7)] of ${}^{252}\mathrm{Cf}$ eigenstates $g^{\pi }$. The fission barrier height $B_{\mathrm{f}}=9.41\mathrm{MeV}$ is marked by the vertical black line.

Figure 4

The tunneling probability $\zeta \left(t\right)$ [Eq. (7)] of eigenstate $n=36,\pi =-1$ as a function of time (inner panel) and the fission fragment mass distributions calculated for denoted times of propagation $(t_1,...,t_6)$. The experimental data were taken from [38] and corrected by an average number of emitted prompt neutrons [42].

Figure 5

The fission fragment mass distributions as a result of propagation of positive (blue solid line) and negative (green dashed lines) states $g^{\pi }$ in the considered range of eigenvalues.

Figure 6

The comparison of mass yields obtained from time evolution of the ground state at energy $E_1=2.05$ MeV (blue line) and the state with eigenvalue $E_{30}=11.07$ MeV (green line). Both states have positive parity.

Figure 7

(a) Types of statistical mixing of eigenstates and fission fragment mass distributions obtained as a results of time evolution of these wave packets (b). The left axis of (a) shows the percentage contribution of each state according to particular statistical distribution used in the mixing procedure. The right axis refers to the tunneling probability $\zeta \left(t\right)$ of considered states.