Dynamics of the tri-nuclear system at spontaneous fission of ${}^{252}\mathrm{Cf}$

To describe the dynamics of ternary fission of ${}^{252}\mathrm{Cf}$ an equation of motion of the tri-nuclear system was obtained and it was solved numerically. The fission of the ${}^{70}\mathrm{Ni}+{}^{50}\mathrm{Ca}+{}^{132}\mathrm{Sn}$ channel was chosen as one of the more probable channels of true ternary fission of ${}^{252}\mathrm{Cf}$. The collinearity of ternary fission was checked by analyzing the results of the equation of motion. The results show that if initially all nuclei are placed collinearly (potential energy of this position is the smallest) and the component of the middle fragment's initial velocity which is perpendicular to this line is zero, then ternary fission is collinear, otherwise noncollinear ternary fission takes place.

Figure 1

Point (${\mathbf{R}}_k$) and relative (${\mathbf{R}}_{ij}$) vectors of the tri-nuclear system. The point $O$ (origin) corresponds to the center of mass.

Figure 2

Total interaction potential as the function of $R_{3x}$ and $R_{3y}$ when $R_{12}=20$ fm.

Figure 3

Contour plot of Fig. 2.

Figure 4

Same as Fig. 2, but for $R_{12}=21$ fm.

Figure 5

Same as Fig. 3, but for $R_{12}=21$ fm.

Figure 6

Same as Fig. 3 but for $R_{12}=22$ fm.

Figure 7

Same as Fig. 3 but for $R_{12}=34$ fm.

Figure 8

$x$ component of coordinates (upper) and velocities (lower) of three nuclei as functions of time.

Figure 9

Trajectories of three decaying nuclei when $R_{3y}(t=0)=0.5$ fm and the same initial velocities as in Fig. 8.

Figure 10

Trajectories of three decaying nuclei when $v_{3y}(t=0)=0.1$ cm/ns and the same initial coordinates as in Fig. 8.