α-Particle Trajectories in Ternary Fission

The trajectories of the $\alpha$ particle and the two main fragments produced in ternary fission are calculated by computer on the basis of initial conditions determined by the statistical theory of fission. The angular and energy distributions of the three particles as functions of the mass ratio of the main fragments are deduced; they compare well with the experimental results of Fraenkel on spontaneous fission of ${\mathrm{Cf}}^{252}$. Calculations are repeated with varied initial conditions; the final results are insensitive to the initial velocities of the fragments and the initial position of the $\alpha$ particle, but are very sensitive to the initial velocity of the $\alpha$ particle. Based on this sensitivity, the experimental angular distribution strongly supports the view of the statistical theory that the fission process is a slow process. The initial positions of the fragments are related to the prompt-neutron distribution; the present results on angular and energy distributions are consistent with experimental results of prompt-neutron distribution.