Calculations of Alpha-Particle Trajectories for Long-Range Alpha Particles Emitted in Spontaneous Fission

Abstract

Calculated angular and energy distributions of the $\ensuremath{\alpha}$ particles in long-range $\ensuremath{\alpha}$-particle fission are presented. The distributions were obtained from calculated $\ensuremath{\alpha}$-particle trajectories based on a three-point-charge model for the scissioning nucleus. The calculation is two dimensional, and spontaneous fission (no preferred direction) is assumed. This reduces the number of free variables of the system to seven (except for the mass ratio). The system is thus parametrized in terms of the following initial dynamical variables: the initial distance between the fission fragments, the initial position of the $\ensuremath{\alpha}$ particle (not restricted to the fission axis), and the initial momenta of the $\ensuremath{\alpha}$ particle and one of the fragments. Reasonably good agreement with the experimental distributions is obtained. The calculations support the view that the scission point moves closer to the light fragment as the mass ratio increases. They also support the assumption that at the moment of scission the fission fragments have already attained a substantial part of their final velocity.