Trajectory calculations for the ternary cold fission of 252 Cf

The cold ternary fission is a rearrangement process of a large group of nucleons from the ground state of the initial nucleus to the ground state of the three final fragments. In order to determine the configuration and the dynamics of the fissioning nucleus at scission, the experimental data for the Light Charged Particle (LCP) emitted in the fragmentation process are analyzed and compared with the theoretical results obtained via trajectory calculations. Various combinations of initial conditions are probed and the trajectories are computed for comparison with the available experimental data. The final characteristics of the LCP emitted in the cold fission of 252 Cf were calculated for different mass splittings. The equations of motion for the three-body problem were derived and solved numerically. The solution of this set of equations provided the final angle of the LPC with respect to the fission axis and its kinetic energy. The initial kinetic energy of the LCP decreases with the tip distance. In our model the α-particle cannot be emitted at a tip distance larger than 8 fm, because the α particle is no longer under the influence of the attractive nuclear forces. Tip distances smaller than 6 fm were disregarded because the LCP wave packet filling the lowest state in the potential well has a small probability to tunnel through the thick transversal barrier. The location of the LCP was fixed at the electro-nuclear saddle point. Due to the finite size and the deformations of the fragments, this location of the electrostatic saddle point and the outcome of the trajectory calculation will be altered to a certain extent. In the cold fission regime, the average kinetic energy of the α particle will approach the value of ∼ 17 MeV. According to the calculations a range between 11 MeV to 22 MeV should be expected for the final kinetic energy of 4 He. The experiment does not show a distinctive α kinetic energy distribution for cold fission, a fact which is in agreement with the calculations presented in this paper. (authors)