J. P. Lestone

A long outstanding problem in fission physics has been the anomalously large fission fragment anisotropies obtained with A < 20 projectiles on actinide targets near and below the Coulomb barrier. Recently, experimental results of Hinde et al.¹ on the ²³⁸U(¹⁶O,f) reaction have led them to claim that they have "conclusive evidence" that the fraction of fission fragments coming from quasi-fission reactions increases as one drops through the Coulomb barrier. The precise mechanism by which this occurs is yet to be established but is believed to be associated with the large ground state deformation of actinide targets. To aid in the understanding of this problem, we have calculated fusion cross sections for A < 20 projectiles on actinides taking into account the deformed Coulomb and nuclear potentials around the actinide nuclei. These results are in good agreement with measured fusion cross sections. Once the fusion barrier is crossed (or penetrated) a one-dimensional symmetric mass split Langevin calculation is performed leading to an ensemble of fissioning times. Our Langevin calculations yield two distinct fission components, one fast and the other slow. The slow component is standard fusion-fission, i.e. with Langevin trajectories passing through the equilibrium deformation before processing to fission. The fast component is similar to, but not exactly the same as, quasi-fission observed with A > 20 projectiles. In order to describe this component let us consider the interaction of sub-barrier ¹⁶O ions with ²³²Th nuclei. Because the incoming ions are sub-barrier the ¹⁶O will preferentially interact with the tips of the deformed ²³²Th target. After the Coulomb barrier is penetrated, a hot deformed system is produced with a distance between the center of masses of the two halves, slightly less than that for the fission saddle point of this system. In a purely deterministic model, 100% of such systems would evolve towards the equilibrium deformation. If the Brownian forces associated with nuclear viscosity are included, then some fraction of the systems will be kicked across the fission saddle point without first proceeding to the equilibrium deformation. Fig. 3.6-1 shows our calculation of the percentage of fission due to quasi-fission as a function of beam energy relative to the fusion barrier. These calculations are qualitatively consistent with the conclusions of Hinde et al., i.e. the quasi-fission increases as one drops through the fusion barrier.

Fig. 3.6-1. Calculations of the percentage of fission due to quasi-fission as a function of beam energy relative to the fusion barrier.