Asymmetric fission ofTb*149from the finite-range, rotating-liquid-drop model: Mean total kinetic energies for binary fragmentation

We have used the finite-range, rotating-liquid-drop model to calculate the conditional saddle-point shapes, fission barriers, and moments of inertia of the nucleus ${}_{}{}^{149}{}_{}{}^{}\mathrm{Tb}$ as functions of mass asymmetry (or fragment charge Z) and angular momentum. A strong motivation in the present work is the potentiality for predicting total kinetic energies (TKE) in asymmetric fission, which may be compared with measurements of intermediate-mass fragments (IMF’s) produced in heavy-ion reactions. From the conditional saddle points, we estimate the TKE in the limit of no post-saddle dissipation, yielding, in effect, upper limits for the TKE’s. Clearly the nuclear shapes at scission will produce lower limits for the TKE’s, and we propose two methods for determining the characteristics of such scission configurations. The first involves a linear extrapolation along the fission normal mode at the conditional saddle point, and the second employs Swiatecki’s scaling rule to determine the effect of dissipation on the nuclear elongation at scission. In comparison to experimental TKE results for IMF’s, corrected for light particle evaporation, we find that the predictions from saddle-point shapes are in rather good agreement with the data over a wide range of mass asymmetry. The calculated estimates from nondissipative scission-point configurations also agree fairly well with the data, but tend to underpredict the TKE’s significantly for the heavier IMF’s. This is not a serious concern, as the calculations have not included any prescission damping. The estimates from fully dissipative scission-point shapes are systematically low, falling appreciably below the data over the whole range studied. Within the confines of the present asymmetric fission model, we can conclude that the motion along the dissipative path is not completely damped, and that asymmetric fission appears to be a less dissipative process than symmetric fission.