Predictions of the macroscopic model of nuclei: Barriers to fusion and to light fragment emission

Fission and fusion barriers have been calculated for decay or formation of the composite nuclei ${}_{}{}^{149}{}_{}{}^{}\mathrm{Tb}_{}^{\mathrm{*}}{}_{}{}^{}$ and ${}_{}{}^{194}{}_{}{}^{}\mathrm{Hg}_{}^{\mathrm{*}}{}_{}{}^{}$ via the Yukawa-plus-exponential-finite-range macroscopic model. The predicted properties of these barriers are used for comparisons to measured total kinetic energies for the emission of light fragments (2≤$Z_L$≤9) and to empirical systematics of s-wave fusion barrier heights. The fusion barriers are consistent with the model. Values of total kinetic energies were calculated with the assumption of no energy loss into excitation beyond the saddle point. For each light fragment, the observed values of total kinetic energies are smaller than those calculated. The deviation increases with $Z_L$ and is correlated with the nuclear shape at the corresponding conditional saddle point. It scales with the neck thickness and the fragment deformation, as does the error involved in our approximation. This suggests (at least for the higher $Z_L$ values) that this macroscopic fission model might apply for light-fragment emission. Dynamical effects must, however, be included.