Comparison of semiclassical and quantum mechanical angular distributions for nuclear fission and evaporation

There is quite a variety of statistical-model equations in the literature that have been derived with different assumptions and for various classes of nuclear reactions. Some have been obtained by consideration of the quantum mechanics and some by semiclassical approximations thereto. Often it is not clear whether or not the results of certain analyses are clouded by these semiclassical approximations. We consider three statistical models that have been heavily employed in recent years: (1) fission decay from a rigid rotor (2) particle evaporation from a spherical system and (3) fission decay from two uncoupled spheres. Comparisons are made of numerical results from semiclassical and from quantum mechanical equations for certain specific reactions. In addition, some general features are displayed and discussed for the differences between these formalisms. For average spins that are often encountered in heavy ion reactions, the results are very similar. We conclude that major differences in current analyses are not due to the methodology; instead they must center on assumptions concerning the physical nature of the transition-state (or decision-point) configurations and their associated level densities.