Randomness in multi-step direct reactions

We propose a quantum-statistical framework that provides an intergrated perspective on the differences and similarities between the many current models for multi-step direct reactions in the continuum. It is argued that to obtain a statistical theory two physically different approaches are conceivable to postulate randomness, respectively called leading-particle statistics and residual-system statistics. We present a new leading-particle statistics theory for multi-step direct reactions. It is shown that the model of Feshbach et al. can be derived as a simplification of this theory and thus can be founded solely upon leading-particle statistics. The models developed by Tamura et al. and Nishioka et al. are based upon residual-system statistics and hence fall into a physically different class of multi-step direct theories, although the resulting cross-section formulae for the important first step are shown to be the same. The widely used semi-classical models such as the generalized exciton model can be interpreted as further phenomenological simplifications of the leading-particle statistics theory.