Alternative statistics in multi-step direct reaction theory

In recent years a variety of statistical theories have been developed concerning multistep direct (MSD) nuclear reactions. In addition, dominant in applications is a whole class of semiclassical models that may be subsumed under the heading of 'generalized exciton model': these are basically MSD-type extensions on top of compound-like concepts. In this report the relationship between their underlying statistical MSD-postulates are highlighted. A common framework is sketched that enables to generate the various MSD theories through assigning statistical properties to different parts of the nuclear Hamiltonian. Then it is shown that distinct forms of nuclear randomness are embodied in the mentioned theories. All these theories appear to be very similar at a qualitative level. In order to explain the high-energy tails and forward-peaked angular distribution typical for particles emitted in MSD reactions, it is imaged that the incident continuum particle stepwise looses its energy and direction in a sequence of collisions, thereby creating new particle-hole pairs in the target system. At each step emission may take place. The statistical aspect comes in because many continuum states are involved in the process. These are supposed to display chaotic behavior, the associated randomness assumption giving rise to important simplifications in the expressions for the MSD emission cross sections. This picture suggests that the mentioned MSD models can be interpreted as variants of essentially one and the same theory. However, this appears not to be the case. To show this the usual MSD distinction within the composite reacting nucleus between the fast continuum particle and the residual system is introduced. One implication is that the mutual residual interactions of the nucleons of the residual core are to be distinguished from those of the leading particle with the residual system. This distinction will turn out to be central to the present analysis. (author). 14 refs.; 4 figs