Pre-equilibrium nuclear reactions: The overlapping-doorway model for multi-step compound processes

Abstract

Griffin's simple exciton model, designed to describe the spectra of pre-equilibrium particles emitted in compound-nuclear reactions, has recently been developed into a full-fledged doorway theory of multi-step compound reactions by three separate groups: Feshbach et al., Agassi et al., and Friedman et al. All three groups employ a time-independent scattering formalism, but since the time-sequence in which probability diffuses through the system of N doorway classes (e.g., 2p-1h, 3p-2h, etc. in the exciton model) is essential to a full understanding of the process, we have re-analyzed the problem in a time-dependent formalism. This shows explicitly how the statistical assumptions of the theory produce an irreversible flow of probability through the classes, described by a master equation. The solution of this equation demonstrates that the occupation probability of the compound system decays in time like a superposition of exponentials, with decay rates equal to the energy autocorrelation widths of the N “eigenclasses” of the system. Althrough intercomparison of the three theoretical approaches is also given, indicating which ones can be derived from the others and pointing out the differences in their basic statistical assumptions.