Eigenclass sum rules in multi-step compound reactions

Abstract

In a doorway model of pre-compound reactions (such as the exciton model), the fine-structure levels of Bohr's compound-nucleus model are generalized to include one or more classes of doorway states, through which flux percolates during the relaxation of the system toward equilibrium. In the 1-class model (i.e., normal compound-nucleus model) with Γ ⪢ D, Wiedenmuller and collaborators have noted the unitarity sum rule Σ cT c= 2πΓ corr D . W show that, in the N-class case, N sum rules of analogous form exist, one for each eigenclass.