Level-level correlations in Hauser-Feshbach theory and Moldauer's sum rule for resonance reactions

It is shown that Moldauer's sum rule is equivalent to analyticity and unitarity of the $S$ matrix. Inconsistencies derived from the sum rule with the help of some approximation thus indicate that the approximation violates unitarity. It is also shown that a derivation of the Hauser-Feshbach formula beyond the regime of small absorption in all channels is possible only in the frame of a dynamical model for the compound nucleus.