Why the Hauser--Feshbach formula works

It is shown that flux conservation requires substantial channel-channel correlations of resonance amplitudes. These, together with the effects of level-level correlations and other terms conspire to cancel the large additive corrections to the Hauser-Feshbach formula for the fluctuation cross section. The remaining multiplicative corrections become negligible for nonelastic cross sections when many channels are open. In other cases, approximation formulas provide estimates that are adequate for most purposes. However, the Bohr independence hypothesis is not always satisfied when fewer than about 20 channels are open. The cross section correlation width is shown to differ markedly from the average width. The use of the former for estimating the Hauser-Feshbach denominator is found to be justified. All of these results are verified by means of statistical model calculations of resonance parameters and of cross sections.