Direct reaction effects on compound cross sections

Two effects of a direct reaction on compound processes are discussed: the enhancement of the average compound cross section that competes with the direct process and the cross correlations in the fluctuations of cross sections involving the directly coupled channels. For the case of two directly coupled channels it is shown that both effects are maximized at the causality limit of the average $S$ matrix where the penetration matrix $P$ is singular. Computer experiments demonstrate that both effects fall off sharply when $\overline{S}$ is not near this causality limit and similar reductions in the effects are expected when more than two channels are strongly coupled to one another. A formula based upon the Engelbrecht-Weidenmüller transformation and the $M$-cancellation principle gives an excellent account of the enhancements obtained from the computer experiments. It also gives a qualitative account of the magnitudes of the cross section cross correlation coefficients. A somewhat more complicated formula due to Hofmann et al. also gives a good account of the enhancements. Both of these formulas agree with that of Kawai et al. in the limit of large width-to-spacing ratios.