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We present expressions for the energy-averages of the most general products of fluctuating S-matrix elements required to calculate the variance in the energy-averaged cross-section and related observables for compound-nucleus processes. The results, which are exact and hold from the regime of isolated resonances through to that of strongly-overlapping resonances (independently of the number of open channels), involve no more than straightforward three-dimensional integrals. In line with earlier general arguments, they are functions only of average S-matrix elements. Explicit (asymptotic) expansions which approximate these results in the domain of strongly-overlapping resonances are also determined and the leading order corrections to Ericson's treatment of fluctuations deduced. Contrary to previous studies, we find that the fluctuating S-matrix is not necessarily Gaussian distributed in this regime. In addition, we demonstrate how unitarity can be used to check our results both numerically and analytically. Other technical issues addressed include the casting of the generating function used into an "optimal" form, the treatment of complications due to its non-trivial dependence on the source matrix, and identities for the extraction of the maximal order term. These lay a foundation for other applications of the stochastic model for compound-nucleus processes. PACS: 24.60.Dr

Previous theoretical work has shown that parity and time-reversal symmetry can be tested with particularly high sensitivity in the domain of isolated compound-nucleus resonances. In this domain, experiments will naturally focus on individual resonances rather than on the background cross section. The theoretical analysis of this situation leads to the concept of an ensemble of "onresonance" measurements. This concept naturally emerges by combining two previous theoretical approaches to tests of fundamental symmetries. %'e investigate the properties of this new ensemble and show how to convert "on-resonance" data into statistically significant information on symmetry violation. 421718

We examine the autocorrelation function of the 235 U(n,f) reaction with a view to quantify the presence of intermediate structure in the cross section. Fluctuations due to compound nucleus resonances on the eV energy scale are clearly visible up to ≈ 100 keV neutron energies. Structure on the one-keV energy scale is not present as a systematic feature of the correlation function, although it is present in the data covering the region around 20 keV.