  In open-shell atoms and ions, processes such as photoionization, combination
(Raman) scattering, electron scattering and recombination, are often mediated
by many-electron compound resonances. We show that their interference
(neglected in the independent-resonance approximation) leads to a coherent
contribution, which determines the energy-averaged total cross sections of
electron- and photon-induced reactions obtained using the optical theorem. In
contrast, the partial cross sections (e.g., electron recombination, or photon
Raman scattering) are dominated by the stochastic contributions. Thus, the
optical theorem provides a link between the stochastic and coherent
contributions of the compound resonances. Similar conclusions are valid for
reactions via compound states in molecules and nuclei.
