Imprints of compound-nucleus and direct-interaction processes in energy-averaged cross sections and durations of nuclear reactions

New analytical expressions for the energy-averaged S-matrix and nuclear-reaction cross sections are obtained on the basis of the unitary S-matrix parametrization. Some approximations are analysed when compound-nucleus cross sections are described with and without the Hauser-Feshbach formula with the partial-width-fluctuation correction. The connection of the S-matrix parameters in the Simonius representation with the dynamics of compound-nucleus processes is clarified. An explicit expression for the averaged duration of the nuclear reaction is obtained for the range of closely situated resonances. Possible methods of obtaining information on some compound-nucleus and direct-interaction characteristics from the averaged cross sections and durations are examined. (orig.)