  Statistical properties of cross sections are studied for an open system of
interacting fermions. The description is based on the effective non-Hermitian
Hamiltonian that accounts for the existence of open decay channels preserving
the unitarity of the scattering matrix. The intrinsic interaction is modelled
by the two-body random ensemble of variable strength. In particular, the
crossover region from isolated to overlapping resonances accompanied by the
effect of the width redistribution creating super-radiant and trapped states is
studied in detail. The important observables, such as average cross section,
its fluctuations, autocorrelation functions of the cross section and scattering
matrix, are very sensitive to the coupling of the intrinsic states to the
continuum around the crossover. A detailed comparison is made of our results
with standard predictions of statistical theory of cross sections, such as the
Hauser-Feshbach formula for the average cross section and Ericson theory of
fluctuations and correlations of cross sections. Strong deviations are found in
the crossover region, along with the dependence on intrinsic interactions and
degree of chaos inside the system.
