  The recently derived distributions for the scattering-matrix elements in
quantum chaotic systems are not accessible in the majority of experiments,
whereas the cross sections are. We analytically compute distributions for the
off-diagonal cross sections in the Heidelberg approach, which is ap- plicable
to a wide range of quantum chaotic systems. We thus eventually fully solve a
problem which already arose more than half a century ago in compound-nucleus
scattering. We compare our results with data from microwave and
compound-nucleus experiments, particularly addressing the transition from
isolated resonances towards the Ericson regime of strongly overlapping ones.
