  Scattering is an important phenomenon which is observed in systems ranging
from the micro- to macroscale. In the context of nuclear reaction theory the
Heidelberg approach was proposed and later demonstrated to be applicable to
many chaotic scattering systems. To model the universal properties,
stochasticity is introduced to the scattering matrix on the level of the
Hamiltonian by using random matrices. A long-standing problem was the
computation of the distribution of the off-diagonal scattering-matrix elements.
We report here an exact solution to this problem and present analytical results
for systems with preserved and with violated time-reversal invariance. Our
derivation is based on a new variant of the supersymmetry method. We also
validate our results with scattering data obtained from experiments with
microwave billiards.
