The problem of quantum chaotic scattering with direct processes reduced to the one without

We show that the study of the statistical properties of the scattering matrix S for quantum chaotic scattering in the presence of direct processes (characterized by $\overline S \neq 0$, $\overline S$ being the average S-matrix) can be reduced to the simpler case where direct processes are absent ($\overline S = 0$). Our result is verified with a numerical simulation of the two-energy autocorrelation for two-dimensional S-matrices. It is also used to extend Wigner's time delay distribution for one-dimensional S-matrices, recently found for $\overline S = 0$, to the case $\overline S \neq 0$; this extension is verified numerically. As a consequence of our result, future calculations can be restricted to the simpler case of no direct processes