  The $M$-dimensional scattering matrix $S(E)$ which connects incoming to
outgoing waves in a chaotic systyem is always unitary, but shows complicated
dependence on the energy. This is partly encoded in correlators constructed
from traces of powers of $S(E+\epsilon)S^\dagger(E-\epsilon)$, averaged over
$E$, and by the statistical properties of the time delay operator,
$Q(E)=-i\hbar S^\dagger dS/dE$. Using a semiclassical approach for systems with
broken time reversal symmetry, we derive two kind of expressions for the energy
correlators: one as a power series in $1/M$ whose coefficients are rational
functions of $\epsilon$, and another as a power series in $\epsilon$ whose
coefficients are rational functions of $M$. From the latter we extract an
explicit formula for $\rm{Tr}(Q^n)$ which is valid for all $n$ and is in
agreement with random matrix theory predictions.
