  Consider a semiclassical Hamiltonian $H := h^{2} \Delta + V - E$ where
$\Delta$ is the positive Laplacian on $\mathbb{R}^{d}$, $V \in
C^{\infty}_{0}(\mathbb{R}^{d})$ and $E > 0$ is an energy level. We prove that
under an appropriate dynamical hypothesis on the Hamilton flow corresponding to
$H$, the eigenvalues of the scattering matrix $S_{h}(V)$ define a measure on
$\mathbb{S}^{1}$ that converges to Lebesgue measure away from $1 \in
\mathbb{S}^{1}$ as $h \to 0$.
