  We consider scattering matrix for Schr\"odinger-type operators on
$\mathbb{R}^d$ with perturbation $V(x)=O(\langle x\rangle^{-1})$ as
$|x|\to\infty$. We show that the scattering matrix (with time-independent
modifiers) is a pseudodifferential operator, and analyze its spectrum. We
present examples of which the spectrum of the scattering matrices have dense
point spectrum, and absolutely continuous spectrum, respectively.
