  In this paper, the scattering and spectral theory of $H=\Delta_g+V$ is
developed, where $\Delta_g$ is the Laplacian with respect to a scattering
metric $g$ on a compact manifold $X$ with boundary and $V\in C^\infty(X)$ is
real; this extends our earlier results in the two-dimensional case. Included in
this class of operators are perturbations of the Laplacian on Euclidean space
by potentials homogeneous of degree zero near infinity. Much of the particular
structure of geometric scattering theory can be traced to the occurrence of
radial points for the underlying classical system; a general framework for
microlocal analysis at these points forms the main part of the paper.
