  We consider the classical three-dimensional motion in a potential which is
the sum of $n$ attracting or repelling Coulombic potentials. Assuming a
non-collinear configuration of the $n$ centres, we find a universal behaviour
for all energies $E$ above a positive threshold.
  Whereas for $n=1$ there are no bounded orbits, and for $n=2$ there is just
one closed orbit, for $n\geq 3$ the bounded orbits form a Cantor set. We
analyze the symbolic dynamics and estimate Hausdorff dimension and topological
entropy of this hyperbolic set.
  Then we set up scattering theory, including symbolic dynamics of the
scattering orbits and differential cross section estimates.
  The theory includes the $n$--centre problem of celestial mechanics, and
prepares for a geometric understanding of a class of restricted $n$-{\em body}
problems.
  To allow for applications in semiclassical molecular scattering, we include
an additional smooth (electronic) potential which is arbitrary except its
Coulombic decay at infinity. Up to a (optimal) relative error of order 1/E, all
estimates are independent of that potential but only depend on the relative
positions and strengths of the centres.
  Finally we show that different, non-universal, phenomena occur for collinear
configurations.
