The interaction of fast charged particles with a semi-infinite medium
is described using both quantum-mechanical and semiclassical dielectri
c formulations. We consider the coupling with bulk and surface excitat
ions for arbitrary trajectories of the particle and apply the solution
s to several cases of special interest. Interference effects in bulk a
nd surface excitations for some particular trajectories are described.
We analyze in detail the process of reflection-electron-energy-loss s
pectroscopy, obtaining results for the probabilities of multiple bulk-
and surface-plasmon excitations. The calculations are compared with av
ailable experimental results, showing a good description of the angula
r dependence of the excitation phenomenon.