Electron-energy losses in hemispherical targets

In the framework of classical dielectric theory, the hemispherical geometry is studied. Calculations on surface modes are carried out for isolated Drude-like hemispheres. The convergence of the results with respect to the number of coupled terms in the expressions of the potential is discussed. The electron-energy-loss probability is studied for Al and Ag particles involving this geometry. The surface modes and hence the energy-loss probability are given by coupled expressions, the physical meaning of which is the coupling among multipolar terms, because of the particular geometry. The results obtained here present a good quantitative agreement with experiments in the case of clear surfaces (Ag) and provide a qualitative understanding for the experiments in Al, in terms of the position and impact parameter of the beam. This allows us to set the validity of the dielectric theory for cases that seemed to question it.