Interaction of slow electrons with density fluctuations in condensed materials: Calculation of stopping power

Abstract

The calculation of the energy-resolved scattering of slow (\ensuremath{\lesssim}3 eV) electrons from density fluctuations is extended from crystalline semiconductors to amorphous, condensed materials (solid or liquid). In the Born approximation, the scattering is proportional to S(q,\ensuremath{\omega}), the ``dynamical structure factor'' of the material. This factor, which exhibits some basic similarities and differences between solids and liquids, is determined by hydrodynamical parameters in the low-q range relevant to slow electrons. For solids, the scattering law remains unchanged when extended from crystalline to amorphous states, so the stopping power remains unchanged also. The scattering law changes when extended to liquids, but the calculated stopping power remains effectively unchanged.