Coherence of inelastically scattered fast electrons in crystals of finite thickness

The general theory of inelastic scattering of fast electrons in a crystal of finite thickness is re-examined. The effects of averaging over scattering angles for electrons of fixed energy loss are estimated numerically. It is found that the coherence of a scattered beam is largely preserved in practice. For electron-electron scattering, the strong energy dependence of the scattering from plasmons or electron-hole pairs leads to the prediction of strong diffraction-contrast fringes for inelastically scattered beams, consistent with observation.