Electron scattering at high momentum transfer from methane: Analysis of line shapes

The measurement of the energy distribution of keV electrons backscattered elastically from molecules reveals one or more peaks. These peaks are at nonzero energy loss and have an intrinsic width. The usual interpretation of these measurements is attractively simple and assumes billiard-ball-type collisions between the electron and a specific atom in the molecule, and the scattering atom is assumed to behave as a free particle. The peak position is then related to the mass of the scattering atom, and its width is a Compton profile of the momentum distribution of this atom in the molecule. Here we explore the limits of the validity of this picture for the case of electrons scattering from methane. The biggest discrepancy is found for electrons scattering from carbon. For electrons scattering from hydrogen the effects are substantial at relatively low incoming energies and appear to decrease with increasing momentum transfer. The discrepancy is analyzed in terms of the force the atom experiences near the equilibrium position.