This paper deals with the mechanism of grazing incidence (e,2e) events from surfaces. Two different approaches are considered. In both cases, elastic scattering with the crystal lattice assists the inelastic collision; these two steps are coupled either coherently or incoherently. Experimental evidence is given that the "coherent" approach reproduces better the cross section dependence on momentum transfer in the specific case of asymmetric kinematics at moderate electron energies. This model has allowed us to map out the band dispersion of the outermost valence states of highly oriented pyrolytic graphite and to measure the momentum distribution of pi-electron states without invoking the contribution of reciprocal lattice vectors in the momentum conservation. Agreement between theory and experiment is satisfactory, though the presence of events where crystal momentum is reconstructed cannot be ruled out. These results, obtained with a significant reduction of the experiment duration by an implemented apparatus, show that reflection (e,2e) can be used to build up a momentum spectroscopy with high surface sensitivity.
Liscio, A., Ruocco, A., Stefani, G., Iacobucci, S. (2008). Two-step-wise interpretation of highly asymmetric, grazing angle (e,2e) on solids: A real momentum spectroscopy for surfaces and overlayers. PHYSICAL REVIEW. B, CONDENSED MATTER AND MATERIALS PHYSICS, 77(8), 085116 [10.1103/PhysRevB.77.085116].