Selection Rule in Electron-Impact Vibrational Excitation of Adsorbed Molecules

With use of an expression for the $S$ matrix for the inelastic scattering of electrons from adatom vibrations, an explanation is given for the recently observed "specular selection rule" of Ho, Willis, and Plummer. The explanation is based upon (1) the existence of a $C_2$ axis of symmetry and (2) the assumption of nondegeneracy of the ground state of the solid.