Vibrational excitation of molecules by resonant electron scattering: Theory and application to benzene

A formalism to describe the vibrational excitation of molecules via resonances is presented. For the limiting cases of short and long lifetime of the negative ion the excitation probability can be calculated using a golden rule expression and a simple Hamiltonian. The intensity distribution of the electron energy loss spectrum is expressed in terms of electron-vibration coupling constants which depend on the lifetime of the negative ion. Spectra for resonant scattering on benzene-d₆ are calculated and good agreement with experiment is obtained.