Inelastic Scattering of High-Energy Electrons from Atoms: The Helium Atom

A discussion of the inelastic scattering of high-energy electrons from atomic systems using linear-response theory is presented. Following Van Hove, an expression for the differential scattering cross section within the Born approximation is derived. The relationship of this expression to the linear-response function is demonstrated and a practical procedure for its computation using the so-called random-phase approximation is given. Finally, explicit results for the excitation of the lowest singlet $S$ and singlet $P$ state of helium by 500-eV electrons are given.