Excitation of Helium by Electron Impact

Excitation of helium atoms by electron impact is studied for intermediate- and high-energy electrons. Calculations of the differential cross sections for the $1S-2{}_{}{}^1{}_{}{}^{}S$ transition are made by use of a one-dimensional integral representation of the scattering amplitude obtained in the Glauber approximation. Comparisons with the Born approximation and with measurements between 22 and 600 eV are presented. Several sets of ground-state and excited-state wave functions are used. The results are a distinct improvement over the Born approximation at all energies considered and are in good agreement with the measurements above $\sim 90$ eV. At lower energies the Glauber predictions reproduce the qualitative features of the data. The results also show that the more-general one-dimensional integral expression for charged-particle—atom scattering amplitudes, derived earlier, can be used to perform calculations with relative ease.