Precise test of the Coulomb-projected Born approximation for the 2 1S and 3 1S excitation of helium by electron impact

By use of the accurately known generalized oscillator strength (i.e., the result of the first Born approximation due to Kim and Inokuti), we have evaluated the differential cross sections for the 2 1S and 3 1S excitation of helium by electron impact, much more precisely than before, within the Coulomb-projected Born approximation. The results are in good agreement with measurements by Dillon and Lassettre reported in 1975. The method of the present calculation is based on the Fourier decomposition of the Coulomb potential for interactions between the incident electron and electrons in the target atom, and has been used in a few other contexts. We point out here that the same method can be readily extended to many other scattering approximations such as distorted-wave approximations, either with or without account for electron-exchange effects