Excitation of atomic hydrogen in the eikonal-Born-series approximation

The eikonal-Born-series method, developed recently to analyze elastic scattering of electrons by atomic hydrogen and helium, is extended to inelastic scattering. In this paper we investigate the excitation of atomic hydrogen to the $2s$ or $2p$ state by electron bombardment. Important differences from the elastic case are discussed and a careful comparison with the Glauber method is made. Also, for angles greater than 20° comparison is made with recent experimental data on the sum of the differential cross sections for $2s$ and $2p$ excitation. Very good agreement is found.