Inelastic electron-hydrogen scattering in the unrestricted Glauber approximation

The double-integral expression derived previously for Bryon's unrestricted Glauber approximation has been evaluated numerically to obtain scattering amplitudes for elastic collisions of electrons on hydrogen, as well as $2s$ and $2p$ excitation. The resulting values of cross sections and Ly-$\alpha$ polarization fractions are similar to previous Glauber calculations, but the alignment and orientation of Ly-$\alpha$ radiation as a function of scattering angle is markedly different from the predictions of the Born and conventional Glauber calculations.