Polarization fractions in Glauber theory for electron impact excitation of then=3levels of atomic hydrogen

With the use of recently proposed analytic methods, Glauber scattering amplitudes for the excitation of the $3d$ substates of atomic hydrogen by electron impact are obtained in closed form. The individual $n=3\mathrm{}$ cross sections and the Balmer-$\alpha$ cross section predicted by the Glauber theory in the range $18\le E_i\le 500$ eV are compared with experiments and with other calculations. The polarization fractions of $3p-2s$, $3d-2p$, and of the Balmer-$\alpha$ line are also calculated in the Glauber approximation, and comparison is made with the existing experimental data and with the Born predictions. The parameters ($\lambda , \chi$) predicted by the Glauber approximation are also given.