Impact-Parameter Calculation of Hydrogen-Hydrogen Double-Excitation Collisions

Cross sections for the double-excitation collisions $\mathrm{H}\mathrm{}\left(1s\right)+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}\to \mathrm{H}\mathrm{}\left(2lm\right)+\mathrm{H}\left(2\mathrm{}{l}^{\prime }{m}^{\prime }\right)$ are calculated over the range of incident energy 6.25 keV to 3.0 MeV by means of the impact-parameter method. The first Born, distorted Born, and two-state approximations are employed. At low-incident velocities, the inclusion of distortion terms decreases all cross sections below the first Born values. Athigh-incidentvelocities, the distorted Born cross sections for excitation of the projectile atom to the $2p_0$ state exceed the Born values, while all other distorted Born cross sections approach the Born values from below. Back coupling from the final state to the initial state has negligible effect on the double-excitation cross sections. The polarization of the radiation emitted from the excited $\mathrm{H}\mathrm{}\left(2p\right)\mathrm{}$ projectiles is calculated for the double-excitation collisions and found to dominate the polarization for incident energies exceeding 25 keV.