Glauber Amplitudes in Charged Particle Hydrogen Atom Collisions

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Abstract
The Glauber scattering amplitudes for the excitation of the ns and np levels of atomic hydrogen by electrons (or protons) incident upon the ground state have been obtained in closed form. In contradistinction to previously quoted results, these new expressions require no numerical integration. For small n, the amplitudes reduce to simple sums of hypergeometric functions. Hence the Glauber amplitudes for these transitions now can be computed with scarcely more difficulty than the Born amplitudes. A selection rule for arbitrary transitions is derived.