Glauber cross sections for arbitrary excitation of ground-state hydrogen by electron and proton impact

The Glauber scattering amplitude for 1s-nlm excitations of hydrogen by charged particle impact is reduced to a form numerically computable for arbitrary values of n, l, and m. The increasing number of repeated parametric differentiations appearing in earlier methods with the increase of n is replaced in our method by a single contour integration, which is especially useful for large-n states. In addition, whereas the available closed-form expressions would involve the calculation of a large number of hypergeometric functions as l and m increase for a given n, the present integral form involves only one hypergeometric function for any n, l, and m. The asymptotic form of the 1s-nlm amplitude as n→∞ is also presented. The procedure is applied for studying the 1s→ns(n=3, 4, 10, and ∞) and 1s→np(n=3, 4, and ∞) excitations of hydrogen by electron and proton impact. Tabular results of the cross sections are presented for differential and integrated cross sections in e^--H collisions and for integrated cross sections in H⁺-H collisions. The qualitative features observed earlier for low ns and np excitations are found to exist also for n≥3 excitations. The 1s→ns and 1s→np cross sections obey an n^-3 law asymptotically as n^-2→0, which is in conformity with the analytical results obtained quite generally for 1s→nlm excitations. For proton impact 1s→3p excitations, the Glauber results are in excellent agreement with a recent 34-state calculation. A unified graphical representation of various normalized cross sections above some specific energy is presented, whence a knowledge of the high-energy Born cross sections for any 1s→ns or 1s→np excitation suffices to determine the absolute Glauber cross sections for the process.