Calculation of proton-impact excitation of helium using the Glauber approximation

Cross sections for the $1{}_{}{}^1{}_{}{}^{}S\to n{}_{}{}^1{}_{}{}^{}S$ ($n=2,3,4\mathrm{}$) excitations of atomic helium under proton impact are calculated with incident energy ranging from 25 to 1000 keV employing the Glauber approximation. A properly orthogonalized set of He wave functions are used. The generalized oscillator strengths for $1{}_{}{}^1{}_{}{}^{}S\to 2{}_{}{}^1{}_{}{}^{}S$ and $1{}_{}{}^1{}_{}{}^{}S\to 3{}_{}{}^1{}_{}{}^{}S$ excitations are also calculated with these wave functions, and the results are compared with the existing theoretical and experimental data. The full Glauber scattering amplitude is separated into single-and double-scattering parts. The single-scattering amplitude is evaluated from a closed-form expression. A numerical method is employed to calculate some integrals occuring in the double-scattering amplitude. At incident energies above 500 keV, the single-scattering contribution is found to dominate the Glauber result. The effect of the double-scattering term is appreciable at intermediate energies, where it substantially lowers the cross sections from the corresponding single-scattering result. The Glauber result at intermediate energies also underestimates most of the existing theoretical and experimental cross sections, which already show a wide variation among themselves in absolute values. However, the functional dependence of the Glauber cross sections on energy is similar to that depicted by other calculations and measurements. Furthermore, the average ratio of the Glauber cross sections for $3{}_{}{}^1{}_{}{}^{}S$ and $4{}_{}{}^1{}_{}{}^{}S$ excitations at high energies show reasonable agreement with those obtained from other theories, as also from the $n^{-3\mathrm{}}$ law of cross sections.