Excitation of helium by protons and alpha particles

Cross sections for the 1 1S → 4 1S excitation of He under proton and α-particle impact are calculated with incident energy ranging from 10 to 5000 keV using the two-state distortion approximation and a corresponding second-Born approximation. Two sets of wave functions are used. The results are compared with the existing first-Born calculations and the experimental data. The generalized oscillator strengths for the transition are also presented. The nonorthogonality of the wave functions has a very marked effect on the cross sections for almost the entire energy range considered. For proton impact, use of a properly orthogonal set of wave functions reduces the first-Born cross-section values obtained from an improperly orthogonalized set of wave functions by a factor of almost 2 at high energies, in agreement with the experimental values. The second-Born and distortion approximations give better agreement at lower energies also and the latter correctly predicts the functional dependence of cross sections on energy down to an incident energy of 20 keV. The necessity of using properly orthogonal sets of wave functions in the calculation of scattering processes involving high atomic excitations is thereby stressed