The 2s and 2p excitations of hydrogen by proton and helium-ion impact

Abstract

A general formula describing the direct interaction between a hydrogen atom and a positive ion with one electron is derived. Born, two-state and four-state impact-parameter treatments are carried out for the processes H(1s) + He+(1s) -> H(2s or 2p) + He+(1s) with incident hydrogen energies E in the range 4 <or= E <or= 625 kev. The four-state calculation takes full account of distortion, back-coupling, rotational coupling and the virtual transition sequence 1s r arr over l arr 2p r arr over l arr 2s. The long-range 2s-2p dipole coupling produces a marked effect on the 1s-2s excitation cross section, which in the Born and two-state treatments is determined solely by short-range interactions. The rotational coupling and distortion (both long-range in this case) exhibit a much greater influence on the 2p cross section than was in evidence for the excitation of hydrogen by neutral hydrogen or helium. Comparison with a four-state treatment of the excitation of hydrogen by proton impact demonstrates that, at moderate and high velocities, the orbital electron so effectively screens the helium nucleus that the helium ion behaves almost exactly as a singly charged structureless particle. The proton-hydrogen results are also compared with the second Born-wave calculations of Moiseiwitsch and his associates. The percentage polarization of the emitted Lyman α radiation for both proton and helium-ion impact is also determined.