On the single- and double-ionization of He by protons and anti-protons

In this paper we present the calculations of: (a) the single-ionization cross section of He by protons and anti-protons in the incident energy range of about 10 keV-50 MeV, (b) the double-ionization cross sections by both projectiles in the energy rage of about 50 keV-20 MeV and (c) the ratio of double- to single-ionization in the energy range of 50 keV-20 MeV. The calculations have been performed in the two-coupled channel plane wave Born approximation, which is essentially the Born approximation that includes the final channel interaction between two electrons, in addition to the usual projectile-electron potential. The projectile has been represented by plane waves, and a correlated Hylleraas type of wavefunction has been used for the initial ground state. For the single-ionization case the final state electronic wavefunction is taken to be an anti-symmetrized product of a hydrogen-like (ls) and a continuum Coulomb wavefunction. For the double-ionization case, the final state wavefunctions of the two ejected electrons are taken to be Coulomb functions for calculating the matrix elements of the electron-projectile interaction, whereas plane waves are used for calculating the matrix elements of the electron-electron interaction. The calculated results are in reasonable agreement with the data in all three cases. The single-ionization cross section has also been calculated in the Lewis-Merzbacher approximation to determine the range of incident energy where it might represent a suitable approximation.