Deflection effects in inner-shell ionization

Recently a method of calculating inner-shell ionization has been formulated in which Hartree-Fock wave functions are employed and all terms in the Born series retained. Results have so far been presented only in the energy region where projectile deflection effects are of little importance. In this paper it is shown how the time-dependent problem can be solved just as conveniently for hyperbolic classical projectile paths that result from the nuclear repulsion. The method is applied to the impact-parameter dependence of $K$-shell ionization by protons on copper in the energy range 0.5 to 2 MeV. Excellent agreement is found at the lower energy with experiments of Andersen et al. Poorer agreement is obtained in the higher-energy regime.