The half-on-shell Coulomb T-matrix in a double-scattering approximation to the ionization of helium by fast protons

We investigate the application of the Faddeev-Watson multiple-scattering series to the ionization of atoms by ion impact. Singularities in the first- and second-order terms are discussed. Different forms of the half-shell Coulomb T-matrix are used in impulse approximations to double-differential cross sections (DDCSs) for proton-impact ionization of helium, and are compared with experiment. By using the regularized half-shell T-matrix we derive a double-scattering approximation which includes the full projectile-residual-ion interaction. While the latter approximation does not improve on the impulse approximations for DDCSs, in contrast to other models, we conjecture that it might adequately describe triple-differential cross sections for large angles of deflection of the projectile. (author)