Pseudo-state expansions and the second Born approximation for excitation of atomic hydrogen by proton impact

Accurate numerical values are obtained for the probability amplitudes for excitation of hydrogen atoms by proton impact within the second Born approximation for s, p and d intermediate states. The energy range covered is from 50 to 200 keV. These values are compared with those obtained by expanding the Green's function contained in the second-order matrix element in various sets of pseudo-states based on Slater orbitals. The pseudo-state representation can provide a good representation of the contributions from the intermediate continuum states, even when only a small number of functions is employed.