Multistate Impact-Parameter Calculation of Atom-Atom Excitation Cross Sections: Excitation ofH(1s)byHe(1S1)

A general method of calculating the time-dependent matrix elements needed for multistate impact-parameter calculations of atom-atom inelastic cross sections is presented and applied to the collision processes $\mathrm{H}\mathrm{}\left(1s\right)+\mathrm{He}\left(1\mathrm{}{}_{}{}^1{}_{}{}^{}S\right)\to \mathrm{H}(2s, 2p_m)+\mathrm{He}\left(1\mathrm{}{}_{}{}^1{}_{}{}^{}S\right)$. Cross sections calculated in the distorted Born, two-state, and four-state impact-parameter approximations over the incident energy range $1.0 \mathrm{keV}\le E\le 200.0 \mathrm{keV}$ are compared with previous experimental results and first Born-wave calculations. The first Born-wave calculations are in better agreement with the experimental measurements than are the distorted Born, two-state, and four-state impact-parameter calculations, but the fact that the corrections to the first Born become significant for $v\le 1.0$ a.u. suggests that the good agreement may be accidental. Polarization fractions are calculated, and good agreement is shown with experiment for $v\le 0.8$ a.u.