High-energy forward elastic scattering of electrons: Partial-wave approximations

Partial-wave analysis is applied to a parametrized pseudostate excitation model of high-energy electron-atom scattering. Consistency checks are carried out between asymptotic distorted-wave calculations (for coupled differential equations), second-Born-approximation scattering amplitude calculations, and partial-wave second-Born-approximation calculations. Closure formulas for partial-wave amplitude sums are derived for a static model potential and for the second-Born-approximation amplitude due to the asymptotic dipole excitation potential. Calculations using these closure formulas in $e^{\mathrm{-}}$+H and $e^{\mathrm{-}}$+Ar models at 15 keV show cusplike forward elastic scattering peaks, confirming recent exact second-Born-approximation results for an $e^{\mathrm{-}}$+H pseudostate model. Using parameters appropriate to ground-state rare-gas atoms, the computed forward peaks are much too small to account for recent experimental observations. The theory indicates that these structures increase in magnitude rapidly with atomic radius, suggesting that the observed strong forward peaks may arise from excited atoms or ions in the electron beam path.