Multiple-Scattering Effects in High-Energy Electron-Molecule Collisions. I. Diatomic Molecules

The multiple-scattering theory of Glauber is used to investigate the importance of double scattering in the collisions of fast electrons with diatomic molecules. By representing the atomic potentials as a sum of Yukawa terms, comparisons of scattering amplitudes calculated by the partial-wave analysis and the high-energy approximation (Moliere) are made over a wide range for several atoms. At 40 keV the amplitudes are found to be numerically equivalent to within a few percent, with the agreement worsening with decreasing energy. Calculations for N₂ at 0.5 and 40 keV and for I₂ and U₂ for 40-keV incident electron energies are presented; these results can be regarded as quantitative estimates of the importance of double scattering for a system of two atoms as a function of atomic number. Our U₂ calculation is compared with a similar calculation by Hoerni. In contrast to his findings, the double-scattering contribution to the differential cross section is seen to be negative in the small-angle region. In any event, for all cases considered, the multiple-scattering correction is quite small, amounting to no more than ±{}2% of the differential cross section for any angle of scattering.