Factorized distorted-wave approximation for the (e, 2e) reaction on atoms: Coplanar symmetric

Abstract

The coplanar symmetric ($e, 2e$) cross section has been studied in the intermediate-energy region for the valence states of the inert gases He, Ar, and Ne. Experimental measurements at 200, 400, 800, and 1200 eV for He, and at 400, 800, and 1200 eV for Ne and Ar, are compared with calculations based on the factorized half-off-shell distorted-wave impulse approximation. Calculations are carried out using partial-wave-expanded optical-model wave functions which describe elastic scattering for the distorted waves, the eikonal approximation, and the plane-wave approximation. The latter two significantly overestimate the cross sections at small angles and the valence $s$-orbital cross section relative to the valence $p$-orbital one. They also predict the small-angle peak in the $p$-orbital cross section to be at an angle significantly smaller than is observed. Of the two, the eikonal approximation provides the better description of the data. The full calculation, on the other hand, underestimates the cross sections at small angles and the cross section for the more tightly bound $s$-orbital relative to the small-angle $p$-orbital cross section. It also underestimates the ratio of the large- to small-angle peak heights in the $p$-orbital cross section. All three approximations improve as the energy is increased. The full calculation shows that the factorized distorted-wave impulse approximation cannot provide an adequate description of the reaction.