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

Angular and energy correlations for electrons produced in the ionization of neon and xenon by electrons with energies between 400 eV and 2.5 keV have been measured using symmetric noncoplanar kinematics. The reaction yields information about the atomic orbitals and their correlations when analyzed with the distorted-wave off-shell impulse approximation. In the past, either plane waves or various eikonal approximations have been used for the distorted waves, and in the cases where the eikonal parameters are approximately related to elastic scattering, the spectroscopic sum rule has been approximately verified. In the present work, calculations have also been carried out using partial-wave-expanded optical-model wave functions which describe the elastic scattering in detail. The detailed calculation confirms the spectroscopic sum rule, and hence the validity of the structure determination in the case of neon. For xenon the full distorted-wave calculation gives a much improved fit to the shape of the cross section, but overestimates the effect of absorption, and hence underestimates the cross section for ejecting an electron from the valence $s$ state. The plane-wave and eikonal approximations considerably overestimate the magnitude of the valence $s$-orbital cross section relative to the probability of ejecting an outer $p$ electron. The latter two approximations improve as the energy is increased, but they are still inadequate for neon at 2.5 keV.