Asymmetric electron energy sharing in electron-impact double ionization of helium

Abstract

We present the fully fivefold differential cross sections (FDCSs) for ($e,\phantom{\rule{0.16em}{0ex}}3e$) processes in helium within the first Born approximation. The calculation is performed for a coplanar geometry in which the incident electron is fast ($\ensuremath{\sim}6$ keV), the momentum transfer is small (0.24 a.u.), and for an asymmetric energy sharing between both slow ejected electrons at excess energy of 20 eV. Two cases have been considered: ${E}_{1}=15$ eV, ${E}_{2}=5$ eV and ${E}_{1}=8$ eV, ${E}_{2}=12$ eV. While waiting for new theoretical and experimental results for confrontations, in particular for asymmetric energy sharing, our results clearly demonstrate that, for the same incident energy, the same momentum transfer and the same excess energy, the ($e,\phantom{\rule{0.16em}{0ex}}3e$) process in helium with asymmetric energy sharing between ejected electrons is more likely than the case with symmetric energy sharing. The two- and three-dimensional representation of the FDCSs covering all possible values of the angle of ejections are presented and discussed. The theoretical cross sections are calculated by using a compact-kernel-integral-equation approach associated with the Jacobi matrix method to calculate a three-body wave function and which leads to a full convergence in terms of the basis size.