Ab initiostudy of interelectronic correlations in electron-impact ionization of hydrogen

Abstract

Electron-impact ionization of hydrogen is investigated based upon ab initio quantal calculations. In the present calculations, strong interelectronic correlations are represented by the hyperspherical channel functions and accurate numerical solutions of the two-electron atomic Schr\odinger equation are obtained by means of the smooth-variable-discretization method in combination with the $R$-matrix propagation method. The double-continuum boundary condition is represented by matching the numerical solutions to asymptotic solutions, which are described by superpositions of approximate asymptotic channel functions. We obtained the ionization threshold law, which is in good agreement with Wannier's conjecture, and also an almost uniform energy distribution in double-continuum states at low energies, say $\ensuremath{\sim}0.1$ a.u. At low energies, the angular distributions of the electrons in double-continuum states of ${}^{1}{S}^{e}$ localize where the interelectronic angular distance ${\ensuremath{\theta}}_{12}=\ensuremath{\pi}$. As the energy increases, the binary-encounter and the dipolelike transition mechanisms manifest themselves in the angular distribution. The spin-averaged total ionization cross section and the spin asymmetry from the present method agree well with experimental measurements as well as the convergent-close-coupling result, while for the spin asymmetry there is a noticeable disagreement with the hidden-crossing result at moderately low energies. An essential role of the potential ridge during the ionization process is apparent in the convergence of the present calculations.