Threshold ionization laws for electron-hydrogen scattering and their dominant region of configuration space

Abstract

A fully quantal calculation of the ${}^{1}S$ three-body wave function is performed for the Wannier model of electron-hydrogen scattering in the near-ionization threshold region using an exterior complex scaling method. The region of configuration space of the wave function that provides the dominant contribution to the total ionization cross section is demonstrated to be ${r}_{1}\ensuremath{\approx}{r}_{2}$ in accord with the argument of Rau [Phys. Rev. A 4, 207 (1971)], but only in the so-called Coulomb zone. The work confirms to a high precision ${(E}^{1.128\ifmmode\pm\else\textpm\fi{}0.004})$ the Wannier threshold law for the total ionization cross section, which is strictly valid only at the threshold. A threshold law for the ${}^{3}S$ total ionization cross section is determined to be ${E}^{3.37\ifmmode\pm\else\textpm\fi{}0.02},$ in agreement with the semiclassical calculations of Peterkop [J. Phys. B 16, L587 (1983)].