A complete numerical approach to electron–hydrogen collisions

Abstract

This tutorial presents an extensive computational study of electron-impact scattering and ionization of atomic hydrogen and hydrogenic ions, through the solution of the non-relativistic Schrödinger equation in coordinate space using propagating exterior complex scaling (PECS). It details the complete numerical and computational development of the PECS method, which enables highly computationally-efficient solution of these collision systems. Benchmark results are presented for a complete range of electron-hydrogen collisions, including discrete elastic and inelastic scattering both below and above the ionization threshold energy, very low-energy ionizing collisions through to moderately high-energy ionizing collisions, ground-state and excited-state targets and charged hydrogenic targets with Z 4. Total ionization cross sections through to fully differential cross sections, both in-plane and out-ofplane, are given and are found to be in excellent accord with other state-of-theart methods and measurements, where available. We also review our recent confirmation (Bartlett and Stelbovics 2004 Phys. Rev. Lett. 93 233201) of the Wannier and related threshold laws for e-H collisions.

SDCS quantum mechanical flux formula revisited for electron-hydrogen ionization

“…As already mentioned in the Introduction, in some numerical evaluations [7,8] of the singlet SDCS for the e-H process, a discontinuity in the derivative is observed at α = π/4:…”

“…In the last decade, several numerical approaches have been put forward [1][2][3][4][5][6][7][8] to deal, in particular, with the single ionization of atomic hydrogen by electron impact: remarkable good agreement between several theoretical results, and with the available experimental data, was observed.…”

Potential-splitting approach applied to the Temkin–Poet model for electron scattering off the hydrogen atom and the helium ion

“…In this case, the radius R has to be increased to get even better accuracy. Also we would like to mention that the convergence of our results as R → ∞ does not shows any essential oscillatory character and therefore for final result we do not need any averaging unlike it is done in the approach of paper [15].…”

“…[5,20,25,27] and references therein). In this report, however, we focus mainly on the calculation of the wave function, and we consider the differential ionization cross section outside the scope of the paper.…”

“…In order to check accuracy of our cross sections at lower energies, we have compared them to the results presented in paper [15] where the data for energies 2.7 eV -54.4 eV are available. The discrepancy of the results at all given energies and for all states is less than 0.2%.…”