Deep Minima in the Triply Differential Cross Section for Ionization of Atomic Hydrogen by Electron and Positron Impact

C Demars,J Colgan,S Ward,D Madison,S Amami

doi:10.3390/atoms8020026

Abstract

We investigate ionization of atomic hydrogen by electron- and positron-impact. We apply the Coulomb–Born (CB1) approximation, various modified CB1 approximations, the three body distorted wave (3DW) approximation, and the time-dependent close-coupling (TDCC) method to electron-impact ionization of hydrogen. For electron-impact ionization of hydrogen for an incident energy of approximately 76.45 eV, we obtain a deep minimum in the CB1 triply differential cross section (TDCS). However, the TDCC for 74.45 eV and the 3DW for 74.46 eV gave a dip in the TDCS. For positron-hydrogen ionization (breakup) we apply the CB1 approximation and a modified CB1 approximation. We obtain a deep minimum in the TDCS and a zero in the CB1 transition matrix element for an incident energy of 100 eV with a gun angle of 56.13 ° . Corresponding to a zero in the CB1 transition matrix element, there is a vortex in the velocity field associated with this element. For both electron- and positron-impact ionization of hydrogen the velocity field rotates in the same direction, which is anticlockwise. All calculations are performed for a doubly symmetric geometry; the electron-impact ionization is in-plane and the positron-impact ionization is out-of-plane.

Highlights

IntroductionStudies of the angular distributions of ionized atomic electrons by charged-particle impact is a rich field that has long been studied due to its importance to other areas of physics (e.g., plasma, medical physics) and due to the information that is available about the correlated nature of the particle interactions
Studies of the angular distributions of ionized atomic electrons by charged-particle impact is a rich field that has long been studied due to its importance to other areas of physics and due to the information that is available about the correlated nature of the particle interactions.It was thought that structures in differential cross sections of atoms by the impact of fast bare charged particles could be described by using the first and second Born terms [1]
In this paper we show that the CB1 and modified CB1 approximations give a deep minimum in the triply differential cross section (TDCS) in the doubly symmetric geometry [4] for ionization of atomic hydrogen by both electron and positron impact

Summary

Introduction

Studies of the angular distributions of ionized atomic electrons by charged-particle impact is a rich field that has long been studied due to its importance to other areas of physics (e.g., plasma, medical physics) and due to the information that is available about the correlated nature of the particle interactions. The TDCC [28] method obtained a deep minimum in the TDCS for electron-helium ionization for an incident energy of 64.6 eV that compared very well with experimental measurements [4]. For positron-hydrogen ionization a deep minimum in the fully differential cross section has previously been explained in terms of a vortex in the generalized velocity field u that is associated with the transition matrix element T (k+ , k− ), where T (k+ , k− ) depends on the momentum of the scattered positron k+ and the momentum of the ejected electron k− [8,9]. In this paper we show that the CB1 and modified CB1 approximations give a deep minimum in the TDCS in the doubly symmetric geometry [4] for ionization of atomic hydrogen by both electron and positron impact. We report angles in degrees and the incident energies in eV

Theory

Deep Minimum in the TDCS for Electron-Impact Ionization of Hydrogen

Deep Minimum in the CB1 TDCS for Positron-Impact Ionization of Hydrogen

Conclusions