The Single Differential Cross Sections (SDCS) for H(3s) Ionization in the First-Born Approximation by Electron and Positron Impact

TL;DR

This paper presents a theoretical calculation of single differential cross sections for hydrogen 3s state ionization by electron and positron impact using the First-Born Approximation, highlighting energy-dependent asymmetries and providing benchmarks for future models.

Contribution

It introduces an analytical approach within the First-Born Approximation for excited hydrogen atom ionization, emphasizing energy effects and charge asymmetries in SDCS calculations.

Findings

Peak ionization at around 200 eV incident energy

Positron SDCS greater than electron at low energies

Differences diminish at higher incident energies

Abstract

A theoretical study was conducted on the impact of electron and positron impact ionization of excited hydrogen atoms that were in the 3s state; this study was conducted within the First-Born Approximation (FBA), which provides an analytical expression for the transition matrix in terms of the Bethe-Lewis Integral Formalism. This formalism utilized both Coulomb continuum and confluent hypergeometric functions to describe the scattering states involved. Single Differential Cross Sections (SDCS) were calculated for incident energies of 100, 150, 200, and 250 eV. The data obtained indicated a peak in the ionization rates approximately at 200 eV, with the ionization rate decreasing as the incident energy increased further. The diffuse radial nature of the 3s wave function is shown to increase the sensitivity of the ionization dynamics to the incident particle energy. Asymmetries in charge were also detected; specifically, at low energy of the ejected electron, the SDCS values for positrons were greater than the corresponding values for electrons; however, as the energy of the incident particles was increased, these differences disappeared, thereby demonstrating the applicability of the FBA at high energy limits. The residual differences at low energy were due to the omission of exchange and post-collision interactions from the model. The results of this work can be used as benchmarking for the development of more complex distorted wave and multi-scattering theories in excited state ionization processes.