Electron Scattering Cross Sections Introduction:

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• Introduction
• The electron gun and the collimating apertures
• Applications of total cross sections
• Experimental methods for measuring the total electron scattering cross section
• Historical Background
• Computer control interface
• Planned experiment

CHAPTER ONE

Introduction

1.1 Total cross section of electron scattering

When a beam of energetic electrons passes through a gas, a number of different kinetic processes may result from the encounters of electrons with gas atoms or molecules. These processes can be divided into two categories, inelastic collisions and elastic collisions. The processes involving the loss of kinetic energy by electrons are called inelastic collisions while those involving no loss of kinetic energy by electrons are called elastic collisions. In an inelastic collision, electrons lose kinetic energy owing to the ionization of the target molecule, excitation of the target molecule, and other internal processes that occur in the molecule. In principle, during elastic collisions the electrons lose part of their energy due to momentum transfer, but this energy loss is significantly smaller because it is proportional to the ratio of electron mass to molecular mass.

As a result of the elastic and inelastic collisions, electrons scatter in all directions. The probability of scattering due to either of these two processes can be specified by their respective cross sections. In order to understand the concept of scattering cross section, consider a beam of electrons impinging on target atoms as shown in Figure 1.1. Assume the target particles are at the origin of the coordinate system and the intensity of the incident beam is I. The cross section dσ for electrons scattering into a solid angle dΩ is defined as

(1.1).

Fig. 1.1 Schematic diagram of a scattering.

Here the term dσ/dΩ is the differential scattering cross section. It is related to dN(θ), the number of particles per second scattered into a conical wedge define by θ and θ + d θ as follows;

(1.2)

The element of solid angle can be written as

(1.3)

where θ is the angle between the scattered and incident directions, known as the scattering angle. For a given process, the total scattering cross section can be defined as

(1.4).

The total electron scattering cross section is the sum the of the cross sections of all possible interactions between electrons and target atoms or molecules. An inelastic scattering cross section is the summation of the ionization cross section, excitation cross section, and the cross section of other internal processes. Therefore

(1.5)

(1.6)

where is the total cross section of each individual process.

Experimentally, one can measure the individual cross sections , but the most reliable measurement is the total cross section ¹. Experimental results show that individual studies of each effect have much larger errors compared to the total cross section measurements. Total cross sections can be measured within an accuracy of 1-3%¹ and are becoming available for many molecules. The inelastic cross sections are usually available with an accuracy of 5%¹. Using these available inelastic cross sections and total cross sections one can find the elastic cross section.