Electron Scattering Cross Sections Introduction: : 1.2 Applications of total cross sections

1.2 Applications of total cross sections

Total electron scattering cross sections (s_T) are needed in many scientific applications and are essential in developing theoretical models to understand the electron- atom interaction process. For instance, electron scattering cross sections are used in astrophysics, plasma physics, upper atmospheric physics, isotope separation in radiation physics, and electrical discharges. In this section the application of the cross sections are discussed in detail.

Quantitative descriptions of fundamental collision processes in terms of cross sections are required to understand and model plasmas. The production and loss of electrons are the key processes that determine the formation, stability, and decay of the plasma. Electron impact cross sections, the appearance energies and the kinetic energy release play an important role in this context, since they determine plasma-wall interactions and the ionization balance in the plasma. In fusion plasma studies its needed to determine the lifetime of particular excited state of a specific ion or a molecule. Accurate electron scattering cross sections are essential in these determinations ^{2, 3}.

In our solar system, planets have gaseous atmospheres which are exposed to the solar radiation. The solar radiation ionizes the gases in the atmosphere of a given planet resulting the ionosphere, and the magnetosphere. Therefore, the properties of the ionosphere and the magnetosphere are directly related to the solar radiation and atmospherics constitutes. Studying the electron-molecular impact process is important to understanding the complex relationships among our planet’s atmosphere, the sun, and the magnetosphere. Understanding the Earth’s upper atmosphere remains a primary motivation for studying electron-molecular impact processes. A large number of studies have been on O₂ and N₂, since they are dominant throughout the atmospheric region. The natural auroral phenomena are important because they represent the sun, the magnetosphere, and Earth’s ionosphere. This coupling produces a variety of effects on the Earth’s ionosphere that effect the transmission and reception of radio waves^{2, 4}.

The role of electron-impact processes in the auroral phenomena are nearly the same as ionosphere processes except that there are more electrons with energies greater than 50 eV and the resulting photo emission is more intense than in the ionosphere¹. The primary source for the auroral process is the flux of electrons from outside the earth’s atmosphere with energies of 1 – 10 keV. In this auroral region, electronic excitation and ionization are more extensive than in the ionosphere. The coupling between the aurora and earth’s ionosphere is of considerable interest. This coupling is accomplished mainly by transport of both neutral and charged particles. For a more complete understanding of these processes, cross section values are needed in order to correctly incorporate elastic and inelastic scattering^{2, 5}.

Probabilities of fundamental collision processes in terms of effective collision cross sections are required for the understanding of electrical discharges. Electrical discharges are employed in ion implantation devices, semiconductor etching and microcircuit fabrication devices, chemical vapor deposition on thin films, and air purification devices. Total cross sections play an important role since they determine mobility and electron-ion recombination in reactions those help in understanding and modeling of the electrical discharge phenomena. The cross sections relevant to these discharges are still unavailable for many gases at higher electron energies^{6, 7}. For example, SF₆, C₂F₄ and C₄F₈ are gases often used in electrical discharges, but the total electron scattering cross sections of these have not been reported in the literature.

1.3 Experimental methods for measuring the total electron scattering cross section

There are two major successful experimental methods for finding total cross section: the Ramsauer Method and the Linear Beam Method (Linear Transmission Technique). At the beginning of research in this area, many experiments have were carried out for low electron energies using the Ramsauer method. The Linear beam method was developed after the invention of electrostatic analyzers.

Figure 1.2 Ramsauer’s apparatus for measuring total collision cross sections. The shaded area represents the interaction region.

The Ramsauer method uses a uniform magnetic field oriented transverse to the plane of motion of the electron beam. Free electrons were produced at a photo-cathode. The energies of emitted electrons were changed by controlling the wavelength of the light. The electrons were then accelerated through a potential difference between the photo-cathode and the first slit. As illustrated in Figure 1.2, electrons move about 270^o from cathode to collector in an arc through slits S₁ – S₈. The scattering chamber occupies the last 90^o of the trajectory. The purpose of the magnetic field is to enhance angular resolution and for energy selection for both elastic and inelastic scattering. Those electrons that suffer inelastic collisions fail to pass through the slits; instead they move in a new circular path of smaller radius in the magnetic field. In the course of the experiment, current “j” to the collector and “i” to the scattering chamber were measured at various pressures. According to the Beer Lambert attenuation formula “i” and “j” are related to the pressure “p” as

(1.7)

where L is the length of the path between slits S₆ and S₇, and σ is the total scattering cross section. At a given energy, σ was determined by studying the slope of line against the pressure.

In this experiment, the coupling of energy selection and scattering process together produce some experimental errors. As required by the experimental arrangement, both the applied voltage and magnetic field are changed for every energy. This leads to some uncertainty in systematic changes. Also, if the energy is obtained from a retarding potential measurement, the transverse magnetic field will introduce an uncertainty, whose energy has never been quantitatively analyzed.

The transmission beam technique is based on the measurement of the electron beam attenuation through a long gas cell. When an electron current beam I_o enters a gas cell containing a target gas, the fractional lost of current intensity is given in terms of the total cross section,

(1.8)

where N is the number density, P is the pressure, L is the effective length of the gas cell and I is the electron current emerging at the other end of the gas cell. In this technique an electrostatic analyzer is used to distinguish the primary electrons from the inelastically scattered electrons. A detailed description of this technique will be given in chapter 2 under the experimental section.

Figure 1.3 Transmission beam technique for measurement of total collision cross sections.