Physics
Collisions of Electrons with Atoms
Collisions of electrons with atoms refer to the interactions between free electrons and atoms, leading to various outcomes such as scattering, excitation, or ionization. These collisions play a crucial role in understanding the behavior of matter at the atomic level and are fundamental to fields such as atomic and molecular physics, as well as in the development of technologies like particle accelerators and plasma devices.
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10 Key excerpts on "Collisions of Electrons with Atoms"
- Heinrich F. Beyer, Viateheslav P. Shevelko(Authors)
- 2016(Publication Date)
- CRC Press(Publisher)
Chapter 6 Atomic collisions When electrons or ions collide with atomic or ionic targets, a large variety of atomic processes can occur. The main characteristics of these processes including the effective cross sections and the rate coefficients are considerable in this chapter. 6.1 Collisional and photo processes in plasmas A plasma is an ionized gas, sometimes titled as the fourth state of matter, and consists of electrons, ions, atoms and molecules. The name plasma was given to this state of matter by Langmuir who was a pioneer in the study of ionized gases. In Greek, πλασµα means ‘moldable substance’, or ‘jelly’. A plasma is characterized by two main properties. It contains charged particles (electrons, ions) but is electrically neutral as a whole and the motion of plasma particles is correlated, i.e. collective effects take place. Due to the influence of long-range Coulomb forces, all charged particles in a plasma may simultaneously interact with each other, i.e. undergo atomic collisions with electrons, atoms and ions until a certain degree of ionization is achieved. Since atoms and ions have an atomic structure, as considered in chapter 5, they can be excited into higher electronic states or ionized, decay into lower states emitting photons. All these elementary atomic processes including ionization, recombination and radiative processes, determine the plasma microparameters such as its temperature, density, degree of ionization and radiation spectra. The range of plasma temperatures and densities in different types of laboratory and astrophysical plasmas is very wide (see figure 1.4 for a temperature–density map in a plasma). As a rule, free electrons play the main role in a plasma because their low mass results in velocities that are much higher than those of heavy particles. Therefore collisions between electrons and massive particles are the most effective in a wide temperature range.
eBook - PDF- Juda Shohet(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
Such calculations usually include only some of the effects due to (a), (b), and (c). The results of these computer experiments are still often quite useful and are of great help in understanding plasma phenomena. However, these methods are very often lossless. That is, no damping of energies by collisions can occur. Then, the remaining effects of collisions are usually exaggerated, much more than in reality. In order to consider collision phenomena amenable to analytic solution, there must be a method for carefully considering collisions. The results of a collision ( short -time interaction) may be a net change in energy, velocity, momentum, or position of the particles making the collision. The next question is, how many particles are reacting in a collision? In principle, all particles with a charge are always colliding with each other (TV-body interaction). However, we will assume initially that the interaction can be separated into two-body interactions', that is, only two particles need to be considered for each interaction. This chapter begins with a set of elementary concepts that are of great value in understanding collision phenomena. After covering the behavior of a single set of two interacting particles, the behavior of a large collection of particles is considered. A. ELEMENTARY CONCEPTS We begin investigating collisions by considering particles that have some mechanism of interaction with one another. We call this a collision if it takes place over a short time. Collisions may be long range or short range, depend-ing on the nature of the interaction. Often, long-range interactions, which occur when the particles are far apart, may be significant in plasma behavior. In any event, we can define some quantities that will help us to work with these collision processes. The first quantity is the collision cross section. We consider a collection of particles characterized by a density N per cubic meter.
- L Christophorou(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
However, the role of electron-molecule collisions in the areas of new, and renewed, interest will be outlined as examples of where electron-impact cross sections are needed. This is not meant to be a comprehensive review of these fields of research, but rather just a sampling to provide perspective on the role of electron-molecule collisions in various processes. 7. Electron-Beam Transport There is now considerable interest in the transport properties of, and the extraction of energy from, relativistic electron beams passing through atomic and molecular gases. Depending on the composition of the gas medium, its pressure, and the electron-beam energy, a variety of phenomena occur which are currently incompletely understood. In the case of H 2 as the gas medium, it has been determined (de Haan et al, 1981a) experimentally that there is a region around an H 2 pressure of 1 Torr for which the electron-beam energy loss is relatively small and the propagation is stable. A quantitative understanding of the reasons for this behavior is difficult because the energy coupling to the medium comes not only from the electron beam, but also from plasma-wave instabilities produced in the plasma. Under conditions of partial ionization, nearly all possible atomic and molecular species (e.g., H 3 + as well as H 2 , H, and H + ) are present (de Haan et a/., 1981b). Such phenomena are not in thermal equilibrium and the detailed response of the gas medium for a given incident beam energy (e.g., dissipation of plasma waves, buildup of plasma instabilities, power balance, plasma current, and plasma decay), has to depend on the fundamental characteristics of the medium. For example, N 2 is very stable against electron-impact dissociation relative to H 2 and 0 2 , which dissociate readily.
eBook - PDFRadioisotope and Radiation Physics
An Introduction
- M Miladjenovic(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
Dominant Effect of an Elastic Collision with a Nucleus. Projectiles usually have a mass considerably smaller than that of a nuclear mass. From the above relations it follows that the dominant effect in a collision with a heavier particle is deflection, whereas the energy loss is very small. For a and β particles it can be assumed that elastic collisions with nuclei lead only to deflection, that is, that the energy loss can be neglected. 4.1.2. INELASTIC C O L L I S I O N S W I T H AN E L E C T R O N C L O U D In an inelastic collision between a charged particle and a bound electron, the particle transfers a part of its energy to the atom. The energy trans-ferred is expended for overcoming the binding energy of the struck electron. If the bond is not broken but only loosened, then the atom or molecule is said to be in an excited state. If the collision leads to the ejec-tion of the struck electron, then the atom or molecule becomes ionized. We shall consider some basic properties of the two processes. Excitation. The processes of excitation are very diverse, and depend on the system to which the atoms belong. In Chapter 2, we mentioned the 4.1. Collisions 81 modes of excitation of a molecule. The solid state also has particular forms of excitation. In this section we shall concentrate mainly on the excitation of an isolated atom, since this is the starting point for the study of the more complex processes. The excitation of an atom is a quantum mechanical process by which an electron of the atom passes to a vacancy in one of the states in which it is less tightly bound to the nucleus. An electron from the Κ shell cannot make the jump to the L shell if the latter is filled, but must go on toward the periphery until it finds a vacancy. Therefore, the excitation energy would be close to the ionization energy. If an electron from an outer shell is excited, it does not need a large amount of energy to find a vacancy.
eBook - PDF- P. M. Banks, G. Kockarts(Authors)
- 2013(Publication Date)
- Academic Press(Publisher)
9.5 Elastic Collisions of Electrons with Neutral Particles 197 TABLE 9.4 (Continued) z (km) 74 75 76 77 78 79 80 81 82 83 84 85 86 87 T (°K) 206 204 194 203 191 201 187 200 184 199 181 197 177 196 174 194 170 193 167 192 164 190 160 192 164 193 167 Pressure (Torr) 2.3 x 2.0 1.9 1.7 1.6 1.4 1.3 1.2 1.1 1.0 9.5 x 8.6 7.9 7.3 6.5 6.1 5.4 5.2 4.4 4.3 3.6 3.6 2.9 3.1 2.4 2.6 2.0 io-2 io-3 Collision frequency (sec -1 ) 4.2 x 3.6 3.4 3.0 2.8 2.5 2.3 2.1 2.0 1.8 1.7 1.5 1.4 1.3 1.2 1.1 9.7 x 9.3 7.8 7.8 6.6 6.6 5.3 5.5 4.2 4.7 3.6 10« IO 5 z (km) 88 89 90 91 92 93 94 95 96 97 98 99 100 T (°K) 194 170 195 173 197 177 198 180 199 183 200 186 202 190 203 193 204 196 205 200 207 203 208 206 209 209 Pressure (Torr) 2.2 x 1.6 1.8 1.3 1.5 1.1 1.3 x 9.1 x 1.1 x 7.6 x 9.4 x 6.3 7.9 5.3 6.7 4.5 5.7 3.8 4.8 3.2 4.1 2.7 3.5 2.3 3.0 2.0 io-3 io-3 io-4 io-3 io-4 io-4 Collision frequency (sec -1 ) 3.8 x 10 5 3.0 3.4 2.3 2.8 2.0 2.3 1.6 2.0 1.4 1.7 1.1 1.4 9.5 x IO 4 1.2 x IO 5 8.0 x IO 4 1.0 x IO 5 6.8 x IO 4 8.7 5.7 7.4 4.9 6.4 4.0 5.5 3.6 198 9 Collision Processes 9.5 Inelastic Electron Collisions with Neutral Particles The cross sections and collision frequencies considered in the last section refer exclusively to elastic processes where internal energy states of the target atom, molecule, or ion are not excited. For many aspects of aeronom-ical studies, however, the collisions of energetic electrons with neutral particles which lead to excited atomic and molecular states must be considered [10-13]. Important consequences of inelastic collisions be-tween electrons and the atmospheric gases include the auroral emissions, the photoelectron dayglow, and the cooling of the ionospheric electron gas. The electron impact excitation of rotational states in molecules possessing a permanent dipole moment can provide an important loss of electron kinetic energy.
eBook - PDFQuantum Theory
Elements
- D. R. Bates(Author)
- 2013(Publication Date)
- Academic Press(Publisher)
9. THEORY OF COLLISIONS 3 9 5 We consider an inelastic collision in which an electron in the state 0 makes a transition to the state n. The initial and final wave functions may then be written as Slater determinants involving wave functions of individual electrons moving in the field of the nucleus and of the other electrons. In the integrations over the coordinates of all the electrons, all the terms vanish as a result of orthogonality except those involving the two states 0 and n, and the expression for the cross section given by Born's approximation reduces to the form ( 3 0 7 ) , where now 0 Q , are wave functions for individual electrons in the field of the nucleus and the other electrons. In many calculations these functions have been taken to be similar to those for a hydrogen atom, with approximate adjustments of the nuclear charge to allow for screening of the nucleus by other electrons, according to rules obtained by Slater.^^ Better results would be expected however by using wave functions corresponding to the motion of the electron in a Fermi-Thomas or a Hartree-Fock field. 12.2 Effect of Allowing for Electron Exchange In § 11 .5 we have discussed the method of studying inelastic scattering of electrons by hydrogen atoms when allowance is made for the identity of the incident electrons and the electrons in the atom. Allowing for inelastic collisions in which excitation through intermediate states is ignored, the solution of the problem reduced to the solution of the two integro-differential Eqs. ( 2 8 8 ) and ( 2 8 9 ) . The distorted wave method of solving these equations gave ( 2 9 7 ) for the scattering amplitude where the first term corresponds to direct scattering. If and φ^ are replaced by plane waves this term reduces to Born's approximation and the results it gives have been discussed above. A Similar substitution in the second term leads to the Born-Oppen-heimer approximation.
eBook - PDFAtomic Processes and Application
In Honour of David R. Bates' 60th Birthday
- P. G. Burke, B. L. Moiseiwitsch, P. G. Burke, B. L. Moiseiwitsch(Authors)
- 2013(Publication Date)
- North Holland(Publisher)
§3] High-energy atom-atom collisions 513 Included Böttcher and Flannery Ritchie Nuclear symmetry Yes N o Rotation of the nuclear axis during the collision Yes N o Translational motion of the electron N o Yes Clearly both approaches contain unphysical assumptions and the theory of electron exchange must be examined further in the light of their divergent results. 3. Classical treatment In their first paper applying the classical impulse approximation to atom-atom colhsions Bates and Walker (1966) studied the electron loss from excited states of hydrogen in coUision with other atoms and molecules H(n/) + B ^ H + e + B. (16) They consider the nucleus A of the incident hydrogen atom moving with constant velocity U relative to the target atom Β and the projectile electron e moving with velocity W relative to A. It is assumed that the energy required to ionize the hydrogen atom is provided by an elastic collision between e and Β at relative velocity V = l / -f W . (17) If the polar axis is parallel to V and (Θ, ) are the scattering angles then it may be shown that the electron of the hydrogen atom receives enough energy to ionize it if L/[([/+ V c o s ( p ) ( l -c o s Ö ) + W s i n e sin φ cos φ]^ I (18) = the ionization potential impact parameter calculation. For 2s excitation, the difference between their results is enormous (cf. fig. 1), and the discrepancy raises doubts as to how electron exchange should be treated. Table 1 indicates the main differences between the two calculations: Table 1.
eBook - PDFAtomic-Molecular Ionization by Electron Scattering
Theory and Applications
- K. N. Joshipura, Nigel Mason(Authors)
- 2019(Publication Date)
- Cambridge University Press(Publisher)
(2014); and in combustion processes, where the removal of electrons by electronegative gases provides a means to extinguish a fire without withdrawing oxygen and is thus used in aircraft to extinguish cabin fires. The study of electron scattering from atoms and molecules has grown rapidly since the Frank and Hertz experiment in 1914 and the first quantum mechanical treatments in the 1930s. The wide range of applications ensure that the study of such processes will be important in times to come. Much of the data required for such applications will necessarily be generated by theoretical methods, as explained in this book, with benchmarks being provided by a few definitive experiments. In conclusion, we look back and wonder at the long conceptual journey from hydrogen to complex atoms, from the small and the common to large and exotic molecular systems, which include fascinating radicals and metastable species. Larger targets such as biomolecules offer challenges as well as opportunities. Collisions and scattering that we dealt with in the first five chapters are essentially micro-level phenomena but micro rules the macro, and that was the guiding principle behind the discourses of this concluding chapter. For, it is the basic knowledge that opens up possibilities of potential application in diverse fields of technology today. Though we are in the second decade of the twenty-first century, it would be most appropriate to end with a famous and relevant quote from none other than Richard Feynman. ‘We are at the very beginning of time for the human race. It is not unreasonable that we grapple with problems. But there are tens of thousands of years in the future. Our responsibility is to do what we can, learn what we can, improve the solutions, and pass them on.’ – Richard P. Feynman ✪ ✪ ✪ Abdel-Naby, S. A., M. S. Pindzola, A. J. Pearce, C. P.
eBook - PDF- Peter J. Goodhew, John Humphreys, John Humphreys(Authors)
- 2000(Publication Date)
- CRC Press(Publisher)
There are many interaction processes which could cause energy to be lost by the primary electron and transferred to the electrons or atoms of the specimen. We will only consider four of the most probable types of scattering event. It is important to realize that the inelastic scattering processes (probably in combi-nation) are eventually responsible for the stopping of an electron by a solid. Almost all of the kinetic energy which was carried by the primary electron will end up as heat in the specimen. A small proportion of the energy may escape as X-rays, light or secondary electrons and these may prove extremely useful for both imaging and analysis, as we show in Chapters 5 and 6. Secondary effects are dealt with in the next section; first let us consider the main types of inelastic scattering process. 2.7./ Phonon scattering Phonons are the quanta of elastic waves, that is of atomic vibrations in a solid. A primary electron can lose energy by exciting a phonon and effectively heating the solid slightly. The amount of energy lost in doing this is rather small, generally less than 1 eV, and the mean free path for high energy electrons is quite large, of the order of jam. These facts do not mean that phonon scattering is unimportant, for two main reasons. All electrons which remain in the solid are likely to excite phonons eventually, perhaps after they have lost larger amounts of energy by other means (see below) and this is how the solid is heated by the electron beam. Also, when phonon scattering occurs the scattered electron is generally deflected through quite a large angle, typically 10 degrees. This will be significant in the discussion of image contrast in Chapter 4. 2.7.2 Plasmon scattering A plasmon is a wave in the ‘sea’ of electrons in the conduction band of a metal. There are similar effects among the bonding electrons of non-metals.
eBook - PDF- Bernd Crasemann(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
2 Ion-Atom Collisions PATRICK RICHARD Department of Physics Kansas State University Manhattan, Kansas 2.1. Introduction 74 2.2. Reaction Mechanisms 79 2.3. Experimental Measurements on Ion-Atom Collisions 85 2.3.1. Κ x-Ray Cross Sections 85 2.3.2. L x-Ray Cross Sections 94 2.3.3. High-Resolution x-Ray Measurements 99 2.3.4. Impact-Parameter Dependence of x-Ray Production 110 2.3.5. Nonmonotonic Ζ Dependence of x-Ray Production Cross Sections 115 2.3.6. x-Ray Cross-Section Measurements in Gas Targets 119 2.3.7. High-Resolution x-Ray Measurements in Gas Targets 121 2.3.8. Auger-Electron Measurements 123 2.3.9. Radiative Electron Capture and Bremsstrahlung 126 2.3.10. United Atom Phenomena 129 2.3.11. Plasmon and Hypersatellite Excitations in Ion-Atom Colli-sions 131 2.3.12. Electron Capture, Excitation, and Exchange in Collisions of Few-Electron Projectiles with Gas Targets 132 2.3.13. Inelastic Energy-Loss Method 133 2.4. Metastable States with K-Shell Vacancies 135 2.4.1. Introduction 135 2.4.2. Experimental Techniques 136 2.4.3. Results 140 References 152 73 74 Patrick Richard 2.1. Introduction The subject of ion-atom collisions as related to inner-shell ionization is reviewed in this chapter with particular emphasis on the experimental methods and results. The review includes collisions studied with all types of ions from protons (Z = 1) to the heaviest available projectile ions, but specifically excludes collisions with incident electron beams. The study of inner-shell ionization dates back to the discovery of χ rays by Rontgen (1895, 1898) who first observed the mysterious radiation produced by high-energy electrons. During the next 18 years, rigorous study led to the discovery by W. H. Bragg (1913) that the radiation from an x-ray tube consists of a continuous spectrum upon which a number of distinct peaks characteristic of the anode material are superimposed.
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