Physics
Compton Scattering
Compton scattering is a phenomenon in which a photon collides with an electron, resulting in the photon losing energy and changing direction. This process demonstrates the particle-like behavior of light and provides evidence for the dual nature of electromagnetic radiation. Compton scattering is a crucial concept in understanding the interaction between photons and matter.
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11 Key excerpts on "Compton Scattering"
- Mikhail V Fedorov(Author)
- 1998(Publication Date)
- World Scientific(Publisher)
CHAPTER 3 MULTIPHOTON Compton Scattering AND PONDEROMOTIVE FORCES IN AN INHOMOGENEOUS LIGHT FIELD 3.1. Spontaneous and stimulated Compton Scattering As in the previous chapter, let us begin with the main definitions. The usual Compton Scattering is a well-known second-order process in which an external photon (with a frequency © and a wave vector k) is absorbed by an electron, and simultaneously a different photon (with some different frequency a>' and wave vector k) is emitted. This process is described schematically by the diagram in Fig. 19. As is evident from this definition, Compton Scattering does not require any third body (in contrast with the bremsstrahlung) but does require the presence of external photons. As for the emitted photon, it can either be emitted spontaneously, or its emission can be stimulated by an external field. In the latter case, it is assumed that external photons are present not only in the mode (
eBook - PDFAstrophysics Processes
The Physics of Astronomical Phenomena
- Hale Bradt(Author)
- 2008(Publication Date)
- Cambridge University Press(Publisher)
The synchrotron self-Compton (SSC) process, the Compton limit, and the Comptonization of a photon spectrum will be discussed qualitatively. Finally, we will present the Sunyaev–Zeldovich effect in which photons of the cosmic microwave background (CMB) are scattered by electrons of the plasmas in clusters of galaxies. 9.2 Classic Compton Scattering A photon interacts with a stationary electron and gives it some of its energy. We derive the reduced energy of the scattered photon as a function of its angle of scatter. Compton wavelength Consider the collision of a photon with a stationary, free electron shown in Fig. 9.1. The photon loses energy as it scatters into angle u , and this energy is given to the electron. The famous Compton relation between the incoming and scattered wavelengths, l and l s , respectively, follows from energy and momentum conservation, ➡ l s − l = h mc (1 − cos u ) , (m; wavelength shift; Compton effect) (9.1) where m is the electron mass. This result is relativistically correct; it is derived in this section. The quantity h / mc is known as the Compton wavelength l C ; its value is l C = h / mc = 2 . 42 × 10 − 12 m = 2 . 42 pm , (Compton wavelength) (9.2) → 1 . 24 × 10 20 Hz → 0 . 511 MeV where we use the relations ln = c and E (eV) = h n /e to obtain the equivalent frequency and photon energy. The energy turns out to be the rest energy of the electron. 9.2 Classic Compton Scattering 331 According to (1), the wavelength shift l s − l at any given angle u is of order 10 − 12 m and independent of the incident wavelength. Compare this with visible wavelengths, which are on the order of ∼ 600 nm. The fractional shift, ( l s − l )/ l , becomes substantial only if the incoming wavelength l is so short as to be comparable to 10 − 12 m, at which point the photon energy approaches that of the electron rest energy, mc 2 = 0.511 MeV; see (2). X-ray photons were used by Arthur Compton in 1922 to verify this effect.
eBook - PDFHigh Energy Radiation from Black Holes
Gamma Rays, Cosmic Rays, and Neutrinos
- Charles D. Dermer, Govind Menon(Authors)
- 2009(Publication Date)
- Princeton University Press(Publisher)
Chapter Six Compton Scattering The astrophysics of the Compton Scattering process for relativistic particles is treated in this chapter, specialized to relativistic electrons. After deriving the elementary Compton Scattering formula, the behavior of the Comp- ton cross section in the Thomson and Klein-Nishina regimes is examined. Compton Scattering regimes are determined by the value of the invariant ¯ = γ (1 − β par µ), which is the photon energy in the electron rest frame ( ¯ = for electrons at rest). In the Thomson regime, ¯ 1, and in the Klein-Nishina regime, ¯ 1. For isotropic photon fields, analysis of the Compton energy-loss rate shows that the two regimes are characterized by the value of the parameter e = 4γ . Expressions for the differential cross section that are useful for calcu- lations of Compton-scattered spectra are derived in the head-on approxi- mation, and the accuracy of the different forms is examined. Applications of this process to γ -ray production from black-hole jet sources are considered. Compton Scattering of surrounding target radiation fields by relativistic jet electrons is treated. 6.1 COMPTON EFFECT Consider a photon with dimensionless energy = λ C /λ and wavelength λ scattering an electron at rest (figure 6.1). After scattering, a photon with energy s = λ C /λ s travels in a direction that makes an angle χ with respect to the direc-tion of the incident photon. The scattered electron acquires Lorentz factor γ e = 1/ 1 − β 2 e and is scattered in the direction θ e with respect to the incident photon direction. Energy conservation requires 1 + = s + γ e , (6.1) and conservation of momenta parallel and transverse to the initial photon direction can be expressed as = s cos χ + β e γ e cos θ e , (6.2) s sin χ = β e γ e sin θ e , (6.3) Compton Scattering 71 χ . θ e s γ e Figure 6.1 The Compton effect. In the electron rest frame (ERF), a photon with energy is scattered by a stationary electron.
eBook - PDF- Samuel D Lindenbaum(Author)
- 1999(Publication Date)
- WSPC(Publisher)
Chapter 27 Compton Scattering Photon-Electron Interaction In interactions of Dirac particles (electrons) with each other and with photons, both negatrons and positrons are viewed as quanta of the Dirac field, represented by complex 4-component spinors, while photons are viewed as quanta of the MaxweUian 4-vector field. In diis chapter we study perhaps die most important of these interactions, namely, the photon-electron interaction known as Compton Scattering. To derive the relations between the momenta involved, consider the process illustrated in Fig. 27-1. A photon of momentum k collides with an electron at rest, and causes a photon of momentum k' and an electron of momentum p to be scattered. We know that photon momentum is given by k, with energy component ififyc, while electron momentum is p with energy component i€/c. If, for simplification purposes, we set % m c - 1, then in 4-vector notation we have: [27-1] Jfc M = (k h ik) for photons. [27-2] /> M -Oi.i'e) for electrons. We are adhering to die usual convention regarding Greek and Latin sub-scripts u (1,2,3,4) and i (1,2,3), respectively. It follows from [27-1] and [27-2] that [27-3] ^ = £-£ = 0. [27-4] p = p 2 - e 2 - / - (p 2 c 2 + mV) --m 2 . Lecture Notes on Quantum Mechanics 315 Conservation of momentum is expressed as p{ + jfc/ -p t + fy , while con-servation of energy is given by jf + £' = Jfc + £, where primes refer to the system after collision and the unprimed quantities refer to the system before collision. These two conservation expressions can be combined as: P7-5] i y + y = /v+v Squaring both sides: [27-6] P ; 2 = P 2 + (* M - y f + y 2 + 1 ? ] ,% -y ) . From [27-3] and [27-4]: [27-7] -m 2 = -m 2 + 2p M (^ - y ) - 2 y y . Substituting [27-1] and [27-2] into [27-7] and expanding: 0 = 2p(k - k') + 2p 4 (fc 4 -* 4 ') - 2(kk' + k 4 k 4 '). For an initial electron at rest, p n = (0, im), so that 0 -2initk-aO-2dk:V*ikilO - 0 --m(k -Id) - kk' + W.
- Sow-Hsin Chen, Michael Kotlarchyk;;;(Authors)
- 1997(Publication Date)
- WSPC(Publisher)
One should be aware, however, that more correctly, the true Compton effect refers to an event where the photon is, in actuality, scattered by an atomic electron, causing the electron to go from a bound state to the continuum in the process. For photon energies that are non-relativistic, i.e., a I A) K^ = (B | (0 kA , l k , A , I V 2 | l k A , ( W ) | -4).
- Sow-Hsin Chen, Michael Kotlarchyk;;;(Authors)
- 2007(Publication Date)
- WSPC(Publisher)
Examples include the following: 1. Scattering of a photon by a free electron (e.g., Thomson scattering) 2. Scattering of a photon by an atom, i.e., (a) Compton Scattering (b) Rayleigh scattering (c) Raman scattering We will examine certain aspects of each of these types of scattering processes. 262 Second-Order Processes and the Scattering of Photons 9.1 Scattering of Electromagnetic Radiation by a Free Electron Let us begin by considering the scattering of a photon having an energy much greater than the binding energy of an atomic electron. It is then quite reasonable to treat the electron as essentially unbound, or free, and initially at rest. Below we show that for this, the simplest of scattering processes, there is a clear link between the quantum-mechanically derived cross-section and the classical result. 9.1.1 Classical Theory For a classical treatment of the problem, one considers the incident radiation to be a monochromatic, polarized EM wave: E i ( r ,t )= epsilon1 E 0 cos( k · r -ωt ) . (9.1) The effect of this oscillating field on a free electron is to produce a harmonic acceler-ation of ˙ v = F i m = e m E i = epsilon1 eE 0 m cos( k · r -ωt ) . (9.2) The electron, in turn, radiates away energy as a scattered EM wave, also at the frequency ω . Assuming the motion of the electron is non-relativistic, the scattered field at position R relative to the electron is given by [59] E s ( R ,t )= e c 2 bracketleftbigg e R × ( e R × ˙ v ) R bracketrightbigg , (9.3) where e R = R /R (Fig. 9.1 shows the scattering geometry). From the Poynting vector (see Eq. 4.129) S s = c 4 π | E s | 2 e R , (9.4) the power radiated per steradian becomes dP d Ω =( S s · e R ) R 2 = e 2 4 πc 3 | e R × ( e R × ˙ v ) | 2 = e 2 4 πc 3 | ˙ v | 2 sin 2 γ, (9.5) where γ is the angle between e R and the polarization vector epsilon1 . Comparison with Eq. 4.130 reminds one that the sin 2 γ angular distribution is characteristic of elec-tric dipole radiation, as previously depicted in Fig.
eBook - PDFThe Propagation of Gamma Quanta in Matter
International Series of Monographs on Nuclear Energy, Volume 6
- O. I. Leipunskii, B. V. Novozhilov, V. N. Sakharov, J. V. Dunworth(Authors)
- 2016(Publication Date)
- Pergamon(Publisher)
The intensity and energy of this radiation is considerably less than that of the primary radiation, so that its effect can be neglected in comparison with the effect of the primary radiation. The three main processes by which quanta interact with matter will be briefly considered below: the photo-electric effect, Compton Scattering and pair production. We shall be interested only in the probability of interaction of y-quanta with matter and in the state of the quantum (its energy and direction of motion) after the interaction. A more detailed description of the processes enumerated above will be found, for example, in [1-4]. Quantities called cross-sections for scattering or absorption of quanta are usually employed as quantitative characteristics of the probability for INTRODUCTION 3 scattering or absorption. The scattering cross-section is defined as follows. Let us suppose that at the point O (Fig. 1) there is an electron, on which is incident along the Z-axis a parallel and homogeneous beam of y-quanta, the beam being infinite in the directions X and Y. Let the flux of the beam of quanta, i.e. the number of quanta passing in unit time through unit area, be 7V 0 and the number of quanta scattered in unit time be N. Then the ratio is called the scattering cross-section. This has the dimensions of length squared. It is evident that if there are n 0 scattering electrons in unit volume, the number of y-quanta scattered per unit time in volume dv is dN = N Q a s n Q dv. The probability of a quantum being scattered while traversing a path length d/is given by dw = -^ -^ = # 0 < 7 β Π ο £ _ _ = a s n 0 dl (1.6) (S is the cross-sectional area of the beam). Thus the cross-section a s is numerically equal to the scattering probability for a quantum in unit path of a substance containing one electron per unit volume. The considerations above would hold for the processes of photo-electric absorption and pair production also.
eBook - PDFPhysics 1922 – 1941
Including Presentation Speeches and Laureates' Biographies
- Sam Stuart(Author)
- 2013(Publication Date)
- Elsevier(Publisher)
Hence the phenomenon cannot be explained as a new characteristic radiation of the same nature as that hitherto known; and Compton deduced a new kind of corpuscular theory, with which all experimental results showed perfect agreement within the limits of exper-imental error. According to this theory, a quantum of radiation is re-emitted in a definite direction by a single electron, which in so doing must recoil in a direction forming an acute angle with that of the incident radiation. In its mathemat-ical dress this theory leads to an augmentation of the wavelength that is independent of the wavelength of the incident radiation and implies a veloc-ity of the recoil electron that varies between zero and about 80% of the velocity of light, when the angle between the incident and the scattered radiation varies between zero and 180 0 . Thus this theory predicts recoil electrons with a velocity generally much smaller than that of the above-mentioned electrons which correspond to the photoelectric effect. It was a triumph for both parties when these recoil elec-trons were discovered by Wilson's experimental method both by Wilson himself and, independently, by another investigator. Hereby the second chief phenomenon of the Compton effect was experimentally verified, and all observations proved to agree with what had been predicted in Compton's theory. Quite apart from the improvements and additions that have been made to this theory by other investigators, the Compton effect has, through the latest evolutions of the atomic theory, got rid of the original explanation based upon a corpuscular theory. The new wave mechanics, in fact, lead as a logical consequence to the mathematical basis of Compton's theory. Thus the effect has gained an acceptable connection with other observations in the sphere of
- Stefano Spezia(Author)
- 2019(Publication Date)
- Arcler Press(Publisher)
This effect, known as the Kapitza–Dirac effect, was proposed in 1933 [4] and we realized this experiment in 2001 [13,14]. The process by which the electron exchanges momentum with light is stimulated Compton Scattering. One photon is absorbed, while the emission of another is stimulated (Fig. 2A). Energy and angular momentum are conserved in this process (Fig. 2B, 2D). As the absorption and stimulated emission are due to photons coming from opposite directions, the electron experiences a recoil of momentum (Fig. 2C), where k = 2π/λ. At a basic level it is easy to verify that the scattering angle θ ≈ /pe and the diffraction angle are identical supporting the explanation of electron diffraction by a “light grating” as stimulated Compton Scattering. At a more formal level, perturbation theory and second quantization of the light field can be used to support this claim [15]. The understanding of the mechanism also leads to predictions. When the polarization of the counter propagating light beams is chosen to be perpendicular, no standing wave forms and the electrons do not diffract. Or in the particle picture; angular momentum conservation does not work for photons that carry opposite angular momentum. Before the interaction the two photons carry a total of zero angular momentum, while after the stimulated emission the two photons carry two units of ~ angular momentum. The electron can at most change its angular momentum by one unit of ~ in a spin flip process [15]. Inspection of the electron diffraction pattern from light, and from the double-slit reveal, not surprisingly, a very similar phenomenology (Fig. 3). And, a standard quantum mechanical description of the experiments gives good agreement in both these cases. The surprise is that the mechanism can be explained for a light-grating, but not the double-slit case. Let’s consider electron diffraction from an ionic crystalline lattice as in the famous Davisson-Germer experiment [16].
- N.J Carron(Author)
- 2006(Publication Date)
- CRC Press(Publisher)
Then, instead of a single element, the scattering center may be a molecule or a crystal cell, or any repeated unit of several elements in an arbitrary mixture. In this case, each of s pe , s C , s Rayl , and s pp is the cross section for scattering from that scattering center; for water s C ¼ 2 s C (H) þ s C (O). 2.9.2 E NERGY T RANSFERRED TO THE T ARGET M ATERIAL : K ERMA Neutral particles (photons or neutrons) passing through matter are referred to as indirectly ionizing particles. Charged particles (electrons, protons, and ions) are directly ionizing . The obvious reason is that photons or neutrons do not directly ionize the material. They do so only after interacting with an *As mentioned previously, our Compton cross section, s C , is what Evans [Ev55] calls the collision cross section. His symbol for it on a single electron is e s . 114 An Introduction to the Passage of Energetic Particles through Matter atom and kicking out an electron (or recoil target nucleus), and that moving charged particle then ionizes by direct ionizing stopping power. Thus, the process by which an indirectly ionizing particle deposits energy in a target material is a two-step process. In the first step, the neutral particle, in the present case a photon, interacts with an atom and ejects one or more charged particles (directly ionizing particles), and perhaps a secondary neutral particle (e.g., Compton scattered photon). The charged particles, in the pre-sent case one or more electrons, are ejected with some kinetic energy. In the second step, those charged particles deposit much of their energy directly in the target by ionization and excitation collisions with target atoms (by collisional stopping power). The quantity kerma , or the energy-transfer coefficient that is directly related to it, is introduced to parameterize the first step. The quantity dose , or the directly related energy-absorption coefficient , is introduced to para-meterize the second step [ICRU80, Ca85].
eBook - PDF- Frederic V. Hartemann(Author)
- 2001(Publication Date)
- CRC Press(Publisher)
It also has a nonzero value for a particle submitted to a constant acceleration, as opposed to the Schott term. On the other hand, the second term in Equation 10.151 is attributed to the energy–momentum exchanged between the scattered wave and the external field. This term allows for the local simultaneous conservation of energy and momentum during the radiation process. The physics of the interaction can be illustrated by consid-ering the process shown in Figure 10.12. Here, we consider the total energy and momentum of the electrodynamical system initially comprising a high intensity, short wavelength incoming laser pulse (pump) and an electron at rest. In general, after the interaction, the electron has gained some energy and momentum (in the minimal case, the electron would be left precisely at rest after the scattering) and is now moving at relativistic velocity, while the scattered wave carries energy and momentum in all spatial directions. In this case, it is clear that all the energy and momentum gained by both the electron and the scattered wave come at the expense of the external field. It is equally clear that, in such a process, the radiated electromagnetic power and the variation of the electron energy cannot be equal, therefore invalidating any theoretical model based on the local conservation of four-momentum between the electron and the radiated field only. We also note that while the backscattered radiation does not interfere with the laser pulse, the forward scattered radiation, which has the same spectral characteristics as the pump and copropagates in the positive z -direction, does interfere destructively F τ 0 γ 2 β ˙˙ 3 γ 2 β ˙ β β ˙ ⋅ ( ) γ 2 β β β ˙˙ 3 γ 2 β β ˙ ⋅ ( ) 2 + ⋅ [ ] + + { } . = d γ dt -----τ 0 γ 4 β β ˙˙ 3 γ 2 β β ˙ ⋅ ( ) 2 + ⋅ [ ] β F . ⋅ = = Compton Scattering, Coherence, and Radiation Reaction 613 with the laser pulse and lowers its energy and momentum, yielding pump-field depletion.
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