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Light–matter interaction |
---|

Low-energy phenomena: |

Photoelectric effect |

Mid-energy phenomena: |

Thomson scattering |

Compton scattering |

High-energy phenomena: |

Pair production |

Photodisintegration |

Photofission |

**Thomson scattering** is the elastic scattering of electromagnetic radiation by a free charged particle, as described by classical electromagnetism. It is the low-energy limit of Compton scattering: the particle's kinetic energy and photon frequency do not change as a result of the scattering.^{ [1] } This limit is valid as long as the photon energy is much smaller than the mass energy of the particle: , or equivalently, if the wavelength of the light is much greater than the Compton wavelength of the particle (e.g., for electrons, longer wavelengths than hard x-rays).^{ [2] }

Thomson scattering is a model for the effect of electromagnetic fields on electrons when the field energy is much less than the rest mass of the electron . In the model the electric field of the incident wave accelerates the charged particle, causing it, in turn, to emit radiation at the same frequency as the incident wave, and thus the wave is scattered. Thomson scattering is an important phenomenon in plasma physics and was first explained by the physicist J. J. Thomson. As long as the motion of the particle is non-relativistic (i.e. its speed is much less than the speed of light), the main cause of the acceleration of the particle will be due to the electric field component of the incident wave. In a first approximation, the influence of the magnetic field can be neglected.^{ [2] }^{: 15 } The particle will move in the direction of the oscillating electric field, resulting in electromagnetic dipole radiation. The moving particle radiates most strongly in a direction perpendicular to its acceleration and that radiation will be polarized along the direction of its motion. Therefore, depending on where an observer is located, the light scattered from a small volume element may appear to be more or less polarized.

The electric fields of the incoming and observed wave (i.e. the outgoing wave) can be divided up into those components lying in the plane of observation (formed by the incoming and observed waves) and those components perpendicular to that plane. Those components lying in the plane are referred to as "radial" and those perpendicular to the plane are "tangential". (It is difficult to make these terms seem natural, but it is standard terminology.)

The diagram on the right depicts the plane of observation. It shows the radial component of the incident electric field, which causes the charged particles at the scattering point to exhibit a radial component of acceleration (i.e., a component tangent to the plane of observation). It can be shown that the amplitude of the observed wave will be proportional to the cosine of χ, the angle between the incident and observed waves. The intensity, which is the square of the amplitude, will then be diminished by a factor of cos^{2}(χ). It can be seen that the tangential components (perpendicular to the plane of the diagram) will not be affected in this way.

The scattering is best described by an emission coefficient which is defined as *ε* where *ε**dt**dV**d*Ω *dλ* is the energy scattered by a volume element in time *dt* into solid angle *d*Ω between wavelengths *λ* and *λ*+*dλ*. From the point of view of an observer, there are two emission coefficients, *ε*_{r} corresponding to radially polarized light and *ε*_{t} corresponding to tangentially polarized light. For unpolarized incident light, these are given by:

where is the density of charged particles at the scattering point, is incident flux (i.e. energy/time/area/wavelength), is the angle between the incident and scattered photons (see figure above) and is the Thomson cross section for the charged particle, defined below. The total energy radiated by a volume element in time *dt* between wavelengths *λ* and *λ*+*dλ* is found by integrating the sum of the emission coefficients over all directions (solid angle):

The Thomson differential cross section, related to the sum of the emissivity coefficients, is given by

expressed in SI units; q is the charge per particle, m the mass of particle, and a constant, the permittivity of free space. (To obtain an expression in cgs units, drop the factor of 4π*ε*_{0}.) Integrating over the solid angle, we obtain the Thomson cross section

in SI units.

The important feature is that the cross section is independent of light frequency. The cross section is proportional by a simple numerical factor to the square of the classical radius of a point particle of mass *m* and charge *q*, namely^{ [2] }^{: 17 }

Alternatively, this can be expressed in terms of , the Compton wavelength, and the fine structure constant:

For an electron, the Thomson cross-section is numerically given by:^{ [3] }

The cosmic microwave background contains a small linearly-polarized component attributed to Thomson scattering. That polarized component mapping out the so-called E-modes was first detected by DASI in 2002.

The solar K-corona is the result of the Thomson scattering of solar radiation from solar coronal electrons. The ESA and NASA SOHO mission and the NASA STEREO mission generate three-dimensional images of the electron density around the Sun by measuring this K-corona from three separate satellites.

In tokamaks, corona of ICF targets and other experimental fusion devices, the electron temperatures and densities in the plasma can be measured with high accuracy by detecting the effect of Thomson scattering of a high-intensity laser beam. An upgraded Thomson scattering system in the Wendelstein 7-X stellarator uses Nd:YAG lasers to emit multiple pulses in quick succession. The intervals within each burst can range from 2 ms to 33.3 ms, permitting up to twelve consecutive measurements. Synchronization with plasma events is made possible by a newly added trigger system that facilitates real-time analysis of transient plasma events.^{ [4] }

In the Sunyaev–Zeldovich effect, where the photon energy is much less than the electron rest mass, the inverse-Compton scattering can be approximated as Thomson scattering in the rest frame of the electron.^{ [5] }

Models for X-ray crystallography are based on Thomson scattering.

In physics, the **cross section** is a measure of the probability that a specific process will take place in a collision of two particles. For example, the Rutherford cross-section is a measure of probability that an alpha particle will be deflected by a given angle during an interaction with an atomic nucleus. Cross section is typically denoted *σ* (sigma) and is expressed in units of area, more specifically in barns. In a way, it can be thought of as the size of the object that the excitation must hit in order for the process to occur, but more exactly, it is a parameter of a stochastic process.

In physics, **electromagnetic radiation** (**EMR**) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. Types of EMR include radio waves, microwaves, infrared, (visible) light, ultraviolet, X-rays, and gamma rays, all of which are part of the electromagnetic spectrum.

**Rayleigh scattering**, named after the 19th-century British physicist Lord Rayleigh, is the predominantly elastic scattering of light, or other electromagnetic radiation, by particles with a size much smaller than the wavelength of the radiation. For light frequencies well below the resonance frequency of the scattering medium, the amount of scattering is inversely proportional to the fourth power of the wavelength, e.g., a blue color is scattered much more than a red color as light propagates through air.

In electromagnetism, the **absolute permittivity**, often simply called **permittivity** and denoted by the Greek letter *ε* (epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more in response to an applied electric field than a material with low permittivity, thereby storing more energy in the material. In electrostatics, the permittivity plays an important role in determining the capacitance of a capacitor.

In particle physics, ** bremsstrahlung** is electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typically an electron by an atomic nucleus. The moving particle loses kinetic energy, which is converted into radiation, thus satisfying the law of conservation of energy. The term is also used to refer to the process of producing the radiation.

**Compton scattering** is the quantum theory of high frequency photons scattering following an interaction with a charged particle, usually an electron. Specifically, when the photon hits electrons, it releases loosely bound electrons from the outer valence shells of atoms or molecules.

In the physical sciences, the **wavenumber**, also known as **repetency**, is the *spatial frequency* of a wave, measured in cycles per unit distance or radians per unit distance. It is analogous to temporal frequency, which is defined as the number of wave cycles per unit time or radians per unit time.

**Thermal radiation** is electromagnetic radiation emitted by the thermal motion of particles in matter. Thermal radiation transmits as an electromagnetic wave through both matter and vacuum. When matter absorbs thermal radiation its temperature will tend to rise. All matter with a temperature greater than absolute zero emits thermal radiation. The emission of energy arises from a combination of electronic, molecular, and lattice oscillations in a material. Kinetic energy is converted to electromagnetism due to charge-acceleration or dipole oscillation. At room temperature, most of the emission is in the infrared (IR) spectrum. Thermal radiation is one of the fundamental mechanisms of heat transfer, along with conduction and convection.

In electromagnetism, the **Mie solution** to Maxwell's equations describes the scattering of an electromagnetic plane wave by a homogeneous sphere. The solution takes the form of an infinite series of spherical multipole partial waves. It is named after German physicist Gustav Mie.

The **Drude model** of electrical conduction was proposed in 1900 by Paul Drude to explain the transport properties of electrons in materials. Basically, Ohm's law was well established and stated that the current *J* and voltage *V* driving the current are related to the resistance *R* of the material. The inverse of the resistance is known as the conductance. When we consider a metal of unit length and unit cross sectional area, the conductance is known as the conductivity, which is the inverse of resistivity. The Drude model attempts to explain the resistivity of a conductor in terms of the scattering of electrons by the relatively immobile ions in the metal that act like obstructions to the flow of electrons.

In particle physics, the **Klein–Nishina formula** gives the differential cross section of photons scattered from a single free electron, calculated in the lowest order of quantum electrodynamics. It was first derived in 1928 by Oskar Klein and Yoshio Nishina, constituting one of the first successful applications of the Dirac equation. The formula describes both the Thomson scattering of low energy photons and the Compton scattering of high energy photons, showing that the total cross section and expected deflection angle decrease with increasing photon energy.

The **classical electron radius** is a combination of fundamental physical quantities that define a length scale for problems involving an electron interacting with electromagnetic radiation. It links the classical electrostatic self-interaction energy of a homogeneous charge distribution to the electron's relativistic mass-energy. According to modern understanding, the electron is a point particle with a point charge and no spatial extent. Nevertheless, it is useful to define a length that characterizes electron interactions in atomic-scale problems. The classical electron radius is given as

The **Compton wavelength** is a quantum mechanical property of a particle, defined as the wavelength of a photon the energy of which is the same as the rest energy of that particle. It was introduced by Arthur Compton in 1923 in his explanation of the scattering of photons by electrons.

In particle physics, a **shower** is a cascade of secondary particles produced as the result of a high-energy particle interacting with dense matter. The incoming particle interacts, producing multiple new particles with lesser energy; each of these then interacts, in the same way, a process that continues until many thousands, millions, or even billions of low-energy particles are produced. These are then stopped in the matter and absorbed.

**Electron scattering** occurs when electrons are displaced from their original trajectory. This is due to the electrostatic forces within matter interaction or, if an external magnetic field is present, the electron may be deflected by the Lorentz force. This scattering typically happens with solids such as metals, semiconductors and insulators; and is a limiting factor in integrated circuits and transistors.

The word *electricity* refers generally to the movement of electrons, or other charge carriers, through a conductor in the presence of a potential difference or an electric field. The speed of this flow has multiple meanings. In everyday electrical and electronic devices, the signals travel as electromagnetic waves typically at 50%–99% of the speed of light in vacuum. The electrons themselves move much more slowly. See drift velocity and electron mobility.

**Surface plasmon polaritons** (**SPPs**) are electromagnetic waves that travel along a metal–dielectric or metal–air interface, practically in the infrared or visible-frequency. The term "surface plasmon polariton" explains that the wave involves both charge motion in the metal and electromagnetic waves in the air or dielectric ("polariton").

**Plasmonic nanoparticles** are particles whose electron density can couple with electromagnetic radiation of wavelengths that are far larger than the particle due to the nature of the dielectric-metal interface between the medium and the particles: unlike in a pure metal where there is a maximum limit on what size wavelength can be effectively coupled based on the material size.

**Non-linear inverse Compton scattering** (**NICS**), also known as **non-linear Compton scattering** and **multiphoton Compton scattering**, is the scattering of multiple low-energy photons, given by an intense electromagnetic field, in a high-energy photon during the interaction with a charged particle, in many cases an electron. This process is an inverted variant of Compton scattering since, contrary to it, the charged particle transfers its energy to the outgoing high-energy photon instead of receiving energy from an incoming high-energy photon. Furthermore, differently from Compton scattering, this process is explicitly non-linear because the conditions for multiphoton absorption by the charged particle are reached in the presence of a very intense electromagnetic field, for example, the one produced by high-intensity lasers.

**Shneider-Miles scattering** is the quasi-elastic scattering of electromagnetic radiation by charged particles in a small-scale medium with frequent particle collisions. Collisional scattering typically occurs in coherent microwave scattering of high neutral density, low ionization degree microplasmas such as atmospheric pressure laser-induced plasmas. Shneider-Miles scattering is characterized by a 90° phase shift between the incident and scattered waves and a scattering cross section proportional to the square of the incident driving frequency. Scattered waves are emitted in a short dipole radiation pattern. The variable phase shift present in semi-collisional scattering regimes allows for determination of a plasma's collisional frequency through coherent microwave scattering.

- ↑ Chen, Szu-yuan; Maksimchuk, Anatoly; Umstadter, Donald (December 17, 1998). "Experimental observation of relativistic nonlinear Thomson scattering".
*Nature*.**396**(6712): 653–655. arXiv: physics/9810036 . Bibcode:1998Natur.396..653C. doi:10.1038/25303. S2CID 16080209. - 1 2 3 Froula, Dustin H. Plasma scattering of electromagnetic radiation. Academic Press is an imprint of Elsevier, 2011.
- ↑ "National Institute of Standards and Technology" . Retrieved 3 February 2015.
- ↑ Damm, H.; Pasch, E.; Dinklage, A.; et al. (2019). "First results from an event synchronized—high repetition Thomson scattering system at Wendelstein 7-X".
*Journal of Instrumentation*.**14**(9): C09037. arXiv: 1907.00492 . Bibcode:2019JInst..14C9037D. doi:10.1088/1748-0221/14/09/C09037. S2CID 195767387. - ↑ Birkinshaw, Mark (1999). "The Sunyaev–Zel'dovich effect".
*Physics Reports*.**310**(2–3): 97–195. arXiv: astro-ph/9808050 . Bibcode:1999PhR...310...97B. doi:10.1016/s0370-1573(98)00080-5. hdl:1983/5d24f14a-26e0-44d3-8496-5843b108fec5. S2CID 119330362 . Retrieved 4 November 2021.

- Billings, Donald E. (1966).
*A guide to the solar corona*. New York: Academic Press. LCCN 66026261. - Johnson W.R.; Nielsen J.; Cheng K.T. (2012). "Thomson scattering in the average-atom approximation".
*Physical Review*.**86**(3): 036410. arXiv: 1207.0178 . Bibcode:2012PhRvE..86c6410J. doi:10.1103/PhysRevE.86.036410. PMID 23031036. S2CID 10413904.

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