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Compton scattering, discovered by
Arthur Holly Compton Arthur Holly Compton (September 10, 1892 – March 15, 1962) was an American physicist who won the Nobel Prize in Physics in 1927 for his 1923 discovery of the Compton effect, which demonstrated the particle nature of electromagnetic radia ...
, is the
scattering Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including ...
of a high frequency
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are Massless particle, massless ...
after an interaction with a charged particle, usually an
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no ...
. If it results in a decrease in
energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of h ...
(increase in
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tr ...
) of the photon (which may be an
X-ray An X-ray, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10  picometers to 10 nanometers, corresponding to frequencies in the range 30  ...
or
gamma ray A gamma ray, also known as gamma radiation (symbol γ or \gamma), is a penetrating form of electromagnetic radiation arising from the radioactive decay of atomic nuclei. It consists of the shortest wavelength electromagnetic waves, typically ...
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are Massless particle, massless ...
), it is called the Compton effect. Part of the energy of the photon is transferred to the recoiling electron. Inverse Compton scattering occurs when a charged particle transfers part of its energy to a photon.


Introduction

Compton scattering is an example of
elastic scattering Elastic scattering is a form of particle scattering in scattering theory, nuclear physics and particle physics. In this process, the kinetic energy of a particle is conserved in the center-of-mass frame, but its direction of propagation is modif ...
of light by a free charged particle, where the wavelength of the scattered light is different from that of the incident radiation. In Compton's original experiment (see Fig. 1), the energy of the X ray photon (≈17 keV) was significantly larger than the binding energy of the atomic electron, so the electrons could be treated as being free after scattering. The amount by which the light's wavelength changes is called the Compton shift. Although nucleus Compton scattering exists, Compton scattering usually refers to the interaction involving only the electrons of an atom. The Compton effect was observed by
Arthur Holly Compton Arthur Holly Compton (September 10, 1892 – March 15, 1962) was an American physicist who won the Nobel Prize in Physics in 1927 for his 1923 discovery of the Compton effect, which demonstrated the particle nature of electromagnetic radia ...
in 1923 at Washington University in St. Louis and further verified by his graduate student Y. H. Woo in the years following. Compton earned the 1927
Nobel Prize in Physics ) , image = Nobel Prize.png , alt = A golden medallion with an embossed image of a bearded man facing left in profile. To the left of the man is the text "ALFR•" then "NOBEL", and on the right, the text (smaller) "NAT•" then " ...
for the discovery. The effect is significant because it demonstrates that light cannot be explained purely as a
wave In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (re ...
phenomenon.
Thomson scattering 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 frequenc ...
, the classical theory of an
electromagnetic wave In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) ligh ...
scattered by charged particles, cannot explain shifts in wavelength at low intensity: classically, light of sufficient intensity for the electric field to accelerate a charged particle to a relativistic speed will cause radiation-pressure recoil and an associated Doppler shift of the scattered light, but the effect would become arbitrarily small at sufficiently low light intensities ''regardless of wavelength''. Thus, if we are to explain low-intensity Compton scattering, light must behave as if it consists of particles. Or the assumption that the electron can be treated as free is invalid resulting in the effectively infinite electron mass equal to the nuclear mass (see e.g. the comment below on elastic scattering of X-rays being from that effect). Compton's experiment convinced physicists that light can be treated as a stream of particle-like objects (quanta called photons), whose energy is proportional to the light wave's frequency. As shown in Fig. 2, the interaction between an electron and a photon results in the electron being given part of the energy (making it recoil), and a photon of the remaining energy being emitted in a different direction from the original, so that the overall
momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass a ...
of the system is also conserved. If the scattered photon still has enough energy, the process may be repeated. In this scenario, the electron is treated as free or loosely bound. Experimental verification of momentum conservation in individual Compton scattering processes by Bothe and Geiger as well as by Compton and Simon has been important in disproving the
BKS theory The Bohr–Kramers–Slater theory (BKS theory) was perhaps the final attempt at understanding the interaction of matter and electromagnetic radiation on the basis of the so-called old quantum theory, in which quantum phenomena are treated by impos ...
. Compton scattering is one of four competing processes when photons interact with matter. At energies of a few eV to a few keV, corresponding to
visible light Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 tera ...
through soft X-rays, a photon can be completely absorbed and its energy can eject an electron from its host atom, a process known as the
photoelectric effect The photoelectric effect is the emission of electrons when electromagnetic radiation, such as light, hits a material. Electrons emitted in this manner are called photoelectrons. The phenomenon is studied in condensed matter physics, and solid sta ...
. High-energy photons of and above may bombard the nucleus and cause an electron and a positron to be formed, a process called
pair production Pair production is the creation of a subatomic particle and its antiparticle from a neutral boson. Examples include creating an electron and a positron, a muon and an antimuon, or a proton and an antiproton. Pair production often refers specific ...
; even-higher-energy photons (beyond a threshold energy of at least , depending on the nuclei involved), can eject a nucleon or
alpha particle Alpha particles, also called alpha rays or alpha radiation, consist of two protons and two neutrons bound together into a particle identical to a helium-4 nucleus. They are generally produced in the process of alpha decay, but may also be produce ...
from the nucleus in a process called
photodisintegration Photodisintegration (also called phototransmutation, or a photonuclear reaction) is a nuclear process in which an atomic nucleus absorbs a high-energy gamma ray, enters an excited state, and immediately decays by emitting a subatomic particle. The ...
. Compton scattering is the most important interaction in the intervening energy region, at photon energies greater than those typical of the photoelectric effect but less than the pair-production threshold.


Description of the phenomenon

By the early 20th century, research into the interaction of
X-ray An X-ray, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10  picometers to 10 nanometers, corresponding to frequencies in the range 30  ...
s with matter was well under way. It was observed that when X-rays of a known wavelength interact with atoms, the X-rays are scattered through an angle \theta and emerge at a different wavelength related to \theta. Although
classical electromagnetism Classical electromagnetism or classical electrodynamics is a branch of theoretical physics that studies the interactions between electric charges and currents using an extension of the classical Newtonian model; It is, therefore, a classical fie ...
predicted that the wavelength of scattered rays should be equal to the initial wavelength, multiple experiments had found that the wavelength of the scattered rays was longer (corresponding to lower energy) than the initial wavelength. In 1923, Compton published a paper in the ''
Physical Review ''Physical Review'' is a peer-reviewed scientific journal established in 1893 by Edward Nichols. It publishes original research as well as scientific and literature reviews on all aspects of physics. It is published by the American Physical Soci ...
'' that explained the X-ray shift by attributing particle-like momentum to light quanta (Einstein had proposed light quanta in 1905 in explaining the photo-electric effect, but Compton did not build on Einstein's work). The energy of light quanta depends only on the frequency of the light. In his paper, Compton derived the mathematical relationship between the shift in wavelength and the scattering angle of the X-rays by assuming that each scattered X-ray photon interacted with only one electron. His paper concludes by reporting on experiments which verified his derived relation: \lambda' - \lambda = \frac(1 - \cos), where *\lambda is the initial wavelength, *\lambda' is the wavelength after scattering, *h is the
Planck constant The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivale ...
, *m_e is the
electron rest mass The electron mass (symbol: ''m''e) is the mass of a stationary electron, also known as the invariant mass of the electron. It is one of the fundamental constants of physics. It has a value of about or about , which has an energy-equivalent of a ...
, *c is the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
, and *\theta is the scattering angle. The quantity is known as the
Compton wavelength The Compton wavelength is a quantum mechanical property of a particle. The Compton wavelength of a particle is equal to the wavelength of a photon whose energy is the same as the rest energy of that particle (see mass–energy equivalence). It wa ...
of the electron; it is equal to . The wavelength shift is at least zero (for ) and at most twice the Compton wavelength of the electron (for ). Compton found that some X-rays experienced no wavelength shift despite being scattered through large angles; in each of these cases the photon failed to eject an electron. Thus the magnitude of the shift is related not to the Compton wavelength of the electron, but to the Compton wavelength of the entire atom, which can be upwards of 10000 times smaller. This is known as "coherent" scattering off the entire atom since the atom remains intact, gaining no internal excitation. In Compton's original experiments the wavelength shift given above was the directly-measurable observable. In modern experiments it is conventional to measure the energies, not the wavelengths, of the scattered photons. For a given incident energy E_\gamma = hc/\lambda, the outgoing final-state photon energy, E_, is given by E_ = \frac.


Derivation of the scattering formula

A photon with wavelength collides with an electron in an atom, which is treated as being at rest. The collision causes the electron to
recoil Recoil (often called knockback, kickback or simply kick) is the rearward thrust generated when a gun is being discharged. In technical terms, the recoil is a result of conservation of momentum, as according to Newton's third law the force re ...
, and a new photon ' with wavelength ' emerges at angle from the photon's incoming path. Let ' denote the electron after the collision. Compton allowed for the possibility that the interaction would sometimes accelerate the electron to speeds sufficiently close to the velocity of light as to require the application of Einstein's
special relativity In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates: # The law ...
theory to properly describe its energy and momentum. At the conclusion of Compton's 1923 paper, he reported results of experiments confirming the predictions of his scattering formula, thus supporting the assumption that photons carry momentum as well as quantized energy. At the start of his derivation, he had postulated an expression for the momentum of a photon from equating Einstein's already established mass-energy relationship of E=mc^2 to the quantized photon energies of h f, which Einstein had separately postulated. If mc^2 = hf, the equivalent photon mass must be hf/c^2. The photon's momentum is then simply this effective mass times the photon's frame-invariant velocity . For a photon, its momentum p=hf/c, and thus can be substituted for for all photon momentum terms which arise in course of the derivation below. The derivation which appears in Compton's paper is more terse, but follows the same logic in the same sequence as the following derivation. The
conservation of energy In physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be ''conserved'' over time. This law, first proposed and tested by Émilie du Châtelet, means that ...
E merely equates the sum of energies before and after scattering. :E_\gamma + E_e = E_ + E_. Compton postulated that photons carry momentum; thus from the
conservation of momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass a ...
, the momenta of the particles should be similarly related by :\mathbf_\gamma = \mathbf_ + \mathbf_, in which () is omitted on the assumption it is effectively zero. The photon energies are related to the frequencies by :E_ = hf :E_ = hf' where ''h'' is Planck's constant. Before the scattering event, the electron is treated as sufficiently close to being at rest that its total energy consists entirely of the mass-energy equivalence of its (rest) mass m_e , :E_e = m_ec^2. After scattering, the possibility that the electron might be accelerated to a significant fraction of the speed of light, requires that its total energy be represented using the relativistic
energy–momentum relation In physics, the energy–momentum relation, or relativistic dispersion relation, is the relativistic equation relating total energy (which is also called relativistic energy) to invariant mass (which is also called rest mass) and momentum. It is ...
:E_ = \sqrt ~. Substituting these quantities into the expression for the conservation of energy gives :hf + m_e c^2 = hf' + \sqrt. This expression can be used to find the magnitude of the momentum of the scattered electron, :Note that this magnitude of the momentum gained by the electron (formerly zero) exceeds the energy/c lost by the photon, :\frac\sqrt > \frac~. Equation (1) relates the various energies associated with the collision. The electron's momentum change involves a relativistic change in the energy of the electron, so it is not simply related to the change in energy occurring in classical physics. The change of the magnitude of the momentum of the photon is not just related to the change of its energy; it also involves a change in direction. Solving the conservation of momentum expression for the scattered electron's momentum gives :\mathbf_ = \mathbf_\gamma - \mathbf_. Making use of the
scalar product In mathematics, the dot product or scalar productThe term ''scalar product'' means literally "product with a scalar as a result". It is also used sometimes for other symmetric bilinear forms, for example in a pseudo-Euclidean space. is an algeb ...
yields the square of its magnitude, :\begin p_^ &= \mathbf_\cdot\mathbf_ = (\mathbf_\gamma - \mathbf_) \cdot (\mathbf_\gamma - \mathbf_) \\ &= p_^ + p_^ - 2 p_\, p_ \cos\theta. \end In anticipation of p_c being replaced with h f, multiply both sides by c^2, :p_^c^2 = p_^c^2 + p_^c^2 - 2c^2 p_\, p_ \cos\theta. After replacing the photon momentum terms with h f/c, we get a second expression for the magnitude of the momentum of the scattered electron, Equating the alternate expressions for this momentum gives : (hf - hf' + m_e c^2)^2 - m_e^c^4 = \left(h f\right)^2 + \left(h f'\right)^2 - 2h^2 ff'\cos, which, after evaluating the square and canceling and rearranging terms, further yields : 2 h f m_e c^2-2 h f' m_e c^2 = 2 h^2 f f' \left( 1 - \cos \theta \right). Dividing both sides by yields : \frac - \frac = \frac\left(1-\cos \theta \right). Finally, since = = , It can further be seen that the angle of the outgoing electron with the direction of the incoming photon is specified by


Applications


Compton scattering

Compton scattering is of prime importance to
radiobiology Radiobiology (also known as radiation biology, and uncommonly as actinobiology) is a field of clinical and basic medical sciences that involves the study of the action of ionizing radiation on living things, especially health effects of radiation. ...
, as it is the most probable interaction of gamma rays and high energy X-rays with atoms in living beings and is applied in
radiation therapy Radiation therapy or radiotherapy, often abbreviated RT, RTx, or XRT, is a therapy using ionizing radiation, generally provided as part of cancer treatment to control or kill malignant cells and normally delivered by a linear accelerator. Rad ...
. Compton scattering is an important effect in
gamma spectroscopy Gamma-ray spectroscopy is the quantitative study of the energy spectra of gamma-ray sources, such as in the nuclear industry, geochemical investigation, and astrophysics. Most radioactive sources produce gamma rays, which are of various energi ...
which gives rise to the Compton edge, as it is possible for the gamma rays to scatter out of the detectors used. Compton suppression is used to detect stray scatter gamma rays to counteract this effect.


Magnetic Compton scattering

Magnetic Compton scattering is an extension of the previously mentioned technique which involves the magnetisation of a crystal sample hit with high energy, circularly polarised photons. By measuring the scattered photons' energy and reversing the magnetisation of the sample, two different Compton profiles are generated (one for spin up momenta and one for spin down momenta). Taking the difference between these two profiles gives the magnetic Compton profile (MCP), given by J_(\mathbf_z) - a one-dimensional projection of the electron spin density. J_(\mathbf_z) = \frac\iint_^\infty (n_ (\mathbf) - n_(\mathbf)) d\mathbf_x d\mathbf_y where \mu is the number of spin-unpaired electrons in the system, n_\uparrow(\mathbf) and n_\downarrow(\mathbf) are the three-dimensional electron momentum distributions for the majority spin and minority spin electrons respectively. Since this scattering process is incoherent (there is no phase relationship between the scattered photons), the MCP is representative of the bulk properties of the sample and is a probe of the ground state. This means that the MCP is ideal for comparison with theoretical techniques such as
density functional theory Density-functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure (or nuclear structure) (principally the ground state) of many-body ...
. The area under the MCP is directly proportional to the spin moment of the system and so, when combined with total moment measurements methods (such as
SQUID True squid are molluscs with an elongated soft body, large eyes, eight arms, and two tentacles in the superorder Decapodiformes, though many other molluscs within the broader Neocoleoidea are also called squid despite not strictly fitting ...
magnetometry), can be used to isolate both the spin and orbital contributions to the total moment of a system. The shape of the MCP also yields insight into the origin of the magnetism in the system.


Inverse Compton scattering

Inverse Compton scattering is important in
astrophysics Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline said, Astrophysics "seeks to ascertain the nature of the he ...
. In X-ray astronomy, the
accretion disk An accretion disk is a structure (often a circumstellar disk) formed by diffuse material in orbital motion around a massive central body. The central body is typically a star. Friction, uneven irradiance, magnetohydrodynamic effects, and other fo ...
surrounding a
black hole A black hole is a region of spacetime where gravity is so strong that nothing, including light or other electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts that a sufficiently compact mass can defo ...
is presumed to produce a thermal spectrum. The lower energy photons produced from this spectrum are scattered to higher energies by relativistic electrons in the surrounding
corona Corona (from the Latin for 'crown') most commonly refers to: * Stellar corona, the outer atmosphere of the Sun or another star * Corona (beer), a Mexican beer * Corona, informal term for the coronavirus SARS-CoV-2, which causes the COVID-19 di ...
. This is surmised to cause the power law component in the X-ray spectra (0.2–10 keV) of accreting black holes. The effect is also observed when photons from the
cosmic microwave background In Big Bang cosmology the cosmic microwave background (CMB, CMBR) is electromagnetic radiation that is a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all space ...
(CMB) move through the hot gas surrounding a
galaxy cluster A galaxy cluster, or a cluster of galaxies, is a structure that consists of anywhere from hundreds to thousands of galaxies that are bound together by gravity, with typical masses ranging from 1014 to 1015 solar masses. They are the second-la ...
. The CMB photons are scattered to higher energies by the electrons in this gas, resulting in the Sunyaev–Zel'dovich effect. Observations of the Sunyaev–Zel'dovich effect provide a nearly redshift-independent means of detecting galaxy clusters. Some synchrotron radiation facilities scatter laser light off the stored electron beam. This Compton backscattering produces high energy photons in the MeV to GeV range subsequently used for nuclear physics experiments.


Non-linear inverse Compton scattering

Non-linear inverse Compton scattering (NICS) is the scattering of multiple low-energy photons, given by an intense electromagnetic field, in a high-energy photon (X-ray or gamma ray) during the interaction with a charged particle, such as an electron. It is also called non-linear Compton scattering and multiphoton Compton scattering. It is the non-linear version of inverse Compton scattering in which the conditions for multiphoton absorption by the charged particle are reached due to a very intense electromagnetic field, for example the one produced by a
laser A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The firs ...
. Non-linear inverse Compton scattering is an interesting phenomenon for all applications requiring high-energy photons since NICS is capable of producing photons with energy comparable to the charged particle rest energy and higher. As a consequence NICS photons can be used to trigger other phenomena such as pair production, Compton scattering,
nuclear reaction In nuclear physics and nuclear chemistry, a nuclear reaction is a process in which two nuclei, or a nucleus and an external subatomic particle, collide to produce one or more new nuclides. Thus, a nuclear reaction must cause a transformation o ...
s, and can be used to probe non-linear quantum effects and non-linear QED.


See also


References


Further reading

* * (the original 1923 paper on the APS website) * Stuewer, Roger H. (1975), The Compton Effect: Turning Point in Physics (New York: Science History Publications)


External links


Compton Scattering
– Georgia State University

– Georgia State University


Compton Scattering – Animation made by BIGS
{{DEFAULTSORT:Compton Scattering Astrophysics Observational astronomy Atomic physics Foundational quantum physics Quantum electrodynamics X-ray scattering