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Encyclopedia > Compton scattering

Feynman diagrams
s-channel
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In physics, Compton scattering or the Compton effect, is the decrease in energy (increase in wavelength) of an X-ray or gamma ray photon, when it interacts with matter. Inverse Compton scattering also exists, where the photon gains energy (decreasing in wavelength) upon interaction with matter. The amount the wavelength increases by is called the Compton shift. Although nuclear 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 in 1923 and further verified by his graduate student Y. H. Woo in the years followed. Arthur Compton earned the 1927 Nobel Prize in Physics for the discovery. A Feynman diagram is a bookkeeping device for performing calculations in quantum field theory, invented by American physicist Richard Feynman. ... Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... Physics (Greek: (phÃºsis), nature and (phusikÃ©), knowledge of nature) is the branch of science concerned with the fundamental laws of the universe. ... The wavelength is the distance between repeating units of a wave pattern. ... In the NATO phonetic alphabet, X-ray represents the letter X. An X-ray picture (radiograph) taken by Röntgen An X-ray is a form of electromagnetic radiation with a wavelength approximately in the range of 5 pm to 10 nanometers (corresponding to frequencies in the range 30 PHz... This article is about electromagnetic radiation. ... The word light is defined here as electromagnetic radiation of any wavelength; thus, X-rays, gamma rays, ultraviolet light, infrared radiation, microwaves, radio waves, and visible light are all forms of light. ... e- redirects here. ... Properties In chemistry and physics, an atom (Greek á¼„Ï„Î¿Î¼Î¿Ï‚ or Ã¡tomos meaning indivisible) is the smallest particle still characterizing a chemical element. ... Arthur Holly Compton (September 10, 1892 – March 15, 1962) won the Nobel Prize in Physics (1927) for discovery of the effect named after him. ... 1923 (MCMXXIII) was a common year starting on Monday (link will display the full calendar). ... Y. H. Woo, physical scientist. ... 1927 (MCMXXVII) was a common year starting on Saturday (link will display full calendar). ... Hannes AlfvÃ©n (1908â€“1995) accepting the Nobel Prize for his work on magnetohydrodynamics [1]. List of Nobel Prize laureates in Physics from 1901 to the present day. ...

The effect is important because it demonstrates that light cannot be explained purely as a wave phenomenon. Thomson scattering, the classical theory of charged particles scattered by an electromagnetic wave, cannot explain any shift in wavelength. Light must behave as if it consists of particles in order to explain the Compton scattering. Compton's experiment convinced physicists that light can behave as a stream of particles whose energy is proportional to the frequency. This article is about waves in the most general scientific sense. ... Thomson scattering is the scattering of electromagnetic radiation by a charged particle. ... Electromagnetic radiation is a propagating wave in space with electric and magnetic components. ...

The interaction between electrons and high energy photons results in the electron being given part of the energy (making it recoil), and a photon containing the remaining energy being emitted in a different direction from the original, so that the overall momentum of the system is conserved. If the photon still has enough energy left, the process may be repeated. In classical mechanics, momentum (pl. ...

Compton scattering occurs in all materials and predominantly with photons of medium energy, i.e. about 0.5 to 3.5 MeV. It is also observed that high-energy photons (photons of visible light or higher frequency, for example) have sufficient energy to even eject the bound electrons from the atom (Photoelectric effect). An electronvolt (symbol: eV) is the amount of energy gained by a single unbound electron when it falls through an electrostatic potential difference of one volt. ... A diagram illustrating the emission of photoelectrons from a metal plate, requiring energy gained from an incoming photon to be more than the work function of the material. ...

1 The Compton shift formula
- 1.1 Derivation
2 Applications
- 2.1 Compton scattering
- 2.2 Inverse Compton scattering
3 See also
4 External links

The Compton shift formula

A photon of wavelength $lambda ,$ comes in from the left, collides with a target at rest, and a new photon of wavelength $lambda ' ,$ emerges at an angle $theta ,$ .

For differential cross section of Compton scattering, see Klein-Nishina formula.

Compton used a combination of three fundamental formulas representing the various aspects of classical and modern physics, combining them to describe the quantum behavior of light. Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... The Klein-Nishina formula provides an accurate prediction of the angular distribution of x-rays and gamma-rays which are incident upon a single electron. ...

Light as a particle, as noted previously in the photoelectric effect.
Relativistic dynamics Special Theory of Relativity
Trigonometry - Law of cosines

The final result gives us the Compton scattering equation: A diagram illustrating the emission of photoelectrons from a metal plate, requiring energy gained from an incoming photon to be more than the work function of the material. ... The special theory of relativity was proposed in 1905 by Albert Einstein in his article On the Electrodynamics of Moving Bodies. Some three centuries earlier, Galileos principle of relativity had stated that all uniform motion was relative, and that there was no absolute and well-defined state of rest... Fig. ...

$lambda' - lambda = frac{h}{m_e c}(1-cos{theta})$

where

λ

is the wavelength of the photon before scattering,

λ'

is the wavelength of the photon after scattering,

m_e is the mass of the electron,

θ is the angle by which the photon's heading changes,

h is Planck's constant, and

c is the speed of light.

h/(m_ec)=2.43×10^-12 meters, is known as the Compton wavelength.

A commemoration plaque for Max Planck on his discovery of Plancks constant, in front of Humboldt University, Berlin. ... A line showing the speed of light on a scale model of Earth and the Moon The speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning swiftness. It is the speed of all electromagnetic radiation... The Compton wavelength of a particle is given by , where is the Planck constant, is the particles mass and is the speed of light. ...

Derivation

Begin with energy and momentum conservation:

$E_gamma + E_e = E_{gamma^prime} + E_{e^prime} quad quad (1) ,$

$vec p_gamma = vec{p}_{gamma^prime} + vec{p}_{e^prime} quad quad quad quad quad (2) ,$

where

$E_gamma ,$ and $p_gamma ,$ are the energy and momentum of the photon and

$E_e ,$ and $p_e ,$ are the energy and momentum of the electron.

Solving (1)

Now we fill in for the energy part:

$E_{gamma} + E_{e} = E_{gamma'} + E_{e'},$

$hf + mc^2 = hf' + sqrt{(p_{e'}c)^2 + (mc^2)^2},$

We solve this for p_e':

$(hf + mc^2-hf')^2 = (p_{e'}c)^2 + (mc^2)^2,$

$frac{(hf + mc^2-hf')^2-m^2c^4}{c^2}= p_{e'}^2 quad quad quad quad quad (3) ,$

Solving (2)

Rearrange equation (2)

$vec{p}_{e'} = vec{p}_gamma - vec{p}_{gamma'} ,$

and square it to see

$p_{e'}^2 = (vec{p}_gamma - vec{p}_{gamma'}) cdot (vec{p}_gamma - vec{p}_{gamma'})$

$p_{e'}^2 = p_{gamma}^2 + p_{gamma'}^2 - 2vec{p_{gamma}} cdot vec{p_{gamma'}}$

$p_{e'}^2 = p_gamma^2 + p_{gamma'}^2 - 2|p_{gamma}||p_{gamma'}|cos(theta) ,$

$p_{e'}^2 = left(frac{h f}{c}right)^2 + left(frac{h f'}{c}right)^2 - 2left( frac{hf}{c} right) left(frac{h f'}{c} right) cos{theta} quad quad quad (4)$

Putting it together

Then we have two equations for $p_{e'}^2$ (eq 3 & 4), which we equate:

$left(frac{h f}{c}right)^2 + left(frac{h f'}{c}right)^2 - frac{2h^2 ff'cos{theta}}{c^2} = frac{(hf + mc^2-hf')^2 -m^2c^4}{c^2} ,$

Now, one simplifies. First by multiplying both sides by c²:

$h^2 f^2 + h^2 f'^2 - 2h^2 ff' cos theta = (hf + mc^2 - hf')^2 - m^2c^4 . ,$

Next, multiply out the right-hand side:

$h^2f^2+h^2f'^2-2h^2ff'cos{theta} = h^2f^2+m^2c^4+h^2f'^2-2h^2ff'+2h(f-f')mc^2 -m^2c^4 .,$

A few terms cancel from both sides, so we have

$-2h^2ff'cos{theta} = -2h^2ff'+2h(f-f')mc^2 .,$

Then divide both sides by ' $- 2 h$ ' to see

$hff'cos{theta} = hff'-(f-f')mc^2 ,$

$(f-f')mc^2 = hff'(1-cos{theta}) .,$

Now divide both sides by $m c 2$ and then by $ff^prime$ :

$frac{f-f^prime}{f f^prime} = frac{h}{mc^2}left(1-cos theta right) . ,$

Now the left-hand side can be rewritten as simply

$frac{1}{f^prime} - frac{1}{f} = frac{h}{mc^2}left(1-cos theta right) ,$

This is equivalent to the Compton scattering equation, but it is usually written using $λ$ 's rather than $f$ 's. To make that switch use

$f=frac{c}{lambda} ,$

so that finally,

$lambda'-lambda = frac{h}{mc}(1-cos{theta}) ,$

Applications

Compton scattering

Compton scattering is of prime importance to radiobiology, as it happens to be the most probable interaction of high energy X rays with atomic nuclei in living beings and is applied in radiation therapy. Radiation biology is the interdisciplinary field of science that studies the biological effects of ionizing and non-ionizing radiation of the whole electromagnetic spectrum, including radioactivity (alpha, beta and gamma), x-rays, ultraviolet radiation, visible light, microwaves, radio wave, low-frequency radiation (such as used in alternate electric transmission, ultrasound... Clinac 2100 C100 accelerator Radiation therapy (or radiotherapy) is the medical use of ionizing radiation as part of cancer treatment to control malignant cells (not to be confused with radiology, the use of radiation in medical imaging and diagnosis). ...

In material physics, Compton scattering can be used to probe the wave function of the electrons in matter in the momentum representation. A wave function is a mathematical tool that quantum mechanics uses to describe any physical system. ...

Compton Scatter is an important effect in Gamma spectroscopy 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. Gamma spectroscopy is a radiochemistry measurement method that determines the energy and count rate of gamma rays emitted by radioactive substances. ... In spectrophotometry, the Compton Edge is a feature of the spectrograph that results from the Compton scattering in the scintillator or detector. ... In gamma ray spectroscopy, Compton suppression is a technique that improves the signal by preventing data which has been corrupted by the incident gamma ray Compton scattering out of the target before depositing all of its energy. ...

Inverse Compton scattering

Inverse Compton scattering is important in astrophysics. In X-ray astronomy, the accretion disk surrounding a black hole is believed 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. This is believed to cause the power law component in the X-ray spectra (0.2-10 keV) of accreting black holes. Spiral Galaxy ESO 269-57 Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties (luminosity, density, temperature, and chemical composition) of celestial objects such as stars, galaxies, and the interstellar medium, as well as their interactions. ... ROSAT image of X-ray fluorescence of, and occultation of the X-ray background by, the Moon. ... An accretion disc (or accretion disk) is a structure formed by material falling into a gravitational source. ... A black hole is an object with a gravitational field so powerful that no form of matter or radiation (including light) can escape once it is less than a certain distance from the center. ... A corona is a type of plasma atmosphere of the Sun or other celestial body, extending millions of kilometres into space, most easily seen during a total solar eclipse, but also observable in a coronagraph. ...

The effect is also observed when photons from the Cosmic microwave background move through the hot gas surrounding a galaxy cluster. The CMB photons are scattered to higher energies by the electrons in this gas, resulting in the Sunyaev-Zel'dovich effect. WMAP image of the CMB anisotropy,Cosmic microwave background radiation(June 2003) The cosmic microwave background radiation (CMB) is a form of electromagnetic radiation that fills the whole of the universe. ... Galaxy groups and clusters are super-structures in the spread of galaxies of the cosmos. ... The Sunyaev-Zeldovich effect (SZ effect or Sunyaev-Zeldovich theory) is due to high energy electrons distorting the cosmic microwave background radiation (CMB) through the inverse Compton effect, in which some of the high energy of the electrons is transferred to the low energy photons. ...

Thomson scattering is the scattering of electromagnetic radiation by a charged particle. ... The Klein-Nishina formula provides an accurate prediction of the angular distribution of x-rays and gamma-rays which are incident upon a single electron. ... A diagram illustrating the emission of photoelectrons from a metal plate, requiring energy gained from an incoming photon to be more than the work function of the material. ... Pair production refers to the creation of an elementary particle and its antiparticle, usually from a photon (or another neutral boson). ... Timeline of cosmic microwave background astronomy 1934 - Richard Tolman shows that black-body radiation in an expanding universe cools but remains thermal 1941 - Andrew McKellar uses the excitation of CN doublet lines to measure that the effective temperature of space is about 2. ... Petrus Josephus Wilhelmus Debije (March 24, 1884 â€“ November 2, 1966) was a Dutch physical chemist. ... Walther Wilhelm Georg Bothe (January 8, 1891 â€“ February 8, 1957) was a German physicist, mathematician, chemist, and Nobel Prize winner. ... This page aims to list articles on Wikipedia that are related to astronomy, astrophysics and cosmology. ... This page aims to list all Wikipedia articles that are related to physics. ... Washington University in St. ...

Quantum electrodynamics

v • d • e

electron | positron | photon
self-energy | vacuum polarization | vertex function
Gupta-Bleuler formalism | ξ gauge | Ward-Takahashi identity
Compton scattering | Bhabha scattering | Møller scattering
anomalous magnetic dipole moment
bremsstrahlung | positronium Quantum electrodynamics (QED) is a relativistic quantum field theory of electromagnetism. ... e- redirects here. ... The first detection of the positron in 1932 by Carl D. Anderson The positron is the antiparticle or the antimatter counterpart of the electron. ... The word light is defined here as electromagnetic radiation of any wavelength; thus, X-rays, gamma rays, ultraviolet light, infrared radiation, microwaves, radio waves, and visible light are all forms of light. ... In theoretical physics, a particles self-energy represents the contribution to the particles energy or effective mass due to interactions between the particle and the system it is apart of. ... In quantum physics, if we expand about the Fock vacuum, the true vacuum contains short-lived virtual particle-antiparticle pairs which are created in pairs out of the Fock vacuum and then annihilate each other. ... In quantum electrodynamics, the vertex function is the one particle irreducible correlation function involving ψ, and the vector potential A. It is unfortunate that the effective action Γeff and the vertex function Γμ happen to be described by the same letter. ... In quantum field theory, the Gupta-Bleuler formalism is a way of quantizing the electromagnetic field. ... In the physics of gauge theories, gauge fixing (also called choosing a gauge) denotes a mathematical procedure for coping with redundant degrees of freedom in field variables. ... In quantum field theory a Ward-Takahashi identity is nowadays used to designate an identity between correlation functions that follows from symmetries, either global or gauged, of the theory, and which remains valid after renormalization. ... In quantum electrodynamics, Bhabha scattering is the electron positron scattering process represented by . ... MÃ¸ller scattering is the name given to electron-electron scattering in Quantum Field Theory. ... In quantum electrodynamics, anomalous magnetic moment of a particle is a contribution of effects of quantum mechanics, expressed by Feynman diagrams with loops, to the magnetic moment of that particle. ... (helpÂ· info), (from the German bremsen, to brake and Strahlung, radiation, thus, braking radiation), is electromagnetic radiation produced by the acceleration of a charged particle, such as an electron, when deflected by another charged particle, such as an atomic nucleus. ... Positronium (Ps) is a quasi-stable system consisting of an electron and its anti-particle, a positron, bound together into an exotic atom. The orbit of the two particles and the set of energy levels is similar to that of the hydrogen atom (electron and proton). ...

External links

Compton Effect (PDF file) by Michael Brandl for Project PHYSNET.
A Quantum Theory of the Scattering of X-Rays by Light Elements - the original 1923 Physical Review paper by Arthur H. Compton (on the AIP website).

Categories: Quantum electrodynamics | Astronomy | Atomic physics | Foundational quantum physics | X-rays Physical Review is one of the oldest and most-respected scientific journals publishing research on all aspects of physics. ... The American Institute of Physics (AIP) is a professional body representing American physicists and publishing physics related journals. ...

Results from FactBites:

Compton scattering - Wikipedia, the free encyclopedia (636 words)
	Compton scattering is of prime importance to radiobiology, as it happens to be the most probable interaction of high energy X rays with atomic nuclei in living beings and is applied in radiation therapy.
	Compton scattering has on occasion been proposed as an alternative explanation for the phenomenon of the redshift by opponents of the Big Bang theory, although this is not generally accepted because the influence of the Compton scattering would be noticeable in the spectral lines of distant objects and this is not observed.
	Compton Scatter is an important effect in Gamma spectroscopy, as it is possible for the gamma rays to scatter out of the detectors used.

Scattering - Wikipedia, the free encyclopedia (2401 words)
	Scattering is a general physical process whereby some form of radiation, such as light, sound, or moving particles, is forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which it passes.
	Rayleigh scattering is a process in which electromagnetic radiation (including light) is scattered by a small spherical volume of variant refractive index, such as a particle, bubble, droplet, or even a density fluctuation.
	In scattering experiments, a target of some material is bombarded with a beam of particles (typically electrons, protons, or neutrons) and the number of particles emerging in various directions is measured.

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