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<title>Compton scattering</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Compton scattering</span></span>

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</style><table class="sidebar nomobile nowraplinks"><tbody><tr><th class="sidebar-title">Light–matter interaction</th></tr><tr><td class="sidebar-image"><span typeof="mw:File"></span></td></tr><tr><th class="sidebar-heading" style="font-weight:normal">

Low-energy phenomena:</th></tr><tr><td class="sidebar-content" style="font-weight:bold">

<a href="Photoelectric_effect" title="Photoelectric effect">Photoelectric effect</a></td>

</tr><tr><th class="sidebar-heading" style="font-weight:normal">

Mid-energy phenomena:</th></tr><tr><td class="sidebar-content" style="font-weight:bold">

<a href="Thomson_scattering" title="Thomson scattering">Thomson scattering</a></td>

</tr><tr><td class="sidebar-content" style="font-weight:bold">

</td>

</tr><tr><th class="sidebar-heading" style="font-weight:normal">

High-energy phenomena:</th></tr><tr><td class="sidebar-content" style="font-weight:bold">

<a href="Pair_production" title="Pair production">Pair production</a></td>

</tr><tr><td class="sidebar-content" style="font-weight:bold">

<a href="Photodisintegration" title="Photodisintegration">Photodisintegration</a></td>

</tr><tr><td class="sidebar-content" style="font-weight:bold">

<a href="Photofission" title="Photofission">Photofission</a></td>

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<p><b>Compton scattering</b> (or the <b>Compton effect</b>) is the <a href="Quantum_mechanics" title="Quantum mechanics">quantum theory</a> of <a href="Scattering" title="Scattering">scattering</a> of a high-frequency <a href="Photon" title="Photon">photon</a> through an interaction with a <a href="Charged_particle" title="Charged particle">charged particle</a>, usually an <a href="Electron" title="Electron">electron</a>. Specifically, when the photon interacts with a loosely bound electron, it releases the electron from an outer <a href="Valence_electron" title="Valence electron">valence shell</a> of an atom or molecule.

</p><p>The effect was discovered in 1923 by <a href="Arthur_Compton" title="Arthur Compton">Arthur Holly Compton</a> while researching the scattering of <a href="X-ray" title="X-ray">X-rays</a> by light elements, which earned him the <a href="Nobel_Prize_in_Physics" title="Nobel Prize in Physics">Nobel Prize in Physics</a> in 1927. The Compton effect significantly deviated from dominating classical theories, using both <a href="Special_relativity" title="Special relativity">special relativity</a> and <a href="Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a> to explain the interaction between high frequency photons and charged particles.

</p><p>Photons can interact with matter at the atomic level (e.g. <a href="Photoelectric_effect" title="Photoelectric effect">photoelectric effect</a> and <a href="Rayleigh_scattering" title="Rayleigh scattering">Rayleigh scattering</a>), at the nucleus, or with only an electron. <a href="Pair_production" title="Pair production">Pair production</a> and the Compton effect occur at the level of the electron.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> When a high-frequency photon scatters due to an interaction with a charged particle, the photon's <a href="Energy" title="Energy">energy</a> is reduced, and thus its <a href="Wavelength" title="Wavelength">wavelength</a> is increased. This trade-off between wavelength and energy in response to the collision is the Compton effect. Because of <a href="Conservation_of_energy" title="Conservation of energy">conservation of energy</a>, the energy that is lost by the photon is transferred to the recoiling particle (such an electron would be called a "Compton recoil electron").

</p><p>This implies that if the recoiling particle initially carried more energy than the photon has, the reverse would occur. This is known as <b>inverse Compton scattering</b>, in which the scattered photon increases in energy.

</p>

<div class="mw-heading mw-heading2"><h2 id="Introduction">Introduction</h2></div>

<p>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 <b>Compton shift</b>. Although Compton scattering from a nucleus exists,<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Compton scattering usually refers to the interaction involving only the electrons of an atom. The Compton effect was observed by <a href="Arthur_Holly_Compton" class="mw-redirect" title="Arthur Holly Compton">Arthur Holly Compton</a> in 1923 at <a href="Washington_University_in_St._Louis" title="Washington University in St. Louis">Washington University in St. Louis</a> and further verified by his graduate student <a href="Wu_Youxun" title="Wu Youxun">Y. H. Woo</a> in the years following. Compton was awarded the 1927 <a href="Nobel_Prize_in_Physics" title="Nobel Prize in Physics">Nobel Prize in Physics</a> for the discovery.

</p><p>The effect is significant because it demonstrates that light cannot be explained purely as a <a href="Wave" title="Wave">wave</a> phenomenon.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> <a href="Thomson_scattering" title="Thomson scattering">Thomson scattering</a>, the classical theory of an <a href="Electromagnetic_wave" class="mw-redirect" title="Electromagnetic wave">electromagnetic wave</a> 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,<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> but the effect would become arbitrarily small at sufficiently low light intensities <i>regardless of wavelength</i>. 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.

</p><p>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 <a href="Momentum" title="Momentum">momentum</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 <a href="Walther_Bothe" title="Walther Bothe">Bothe</a> and <a href="Hans_Geiger" title="Hans Geiger">Geiger</a> as well as by Compton and Simon has been important in disproving the <a href="BKS_theory" title="BKS theory">BKS theory</a>.

</p><p>Compton scattering is commonly described as <a href="Inelastic_scattering#Photons" title="Inelastic scattering">inelastic scattering</a>. This is because, unlike the more common Thomson scattering that happens at the low-energy limit, the energy in the scattered photon in Compton scattering is less than the energy of the incident photon.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> As the electron is typically weakly bound to the atom, the scattering can be viewed from either the perspective of an electron in a potential well, or as an atom with a small ionization energy. In the former perspective, energy of the incident photon is transferred to the recoil particle, but only as kinetic energy. The electron gains no internal energy, respective masses remain the same, the mark of an <a href="Elastic_collision" title="Elastic collision">elastic collision</a>. From this perspective, Compton scattering could be considered elastic because the internal state of the electron does not change during the scattering process. In the latter perspective, the atom's state is changed, constituting an <a href="Inelastic_collision" title="Inelastic collision">inelastic collision</a>. Whether Compton scattering is considered elastic or inelastic depends on which perspective is being used, as well as the context.

</p><p>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 <a href="Visible_light" class="mw-redirect" title="Visible light">visible light</a> 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. High-energy photons of <span class="nowrap">1.022 MeV</span> and above may bombard the nucleus and cause an electron and a positron to be formed, a process called <a href="Pair_production" title="Pair production">pair production</a>; even-higher-energy photons (beyond a threshold energy of at least <span class="nowrap">1.670 MeV</span>, depending on the nuclei involved), can eject a nucleon or <a href="Alpha_particle" title="Alpha particle">alpha particle</a> from the nucleus in a process called <a href="Photodisintegration" title="Photodisintegration">photodisintegration</a>. 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.

</p>

<div class="mw-heading mw-heading2"><h2 id="Description_of_the_phenomenon">Description of the phenomenon</h2></div>

<p>By the early 20th century, research into the interaction of <a href="X-ray" title="X-ray">X-rays</a> 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 <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta }">

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<annotation encoding="application/x-tex">{\displaystyle \theta }</annotation>

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</math></span><img src="./6e5ab2664b422d53eb0c7df3b87e1360d75ad9af.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="{\displaystyle \theta }" loading="lazy"></span> and emerge at a different wavelength related to <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta }">

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<annotation encoding="application/x-tex">{\displaystyle \theta }</annotation>

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</math></span><img src="./6e5ab2664b422d53eb0c7df3b87e1360d75ad9af.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="{\displaystyle \theta }" loading="lazy"></span>. Although <a href="Classical_electromagnetism" title="Classical electromagnetism">classical electromagnetism</a> predicted that the wavelength of scattered rays should be equal to the initial wavelength,<sup id="cite_ref-taylor_136-9_8-0" class="reference"><a href="#cite_note-taylor_136-9-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> multiple experiments had found that the wavelength of the scattered rays was longer (corresponding to lower energy) than the initial wavelength.<sup id="cite_ref-taylor_136-9_8-1" class="reference"><a href="#cite_note-taylor_136-9-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup>

</p><p>In 1923, Compton published a paper that explained the X-ray shift by attributing particle-like momentum to light quanta (<a href="Albert_Einstein" title="Albert Einstein">Albert Einstein</a> 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:

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<annotation encoding="application/x-tex">{\displaystyle \lambda '-\lambda ={\frac {h}{m_{\text{e}}c}}(1-\cos {\theta }),}</annotation>

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where

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<annotation encoding="application/x-tex">{\displaystyle \lambda }</annotation>

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</math></span><img src="./b43d0ea3c9c025af1be9128e62a18fa74bedda2a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.355ex; height:2.176ex;" alt="{\displaystyle \lambda }" loading="lazy"></span> is the initial wavelength,</li>

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<annotation encoding="application/x-tex">{\displaystyle \lambda '}</annotation>

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</math></span><img src="./75ef6ce6e951363fc985487085e2474698e0a632.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:2.509ex;" alt="{\displaystyle \lambda '}" loading="lazy"></span> is the wavelength after scattering,</li>

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<annotation encoding="application/x-tex">{\displaystyle h}</annotation>

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</math></span><img src="./b26be3e694314bc90c3215047e4a2010c6ee184a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.339ex; height:2.176ex;" alt="{\displaystyle h}" loading="lazy"></span> is the <a href="Planck_constant" title="Planck constant">Planck constant</a>,</li>

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<annotation encoding="application/x-tex">{\displaystyle m_{\text{e}}}</annotation>

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</math></span><img src="./c45a5eb082ea4dafd3cb43ca39e033989e4a52eb.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.003ex; height:2.009ex;" alt="{\displaystyle m_{\text{e}}}" loading="lazy"></span> is the <a href="Electron_rest_mass" class="mw-redirect" title="Electron rest mass">electron rest mass</a>,</li>

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<annotation encoding="application/x-tex">{\displaystyle c}</annotation>

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</math></span><img src="./86a67b81c2de995bd608d5b2df50cd8cd7d92455.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c}" loading="lazy"></span> is the <a href="Speed_of_light" title="Speed of light">speed of light</a>, and</li>

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<annotation encoding="application/x-tex">{\displaystyle \theta }</annotation>

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</math></span><img src="./6e5ab2664b422d53eb0c7df3b87e1360d75ad9af.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="{\displaystyle \theta }" loading="lazy"></span> is the scattering angle.</li></ul>

<p>The quantity <span class="texhtml"><style data-mw-deduplicate="TemplateStyles:r1214402035">

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</style><span class="sfrac">⁠<span class="tion"><span class="num"><i>h</i></span><span class="sr-only">/</span><span class="den"><i>m</i><sub>e</sub><i>c</i></span></span>⁠</span></span> is known as the <a href="Compton_wavelength" title="Compton wavelength">Compton wavelength</a> of the electron; it is equal to <span class="nowrap">2.43<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−12</sup> m</span>. The wavelength shift <span class="texhtml"><i>λ</i>′ − <i>λ</i></span> is at least zero (for <span class="texhtml"><i>θ</i> = 0°</span>) and at most twice the Compton wavelength of the electron (for <span class="texhtml"><i>θ</i> = 180°</span>).

</p><p>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.<sup id="cite_ref-taylor_136-9_8-2" class="reference"><a href="#cite_note-taylor_136-9-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> 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.

</p><p>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 <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{\gamma }=hc/\lambda }">

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<annotation encoding="application/x-tex">{\displaystyle E_{\gamma }=hc/\lambda }</annotation>

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</math></span><img src="./d510f81ccc6b931f229c93d352f9dcc9b7ada93e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:10.802ex; height:3.009ex;" alt="{\displaystyle E_{\gamma }=hc/\lambda }" loading="lazy"></span>, the outgoing final-state photon energy, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{\gamma ^{\prime }}}">

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</math></span><img src="./331efc313a86127f91b391cb3b5d474b8357cc94.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.384ex; height:2.843ex;" alt="{\displaystyle E_{\gamma ^{\prime }}}" loading="lazy"></span>, is given by

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<annotation encoding="application/x-tex">{\displaystyle E_{\gamma ^{\prime }}={\frac {E_{\gamma }}{1+(E_{\gamma }/m_{\text{e}}c^{2})(1-\cos \theta )}}.}</annotation>

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</p>

<div class="mw-heading mw-heading3"><h3 id="Derivation_of_the_scattering_formula">Derivation of the scattering formula</h3></div>

<th style="background:#ffdead;"><a href="Feynman_diagrams" class="mw-redirect" title="Feynman diagrams">Feynman diagrams</a> <small>(time from left to right)</small>

</th></tr>

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<td align="center"><b>s channel</b><br><span typeof="mw:File"></span>

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<tr>

<td align="center"><b>u channel</b><br><span typeof="mw:File"></span>

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<p>A photon <span class="texhtml">γ</span> with wavelength <span class="texhtml mvar" style="font-style:italic;">λ</span> collides with an electron <span class="texhtml">e</span> in an atom, which is treated as being at rest. The collision causes the electron to <a href="Recoil" title="Recoil">recoil</a>, and a new photon <span class="texhtml"><i>γ</i>′</span> with wavelength <span class="texhtml"><i>λ</i>′</span> emerges at angle <span class="texhtml mvar" style="font-style:italic;">θ</span> from the photon's incoming path. Let <span class="texhtml">e′</span> 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 <a href="Special_relativity" title="Special relativity">special relativity</a> theory to properly describe its energy and momentum.

</p><p>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 <span class="texhtml"><i>E</i> = <i>mc</i><sup>2</sup></span> to the quantized photon energies of <span class="texhtml"><i>hf</i></span>, which Einstein had separately postulated. If <span class="texhtml"><i>mc</i><sup>2</sup> = <i>hf</i></span>, the equivalent photon mass must be <span class="texhtml"><i>hf</i>/<i>c</i><sup>2</sup></span>. The photon's momentum is then simply this effective mass times the photon's frame-invariant velocity <span class="texhtml mvar" style="font-style:italic;">c</span>. For a photon, its momentum <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p=hf/c}">

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<annotation encoding="application/x-tex">{\displaystyle p=hf/c}</annotation>

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</math></span><img src="./706ff00a4c011a57d2769ba8e1d30df807cff04e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:9.144ex; height:2.843ex;" alt="{\displaystyle p=hf/c}" loading="lazy"></span>, and thus <span class="texhtml"><i>hf</i></span> can be substituted for <span class="texhtml"><i>pc</i></span> 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.

</p><p>The <a href="Conservation_of_energy" title="Conservation of energy">conservation of energy</a> <span class="texhtml"><i>E</i></span> merely equates the sum of energies before and after scattering.

</p>

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<annotation encoding="application/x-tex">{\displaystyle E_{\gamma }+E_{\text{e}}=E_{\gamma '}+E_{{\text{e}}'}.}</annotation>

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</math></span><img src="./d9641a18c1ad814b8df31424fa6594a076a45f4c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:21.537ex; height:2.843ex;" alt="{\displaystyle E_{\gamma }+E_{\text{e}}=E_{\gamma '}+E_{{\text{e}}'}.}" loading="lazy"></span></dd></dl>

<p>Compton postulated that photons carry momentum;<sup id="cite_ref-taylor_136-9_8-3" class="reference"><a href="#cite_note-taylor_136-9-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> thus from the <a href="Conservation_of_momentum" class="mw-redirect" title="Conservation of momentum">conservation of momentum</a>, the momenta of the particles should be similarly related by

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<annotation encoding="application/x-tex">{\displaystyle \mathbf {p} _{\gamma }=\mathbf {p} _{\gamma '}+\mathbf {p} _{{\text{e}}'},}</annotation>

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</math></span><img src="./3ea9d0dc83c4e4c964a9d12dbd7418b8ab4a9236.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:15.329ex; height:2.843ex;" alt="{\displaystyle \mathbf {p} _{\gamma }=\mathbf {p} _{\gamma '}+\mathbf {p} _{{\text{e}}'},}" loading="lazy"></span></dd></dl>

<p>in which <span class="texhtml"><b>p</b><sub>e</sub></span> is omitted as being negligible.

</p><p>The photon energies are related to the frequencies by

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<annotation encoding="application/x-tex">{\displaystyle E_{\gamma }=hf}</annotation>

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</math></span><img src="./d86ef114dba200e53fb46f1f6d5839a1f5386095.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:8.556ex; height:2.843ex;" alt="{\displaystyle E_{\gamma }=hf}" loading="lazy"></span></dd>

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<annotation encoding="application/x-tex">{\displaystyle E_{\gamma '}=hf'}</annotation>

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</math></span><img src="./a6b90be34e9f53551c5d0cf53165db8ef905f67b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:9.827ex; height:3.176ex;" alt="{\displaystyle E_{\gamma '}=hf'}" loading="lazy"></span></dd></dl>

<p>where <span class="texhtml"><i>h</i></span> is the <a href="Planck_constant" title="Planck constant">Planck constant</a>.

</p><p>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 <span class="texhtml"><i>m</i><sub>e</sub></span>,

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<annotation encoding="application/x-tex">{\displaystyle E_{\text{e}}=m_{\text{e}}c^{2}.}</annotation>

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</math></span><img src="./48778cc3cfeee2f9c4cee3665c63e4803c6d5319.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.487ex; height:3.009ex;" alt="{\displaystyle E_{\text{e}}=m_{\text{e}}c^{2}.}" loading="lazy"></span></dd></dl>

<p>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 <a href="Energy%E2%80%93momentum_relation" title="Energy–momentum relation">energy–momentum relation</a>

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<annotation encoding="application/x-tex">{\displaystyle E_{{\text{e}}'}={\sqrt {(p_{{\text{e}}'}c)^{2}+(m_{\text{e}}c^{2})^{2}}}~.}</annotation>

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</math></span><img src="./fecbd76475e9f7630951f9d22ea09b5d80ae09d8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:27.16ex; height:4.843ex;" alt="{\displaystyle E_{{\text{e}}'}={\sqrt {(p_{{\text{e}}'}c)^{2}+(m_{\text{e}}c^{2})^{2}}}~.}" loading="lazy"></span></dd></dl>

<p>Substituting these quantities into the expression for the conservation of energy gives

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<annotation encoding="application/x-tex">{\displaystyle hf+m_{\text{e}}c^{2}=hf'+{\sqrt {(p_{{\text{e}}'}c)^{2}+(m_{\text{e}}c^{2})^{2}}}.}</annotation>

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</math></span><img src="./3abf68c641a8af5ba86663408e10b767d153eb50.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:40.077ex; height:4.843ex;" alt="{\displaystyle hf+m_{\text{e}}c^{2}=hf'+{\sqrt {(p_{{\text{e}}'}c)^{2}+(m_{\text{e}}c^{2})^{2}}}.}" loading="lazy"></span></dd></dl>

<p>This expression can be used to find the magnitude of the momentum of the scattered electron,

</p>

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</style><table role="presentation" class="numblk" style="margin-left: 0em;"><tbody><tr><td class="nowrap"><span class="mwe-math-element mwe-math-element-block"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p_{{\text{e}}'}^{\,2}c^{2}=(hf-hf'+m_{\text{e}}c^{2})^{2}-m_{\text{e}}^{2}c^{4}.}">

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<annotation encoding="application/x-tex">{\displaystyle p_{{\text{e}}'}^{\,2}c^{2}=(hf-hf'+m_{\text{e}}c^{2})^{2}-m_{\text{e}}^{2}c^{4}.}</annotation>

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</math></span></span></td> <td></td> <td class="nowrap"><span id="math_1" class="reference nourlexpansion" style="font-weight:bold;">1</span></td></tr></tbody></table>

<p>Note that this magnitude of the momentum gained by the electron (formerly zero) exceeds the energy/<span class="texhtml"><i>c</i></span> lost by the photon,

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<annotation encoding="application/x-tex">{\displaystyle {\frac {1}{c}}{\sqrt {(hf-hf'+m_{\text{e}}c^{2})^{2}-m_{\text{e}}^{2}c^{4}}}>{\frac {hf-hf'}{c}}~.}</annotation>

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</math></span><img src="./1511915441abcda5d400966bb974de7330f29ab7.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:45.853ex; height:5.509ex;" alt="{\displaystyle {\frac {1}{c}}{\sqrt {(hf-hf'+m_{\text{e}}c^{2})^{2}-m_{\text{e}}^{2}c^{4}}}>{\frac {hf-hf'}{c}}~.}" loading="lazy"></span></dd></dl>

<p>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.

</p><p>Solving the conservation of momentum expression for the scattered electron's momentum gives

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<annotation encoding="application/x-tex">{\displaystyle \mathbf {p} _{{\text{e}}'}=\mathbf {p} _{\gamma }-\mathbf {p} _{\gamma '}.}</annotation>

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</math></span><img src="./2ec1fc2c0a2682aad3f88f757714eea4853fa089.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:15.329ex; height:2.843ex;" alt="{\displaystyle \mathbf {p} _{{\text{e}}'}=\mathbf {p} _{\gamma }-\mathbf {p} _{\gamma '}.}" loading="lazy"></span></dd></dl>

<p>Making use of the <a href="Scalar_product" class="mw-redirect" title="Scalar product">scalar product</a> yields the square of its magnitude,

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<annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}p_{{\text{e}}'}^{\,2}&=\mathbf {p} _{{\text{e}}'}\cdot \mathbf {p} _{{\text{e}}'}=(\mathbf {p} _{\gamma }-\mathbf {p} _{\gamma '})\cdot (\mathbf {p} _{\gamma }-\mathbf {p} _{\gamma '})\\&=p_{\gamma }^{\,2}+p_{\gamma '}^{\,2}-2p_{\gamma }\,p_{\gamma '}\cos \theta .\end{aligned}}}</annotation>

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</math></span><img src="./94cc7643961bc6937e163c7c07c2d5df485a84a0.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:39.756ex; height:7.176ex;" alt="{\displaystyle {\begin{aligned}p_{{\text{e}}'}^{\,2}&=\mathbf {p} _{{\text{e}}'}\cdot \mathbf {p} _{{\text{e}}'}=(\mathbf {p} _{\gamma }-\mathbf {p} _{\gamma '})\cdot (\mathbf {p} _{\gamma }-\mathbf {p} _{\gamma '})\\&=p_{\gamma }^{\,2}+p_{\gamma '}^{\,2}-2p_{\gamma }\,p_{\gamma '}\cos \theta .\end{aligned}}}" loading="lazy"></span></dd></dl>

<p>In anticipation of <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p_{\gamma }c}">

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<annotation encoding="application/x-tex">{\displaystyle p_{{\text{e}}'}^{\,2}c^{2}=p_{\gamma }^{\,2}c^{2}+p_{\gamma '}^{\,2}c^{2}-2c^{2}p_{\gamma }\,p_{\gamma '}\cos \theta .}</annotation>

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<p>After replacing the photon momentum terms with <span class="texhtml"><i>hf</i>/<i>c</i></span>, we get a second expression for the magnitude of the momentum of the scattered electron,

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<annotation encoding="application/x-tex">{\displaystyle p_{e'}^{\,2}c^{2}=(hf)^{2}+(hf')^{2}-2(hf)(hf')\cos {\theta }~.}</annotation>

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</math></span></span></td> <td></td> <td class="nowrap"><span id="math_2" class="reference nourlexpansion" style="font-weight:bold;">2</span></td></tr></tbody></table>

<p>Equating the alternate expressions for this momentum gives

</p>

<msup>

</msup>

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<msup>

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<annotation encoding="application/x-tex">{\displaystyle (hf-hf'+m_{\text{e}}c^{2})^{2}-m_{\text{e}}^{\,2}c^{4}=\left(hf\right)^{2}+\left(hf'\right)^{2}-2h^{2}ff'\cos {\theta },}</annotation>

</semantics>

</math></span><img src="./b5806063ad794692af5b72707597e723a86d4eb6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:60.883ex; height:3.509ex;" alt="{\displaystyle (hf-hf'+m_{\text{e}}c^{2})^{2}-m_{\text{e}}^{\,2}c^{4}=\left(hf\right)^{2}+\left(hf'\right)^{2}-2h^{2}ff'\cos {\theta },}" loading="lazy"></span></dd></dl>

<p>which, after evaluating the square and canceling and rearranging terms, further yields

</p>

<msub>

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<annotation encoding="application/x-tex">{\displaystyle 2hfm_{\text{e}}c^{2}-2hf'm_{\text{e}}c^{2}=2h^{2}ff'\left(1-\cos \theta \right).}</annotation>

</semantics>

</math></span><img src="./21ff686c33fb5867d4ccfa37743455fe6ad3f7d3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:43.014ex; height:3.176ex;" alt="{\displaystyle 2hfm_{\text{e}}c^{2}-2hf'm_{\text{e}}c^{2}=2h^{2}ff'\left(1-\cos \theta \right).}" loading="lazy"></span></dd></dl>

<p>Dividing both sides by <span class="texhtml">2<i>hff</i><span class="nowrap" style="padding-left:0.15em;">′</span><i>m</i><sub>e</sub><i>c</i></span> yields

</p>

<mfrac>

<msup>

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</mrow>

<mfrac>

</mfrac>

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<annotation encoding="application/x-tex">{\displaystyle {\frac {c}{f'}}-{\frac {c}{f}}={\frac {h}{m_{\text{e}}c}}\left(1-\cos \theta \right).}</annotation>

</semantics>

</math></span><img src="./23fc1f99e5423846930ff5429ff357bc52f58c4f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:27.562ex; height:5.843ex;" alt="{\displaystyle {\frac {c}{f'}}-{\frac {c}{f}}={\frac {h}{m_{\text{e}}c}}\left(1-\cos \theta \right).}" loading="lazy"></span></dd></dl>

<p>Finally, since <span class="texhtml"><i>fλ</i></span> = <span class="texhtml"><i>f</i><span class="nowrap" style="padding-left:0.15em;">′</span><i>λ</i>′</span> = <span class="texhtml mvar" style="font-style:italic;">c</span>,

</p>

<msup>

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</mrow>

<annotation encoding="application/x-tex">{\displaystyle \lambda '-\lambda ={\frac {h}{m_{\text{e}}c}}(1-\cos {\theta })~.}</annotation>

</semantics>

</math></span></span></td> <td></td> <td class="nowrap"><span id="math_3" class="reference nourlexpansion" style="font-weight:bold;">3</span></td></tr></tbody></table>

<p>It can further be seen that the angle <span class="texhtml mvar" style="font-style:italic;">φ</span> of the outgoing electron with the direction of the incoming photon is specified by

</p>

<mrow>

<mrow>

<mfrac>

<mrow>

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<msub>

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<msup>

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</msup>

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</mfrac>

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</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \cot \varphi =\left(1+{\frac {hf}{m_{\text{e}}c^{2}}}\right)\tan(\theta /2)~.}</annotation>

</semantics>

</math></span></span></td> <td></td> <td class="nowrap"><span id="math_4" class="reference nourlexpansion" style="font-weight:bold;">4</span></td></tr></tbody></table>

<div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2></div>

<div class="mw-heading mw-heading3"><h3 id="Compton_scattering">Compton scattering</h3></div>

<p>Compton scattering is of prime importance to <a href="Radiobiology" title="Radiobiology">radiobiology</a>, as it is the most probable interaction of gamma rays and high energy X-rays with atoms in living beings and is applied in <a href="Radiation_therapy" title="Radiation therapy">radiation therapy</a>.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup>

</p><p>Compton scattering is an important effect in <a href="Gamma_spectroscopy" title="Gamma spectroscopy">gamma spectroscopy</a> which gives rise to the <a href="Compton_edge" title="Compton edge">Compton edge</a>, as it is possible for the gamma rays to scatter out of the detectors used. <a href="Compton_suppression" class="mw-redirect" title="Compton suppression">Compton suppression</a> is used to detect stray scatter gamma rays to counteract this effect.

</p>

<div class="mw-heading mw-heading3"><h3 id="Magnetic_Compton_scattering">Magnetic Compton scattering</h3></div>

<p>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 <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle J_{\text{mag}}(\mathbf {p} _{z})}">

<msub>

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<msub>

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</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle J_{\text{mag}}(\mathbf {p} _{z})}</annotation>

</semantics>

</math></span><img src="./148b4fa698849af41d382ac433448991abadf1e0.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:8.832ex; height:3.009ex;" alt="{\displaystyle J_{\text{mag}}(\mathbf {p} _{z})}" loading="lazy"></span> – a one-dimensional projection of the electron spin density.

<msub>

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<annotation encoding="application/x-tex">{\displaystyle J_{\text{mag}}(\mathbf {p} _{z})={\frac {1}{\mu }}\iint _{-\infty }^{\infty }(n_{\uparrow }(\mathbf {p} )-n_{\downarrow }(\mathbf {p} ))d\mathbf {p} _{x}d\mathbf {p} _{y}}</annotation>

</semantics>

</math></span></span>

where <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu }">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \mu }</annotation>

</semantics>

</math></span><img src="./9fd47b2a39f7a7856952afec1f1db72c67af6161.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.402ex; height:2.176ex;" alt="{\displaystyle \mu }" loading="lazy"></span> is the number of spin-unpaired electrons in the system, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{\uparrow }(\mathbf {p} )}">

<msub>

</mrow>

</msub>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle n_{\uparrow }(\mathbf {p} )}</annotation>

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</math></span><img src="./e53f311bc1323a0a0ea238c4624da428d069fa32.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:5.744ex; height:3.009ex;" alt="{\displaystyle n_{\uparrow }(\mathbf {p} )}" loading="lazy"></span> and <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{\downarrow }(\mathbf {p} )}">

<msub>

</mrow>

</msub>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle n_{\downarrow }(\mathbf {p} )}</annotation>

</semantics>

</math></span><img src="./fe8b17eedc88980cc49d2fc4488cd69d4d2df9e7.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:5.744ex; height:3.009ex;" alt="{\displaystyle n_{\downarrow }(\mathbf {p} )}" loading="lazy"></span> are the three-dimensional electron momentum distributions for the majority spin and minority spin electrons respectively.

</p><p>Since this scattering process is <a href="Coherence_(physics)" title="Coherence (physics)">incoherent</a> (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 <a href="Density_functional_theory" title="Density functional theory">density functional theory</a>.

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 <a href="SQUID" title="SQUID">SQUID</a> 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.<sup id="cite_ref-Cooper2004_11-0" class="reference"><a href="#cite_note-Cooper2004-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading3"><h3 id="Inverse_Compton_scattering">Inverse Compton scattering</h3></div>

<p>Inverse Compton scattering is important in <a href="Astrophysics" title="Astrophysics">astrophysics</a>. In <a href="X-ray_astronomy" title="X-ray astronomy">X-ray astronomy</a>, the <a href="Accretion_disk" title="Accretion disk">accretion disk</a> surrounding a <a href="Black_hole" title="Black hole">black hole</a> 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 <a href="Stellar_corona" title="Stellar corona">corona</a>. This is surmised to cause the power law component in the X-ray spectra (0.2–10 keV) of accreting black holes.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup>

</p><p>The effect is also observed when photons from the <a href="Cosmic_microwave_background_radiation" class="mw-redirect" title="Cosmic microwave background radiation">cosmic microwave background</a> (CMB) move through the hot gas surrounding a <a href="Galaxy_cluster" title="Galaxy cluster">galaxy cluster</a>. The CMB photons are scattered to higher energies by the electrons in this gas, resulting in the <a href="Sunyaev%E2%80%93Zel'dovich_effect" class="mw-redirect" title="Sunyaev–Zel'dovich effect">Sunyaev–Zel'dovich effect</a>. Observations of the Sunyaev–Zel'dovich effect provide a nearly redshift-independent means of detecting galaxy clusters.

</p><p>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<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> subsequently used for nuclear physics experiments.

</p>

<div class="mw-heading mw-heading3"><h3 id="Non-linear_inverse_Compton_scattering">Non-linear inverse Compton scattering</h3></div>

<p><a href="Non-linear_inverse_Compton_scattering" title="Non-linear inverse Compton scattering">Non-linear inverse Compton scattering</a> (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.<sup id="cite_ref-:0_16-0" class="reference"><a href="#cite_note-:0-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> 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 <a href="Laser" title="Laser">laser</a>.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup>

</p><p>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.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> As a consequence NICS photons can be used to trigger other phenomena such as pair production, Compton scattering, <a href="Nuclear_reaction" title="Nuclear reaction">nuclear reactions</a>, and can be used to probe non-linear quantum effects and non-linear <a href="Quantum_electrodynamics" title="Quantum electrodynamics">QED</a>.<sup id="cite_ref-:0_16-1" class="reference"><a href="#cite_note-:0-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup>

</p>

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</style><div class="div-col" style="column-width: 30em;">

<ul><li><a href="Compton_Gamma_Ray_Observatory" title="Compton Gamma Ray Observatory">Compton Gamma Ray Observatory</a></li>

<li><a href="Klein%E2%80%93Nishina_formula" title="Klein–Nishina formula">Klein–Nishina formula</a></li>

<li><a href="Nuclear_electromagnetic_pulse" title="Nuclear electromagnetic pulse">Nuclear electromagnetic pulse</a></li>

<li><a href="Pair_production" title="Pair production">Pair production</a></li>

<li><a href="Peter_Debye" title="Peter Debye">Peter Debye</a></li>

<li><a href="Photoelectric_effect" title="Photoelectric effect">Photoelectric effect</a></li>

<li><a href="Radiation_pressure#Theory" title="Radiation pressure">Radiation pressure</a></li>

<li><a href="Resonant_inelastic_X-ray_scattering" title="Resonant inelastic X-ray scattering">Resonant inelastic X-ray scattering</a></li>

<li><a href="Thomson_scattering" title="Thomson scattering">Thomson scattering</a></li>

<li><a href="Timeline_of_cosmic_microwave_background_astronomy" class="mw-redirect" title="Timeline of cosmic microwave background astronomy">Timeline of cosmic microwave background astronomy</a></li>

<li><a href="Non-linear_inverse_Compton_scattering" title="Non-linear inverse Compton scattering">Non-linear inverse Compton scattering</a></li></ul></div>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("./mw/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("./mw/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("./mw/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("./mw/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}

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</style><cite id="CITEREFPattison1975" class="citation journal cs1">Pattison, Philip (1975). <a rel="nofollow" class="external text" href="https://wrap.warwick.ac.uk/138656/1/WRAP_Theses_Pattison_1975.pdf">"X-Ray and Gamma Ray Scattering"</a> <span class="cs1-format">(PDF)</span>. <i>Warwick Database</i>. University of Warwick: 10 – via Warwick Library.</cite></span>

</li>

<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite id="CITEREFSeltzer2009" class="citation journal cs1">Seltzer, Stephen (2009-09-17). <a rel="nofollow" class="external text" href="https://dx.doi.org/10.18434/T48G6X">"XCOM: Photon Cross Sections Database"</a>. <i>NIST</i>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.18434%2FT48G6X">10.18434/T48G6X</a>.</cite></span>

</li>

<li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><cite id="CITEREFP._Christillin1986" class="citation journal cs1">P. Christillin (1986). <span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="https://iopscience.iop.org/article/10.1088/0305-4616/12/9/008/meta">"Nuclear Compton scattering"</a></span>. <i>J. Phys. G: Nucl. Phys</i>. <b>12</b> (9): <span class="nowrap">837–</span>851. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1986JPhG...12..837C">1986JPhG...12..837C</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F0305-4616%2F12%2F9%2F008">10.1088/0305-4616/12/9/008</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:250783416">250783416</a>.</cite></span>

</li>

<cite id="CITEREFGriffiths1987" class="citation book cs1">Griffiths, David (1987). <i>Introduction to Elementary Particles</i>. Wiley. pp. 15, 91. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-471-60386-4</bdi>.</cite></span>

</li>

<li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><cite id="CITEREFC._Moore1995" class="citation web cs1">C. Moore (1995). <a rel="nofollow" class="external text" href="http://www.lle.rochester.edu/media/publications/documents/theses/Moore.pdf">"Observation of the Transition from Thomson to Compton Scattering in Optical Multiphoton Interactions with Electrons"</a> <span class="cs1-format">(PDF)</span>.</cite></span>

</li>

<li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><cite id="CITEREFCarron2007" class="citation book cs1">Carron, NJ (2007). <i>An Introduction to the Passage of Energetic Particles through Matter</i>. Boca Raton, FL: CRC Press. p. 61. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>9781420012378</bdi>.</cite></span>

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<li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><cite id="CITEREFChenKotlarchyk2007" class="citation book cs1">Chen, Sow-Hsin; Kotlarchyk, Michael (2007). <i>Interactions of Photons and Neutrons with Matter</i> (2nd ed.). Singapore: World Scientific. p. 271. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>9789810242145</bdi>.</cite></span>

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<li id="cite_note-taylor_136-9-8"><span class="mw-cite-backlink">^ <a href="#cite_ref-taylor_136-9_8-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-taylor_136-9_8-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-taylor_136-9_8-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-taylor_136-9_8-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><cite id="CITEREFTaylorZafiratosDubson2004" class="citation book cs1">Taylor, J.R.; Zafiratos, C.D.; Dubson, M.A. (2004). <i>Modern Physics for Scientists and Engineers</i> (2nd ed.). <a href="Prentice_Hall" title="Prentice Hall">Prentice Hall</a>. pp. <span class="nowrap">136–</span>9. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-13-805715-X</bdi>.</cite></span>

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<li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text">Camphausen KA, Lawrence RC. <a rel="nofollow" class="external text" href="http://www.cancernetwork.com/cancer-management-11/chapter02/article/10165/1399960">"Principles of Radiation Therapy"</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090515031929/http://www.cancernetwork.com/cancer-management-11/chapter02/article/10165/1399960">Archived</a> 2009-05-15 at the <a href="Wayback_Machine" title="Wayback Machine">Wayback Machine</a> in Pazdur R, Wagman LD, Camphausen KA, Hoskins WJ (Eds) <a rel="nofollow" class="external text" href="http://www.cancernetwork.com/cancer-management-11/">Cancer Management: A Multidisciplinary Approach</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20131004224102/http://www.cancernetwork.com/cancer-management-11/">Archived</a> 2013-10-04 at the <a href="Wayback_Machine" title="Wayback Machine">Wayback Machine</a>. 11 ed. 2008.</span>

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Ridwan, S. M., El-Tayyeb, F., Hainfeld, J. F., & Smilowitz, H. M. (2020). Distributions of intravenous injected iodine nanoparticles in orthotopic U87 human glioma xenografts over time and tumor therapy. Nanomedicine, 15(24), 2369–2383. <a rel="nofollow" class="external free" href="https://doi.org/10.2217/nnm-2020-0178">https://doi.org/10.2217/nnm-2020-0178</a></span>

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<li id="cite_note-Cooper2004-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-Cooper2004_11-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFMalcolm_Cooper2004" class="citation book cs1">Malcolm Cooper (14 October 2004). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=m58jXIJDs3QC"><i>X-Ray Compton Scattering</i></a>. <a href="OUP_Oxford" class="mw-redirect" title="OUP Oxford">OUP Oxford</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-19-850168-8</bdi><span class="reference-accessdate">. Retrieved <span class="nowrap">4 March</span> 2013</span>.</cite></span>

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<li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text">Barbiellini, B., Bansil, A. (2020). Scattering Techniques, Compton. Materials Science and Materials Engineering, Elsevier. <a rel="nofollow" class="external free" href="https://doi.org/10.1016/B978-0-323-90800-9.00107-4">https://doi.org/10.1016/B978-0-323-90800-9.00107-4</a></span>

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<li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><cite id="CITEREFDr._Tortosa" class="citation web cs1">Dr. Tortosa, Alessia. <a rel="nofollow" class="external text" href="http://www.matfis.uniroma3.it/Allegati/Dottorato/TESI/tortosa/tesi_PhD_Tortosa_Alessia.pdf">"Comptonization mechanisms in hot coronae in AGN. The NuSTAR view"</a> <span class="cs1-format">(PDF)</span>. DIPARTIMENTO DI MATEMATICA E FISICA.</cite></span>

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<li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.lnf.infn.it/~levisand/graal/graal.html">"GRAAL home page"</a>. Lnf.infn.it<span class="reference-accessdate">. Retrieved <span class="nowrap">2011-11-08</span></span>.</cite></span>

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<li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://tunl.duke.edu/research/our-facilities">"Duke University TUNL HIGS Facility"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2021-01-31</span></span>.</cite></span>

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<li id="cite_note-:0-16"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_16-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_16-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><cite id="CITEREFDi_PiazzaMüllerHatsagortsyanKeitel2012" class="citation journal cs1">Di Piazza, A.; Müller, C.; Hatsagortsyan, K. Z.; Keitel, C. H. (2012-08-16). <a rel="nofollow" class="external text" href="https://link.aps.org/doi/10.1103/RevModPhys.84.1177">"Extremely high-intensity laser interactions with fundamental quantum systems"</a>. <i>Reviews of Modern Physics</i>. <b>84</b> (3): <span class="nowrap">1177–</span>1228. <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1111.3886">1111.3886</a></span>. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2012RvMP...84.1177D">2012RvMP...84.1177D</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FRevModPhys.84.1177">10.1103/RevModPhys.84.1177</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0034-6861">0034-6861</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:118536606">118536606</a>.</cite></span>

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<li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><cite id="CITEREFMeyerhofer1997" class="citation journal cs1">Meyerhofer, D.D. (1997). <span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="https://ieeexplore.ieee.org/document/641308">"High-intensity-laser-electron scattering"</a></span>. <i>IEEE Journal of Quantum Electronics</i>. <b>33</b> (11): <span class="nowrap">1935–</span>1941. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1997IJQE...33.1935M">1997IJQE...33.1935M</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2F3.641308">10.1109/3.641308</a>.</cite></span>

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<li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><cite id="CITEREFRitus1985" class="citation journal cs1">Ritus, V. I. (1985). <span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="http://link.springer.com/10.1007/BF01120220">"Quantum effects of the interaction of elementary particles with an intense electromagnetic field"</a></span>. <i>Journal of Soviet Laser Research</i>. <b>6</b> (5): <span class="nowrap">497–</span>617. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF01120220">10.1007/BF01120220</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0270-2010">0270-2010</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:121183948">121183948</a>.</cite></span>

</li>

</ol></div>

<div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div>

<ul><li><cite id="CITEREFS._ChenH._AvakianV._BurkertL._Vandenaweele2006" class="citation journal cs1">S. Chen; H. Avakian; V. Burkert; L. Vandenaweele; P. Eugenio; the CLAS collaboration; Ambrozewicz; Anghinolfi; Asryan; Bagdasaryan; Baillie; Ball; Baltzell; Barrow; Batourine; Battaglieri; Beard; Bedlinskiy; Bektasoglu; Bellis; Benmouna; Berman; Biselli; Bonner; Bouchigny; Boiarinov; Bosted; Bradford; Branford; et al. (2006). "Measurement of Deeply Virtual Compton Scattering with a Polarized Proton Target". <i><a href="Physical_Review_Letters" title="Physical Review Letters">Physical Review Letters</a></i>. <b>97</b> (7): 072002. <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/hep-ex/0605012">hep-ex/0605012</a></span>. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2006PhRvL..97g2002C">2006PhRvL..97g2002C</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.97.072002">10.1103/PhysRevLett.97.072002</a>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/17026221">17026221</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:15326395">15326395</a>.</cite></li>

<li><cite id="CITEREFCompton,_Arthur_H.1923" class="citation journal cs1">Compton, Arthur H. (May 1923). <a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRev.21.483">"A Quantum Theory of the Scattering of X-Rays by Light Elements"</a>. <i><a href="Physical_Review" title="Physical Review">Physical Review</a></i>. <b>21</b> (5): <span class="nowrap">483–</span>502. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1923PhRv...21..483C">1923PhRv...21..483C</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRev.21.483">10.1103/PhysRev.21.483</a></span>.</cite> (the original 1923 paper on the <a href="American_Physical_Society" title="American Physical Society">APS</a> website)</li>

<li>Stuewer, Roger H. (1975), The Compton Effect: Turning Point in Physics (New York: Science History Publications)</li></ul>

<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li><a rel="nofollow" class="external text" href="http://hyperphysics.phy-astr.gsu.edu/Hbase/quantum/comptint.html">Compton Scattering</a> – Georgia State University</li>

<li><a rel="nofollow" class="external text" href="http://hyperphysics.phy-astr.gsu.edu/Hbase/quantum/compdat.html#c1">Compton Scattering Data</a> – Georgia State University</li>

<li><a rel="nofollow" class="external text" href="http://www.miniphysics.com/derivation-of-compton-shift-equation.html">Derivation of Compton shift equation</a></li></ul>

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</style></div><div role="navigation" class="navbox" aria-labelledby="Quantum_electrodynamics196" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Quantum_electrodynamics196" style="font-size:114%;margin:0 4em"><a href="Quantum_electrodynamics" title="Quantum electrodynamics">Quantum electrodynamics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Formalism</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Euler%E2%80%93Heisenberg_Lagrangian" title="Euler–Heisenberg Lagrangian">Euler–Heisenberg Lagrangian</a></li>

<li><a href="Feynman_diagram" title="Feynman diagram">Feynman diagram</a></li>

<li><a href="Gupta%E2%80%93Bleuler_formalism" title="Gupta–Bleuler formalism">Gupta–Bleuler formalism</a></li>

<li><a href="Path_integral_formulation" title="Path integral formulation">Path integral formulation</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Particles</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Dual_photon" title="Dual photon">Dual photon</a></li>

<li><a href="Electron" title="Electron">Electron</a></li>

<li><a href="Faddeev%E2%80%93Popov_ghost" title="Faddeev–Popov ghost">Faddeev–Popov ghost</a></li>

<li><a href="Photon" title="Photon">Photon</a></li>

<li><a href="Positron" title="Positron">Positron</a></li>

<li><a href="Positronium" title="Positronium">Positronium</a></li>

<li><a href="Virtual_particle" title="Virtual particle">Virtual particles</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Anomalous_magnetic_dipole_moment" title="Anomalous magnetic dipole moment">Anomalous magnetic dipole moment</a></li>

<li><a href="Furry's_theorem" title="Furry's theorem">Furry's theorem</a></li>

<li><a href="Klein%E2%80%93Nishina_formula" title="Klein–Nishina formula">Klein–Nishina formula</a></li>

<li><a href="Landau_pole" title="Landau pole">Landau pole</a></li>

<li><a href="QED_vacuum" title="QED vacuum">QED vacuum</a></li>

<li><a href="Self-energy" title="Self-energy">Self-energy</a></li>

<li><a href="Schwinger_limit" title="Schwinger limit">Schwinger limit</a></li>

<li><a href="Uehling_potential" title="Uehling potential">Uehling potential</a></li>

<li><a href="Vacuum_polarization" title="Vacuum polarization">Vacuum polarization</a></li>

<li><a href="Vertex_function" title="Vertex function">Vertex function</a></li>

<li><a href="Ward%E2%80%93Takahashi_identity" title="Ward–Takahashi identity">Ward–Takahashi identity</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Processes</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Bhabha_scattering" title="Bhabha scattering">Bhabha scattering</a></li>

<li><a href="Breit%E2%80%93Wheeler_process" title="Breit–Wheeler process">Breit–Wheeler process</a></li>

<li><a href="Bremsstrahlung" title="Bremsstrahlung">Bremsstrahlung</a></li>

<li><a href="Delbr%C3%BCck_scattering" title="Delbrück scattering">Delbrück scattering</a></li>

<li><a href="Lamb_shift" title="Lamb shift">Lamb shift</a></li>

<li><a href="M%C3%B8ller_scattering" title="Møller scattering">Møller scattering</a></li>

<li><a href="Schwinger_effect" title="Schwinger effect">Schwinger effect</a></li>

<li><a href="Two-photon_physics" title="Two-photon physics">Photon-photon scattering</a></li></ul>

</div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div><i>See also:</i> <span class="noviewer" typeof="mw:File"><span title="Template"></span></span> Template:Quantum mechanics topics</div></td></tr></tbody></table></div>

<div class="navbox-styles"></div><div role="navigation" class="navbox" aria-labelledby="X-ray_science96" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="X-ray_science96" style="font-size:114%;margin:0 4em"><a href="X-ray" title="X-ray">X-ray science</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%;background:#e5e5ff;">Characteristics</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="Absorption_edge" title="Absorption edge">Absorption edge</a></li>

<li><a href="Moseley's_law" title="Moseley's law">Moseley's law</a></li>

<li><a href="Synchrotron_radiation" title="Synchrotron radiation">Synchrotron radiation</a></li>

<li><a href="Water_window" title="Water window">Water window</a></li>

<li><a href="Siegbahn_notation" title="Siegbahn notation">Siegbahn notation</a></li>

<li><a href="Characteristic_X-ray" title="Characteristic X-ray">Characteristic X-ray</a></li>

<li><a href="High-energy_X-rays" title="High-energy X-rays">High-energy X-rays</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;background:#e5e5ff;">Sources and instruments</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="Betatron" title="Betatron">Betatron</a></li>

<li><a href="Synchrotron" title="Synchrotron">Synchrotron</a></li>

<li><a href="Synchrotron_light_source" title="Synchrotron light source">Synchrotron light source</a></li>

<li><a href="Free-electron_laser" title="Free-electron laser">Free-electron laser</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;background:#e5e5ff;">Interaction with matter</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Rayleigh_scattering" title="Rayleigh scattering">Rayleigh scattering</a></li>

<li><a href="Photoelectric_effect" title="Photoelectric effect">Photoelectric effect</a></li>

<li><a href="Auger_effect" title="Auger effect">Auger effect</a></li>

<li><a href="Photoionization" title="Photoionization">Photoionization</a></li>

<li><a href="Photodisintegration" title="Photodisintegration">Photodisintegration</a></li>

<li><a href="Radiation_damage" title="Radiation damage">Radiation damage</a></li>

<li><a href="Anomalous_X-ray_scattering" title="Anomalous X-ray scattering">Anomalous X-ray scattering</a></li>

<li><a href="X-ray_diffraction" title="X-ray diffraction">X-ray diffraction</a></li>

<li><a href="X-ray_fluorescence" title="X-ray fluorescence">X-ray fluorescence</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;background:#e5e5ff;">Applications</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Imaging</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="X-ray_radiography" class="mw-redirect" title="X-ray radiography">X-ray radiography</a></li>

<li><a href="Panoramic_radiograph" title="Panoramic radiograph">Panoramic radiography</a></li>

<li><a href="Tomosynthesis" title="Tomosynthesis">Tomosynthesis</a></li>

<ul><li><a href="Helical_CT" class="mw-redirect" title="Helical CT">Helical CT</a></li></ul></li>

<li><a href="Soft_x-ray_microscopy" class="mw-redirect" title="Soft x-ray microscopy">Soft x-ray microscopy</a></li>

<li><a href="Ptychography" title="Ptychography">Ptychography</a></li>

<li><a href="Diffraction_tomography" title="Diffraction tomography">Diffraction tomography</a>

<li><a href="X-Ray_Fluorescence_Imaging" class="mw-redirect" title="X-Ray Fluorescence Imaging">X-Ray Fluorescence Imaging</a></li>

<li><a href="X-ray_telescope" title="X-ray telescope">X-ray telescope</a></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Spectroscopy</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="Angle-resolved_photoemission_spectroscopy" title="Angle-resolved photoemission spectroscopy">ARPES</a></li>

<li><a href="Extended_X-ray_absorption_fine_structure" title="Extended X-ray absorption fine structure">EXAFS</a></li>

<li><a href="X-ray_absorption_near_edge_structure" title="X-ray absorption near edge structure">XANES</a></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="X-ray_scattering_techniques" title="X-ray scattering techniques">Scattering</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="X-ray_crystallography" title="X-ray crystallography">X-ray crystallography</a></li>

<li><a href="X-ray_diffraction" title="X-ray diffraction">X-ray diffraction</a></li>

<li><a href="Backscatter_X-ray" title="Backscatter X-ray">Backscatter X-ray</a></li>

<li><a href="Grazing-incidence_small-angle_scattering" title="Grazing-incidence small-angle scattering">GISAXS</a></li>

<li><a href="X-ray_reflectivity" title="X-ray reflectivity">X-ray reflectivity</a></li>

<li><a href="Energy-dispersive_X-ray_diffraction" title="Energy-dispersive X-ray diffraction">EDXRD</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Others</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="X-ray_astronomy" title="X-ray astronomy">X-ray astronomy</a>

<ul><li><a href="History_of_X-ray_astronomy" title="History of X-ray astronomy">History</a></li></ul></li>

<li><a href="X-ray_lithography" title="X-ray lithography">X-ray lithography</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr></tbody></table></div>

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