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| |abovestyle = background:#CEF2E0;
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| |above = Electron Scattering
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| |image = [[File:Electron-beam interaction and transmission with sample.jpg|250px|centre]]
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| |caption = Pictorial description of how an electron beam may interact with a sample with nucleus N, and electron cloud of electron shells K,L,M. Showing transmitted electrons and elastic/inelastic-ally scattered electrons. SE is a '''S'''econdary '''E'''lectron ejected by the beam electron, emitting a characteristic photon (X-Ray) γ. BSE is a '''B'''ack-'''S'''cattered '''E'''lectron, an electron which is scattered backwards instead of being transmitted through the sample.
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| |headerstyle = background:#CEF2E0;
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| |header1 = Electron ({{SubatomicParticle|Electron}}, {{SubatomicParticle|beta-}})
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| |label2 = Particle
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| |data2 = [[Electron]]
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| |label3 = Mass
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| |data3 = {{val|9.10938291|(40)|e=-31|ul=kg}}<ref name=NISTRef>{{cite web|title=CODATA Internationally recommended values of the Fundamental Physical Constants|url=http://physics.nist.gov/cuu/Constants/index.html|work=NIST Standard Reference Database 121|publisher=National Institute of Standards and Technology|accessdate=23 November 2013}}</ref><br /><!--
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| -->{{val|5.4857990946|(22)|e=-4|ul=u}}<ref name=NISTRef /><br /><!--
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| -->[{{val|1822.8884845|(14)}}]<sup>−1</sup> u<ref group=note>The fractional version's denominator is the inverse of the decimal value (along with its relative standard uncertainty of {{val|4.2|e=-13|ul=u}}).</ref><br /><!--
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| -->{{val|0.510998928|(11)|ul=MeV/c2}}<ref name=NISTRef />
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| |label4 = Electric Charge
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| |data4 = {{val|-1|el=e|ul=e}}<ref group=note>The electron's charge is the negative of [[elementary charge]], which has a positive value for the proton.</ref><br /><!--
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| -->{{val|-1.602176565|(35)|e=-19|ul=C}}<ref name=NISTRef /><br /><!--
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| -->{{val|-4.80320451|(10)|e=-10|ul=[[Statcoulomb|esu]]}}
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| |label5 = Magnetic Moment
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| |data5 = {{gaps|−1.001|159|652|180|76(27)|u=[[Bohr magneton|μ<sub>B</sub>]]}}<ref name=NISTRef />
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| |label6 = Spin
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| |data6 = {{frac|1|2}}
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| |headerstyle = background:#CEF2E0;
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| |header7 = Scattering
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| |label8 = Forces/Effects
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| |data8 = [[Lorentz force]], [[Electrostatic force]], [[Gravitation]], [[Weak interaction]]
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| |label9 = Measures
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| |data9 = [[Electric charge|Charge]], [[Electric current|Current]]
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| |label10 = Categories
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| |data10 = [[Elastic collision]], [[Inelastic collision]], [[Particle physics|High energy]], [[Low-energy electron diffraction|Low energy]]
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| |label11 = Interactions
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| |data11 = [[Electron scattering#Møller scattering|{{SubatomicParticle|Electron}}— {{SubatomicParticle|Electron}}]]<br /><!--
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| -->[[Electron scattering#Compton scattering|{{SubatomicParticle|Electron}}— {{SubatomicParticle|Photon}}]]<br /><!--
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| -->[[Electron scattering#Bhabha scattering|{{SubatomicParticle|Electron}}— {{SubatomicParticle|Positron}}]]<br /><!--
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| -->[[Electron|{{SubatomicParticle|Electron}}]]— [[Proton|{{SubatomicParticle|Proton}}]]<br /><!--
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| -->[[Electron|{{SubatomicParticle|Electron}}]]— [[Neutron|{{SubatomicParticle|Neutron}}]]<br /><!--
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| -->[[Electron|{{SubatomicParticle|Electron}}]]— [[Atomic nucleus|Nuclei]]
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| |label12 = Types
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| |data12 = [[Compton scattering]]<br /><!--
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| -->[[Møller scattering]]<br /><!--
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| -->[[Mott scattering]]<br /><!--
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| -->[[Bhabha scattering]]<br /><!--
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| -->[[Bremsstrahlung]]<br /><!--
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| -->[[Deep inelastic scattering]]<br /><!--
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| -->[[Synchrotron emission]]<br /><!--
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| -->[[Thomson scattering]]
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| }}
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| | |
| '''Electron scattering''' occurs when electrons are deviated from their original trajectory. This is due to the electrostatic forces within matter interaction or,<ref name=Britannica>{{cite web|title=electron scattering|url=http://www.britannica.com/EBchecked/topic/183635/electron-scattering|work=Encyclopædia Britannica|publisher=Encyclopædia Britannica, Inc.|accessdate=13 October 2013}}</ref><ref name=Ioffe>{{cite web|title=Electron scattering in solids|url=http://www.ioffe.rssi.ru/ES/|work=Ioffe Institute|publisher=Department of Applied Mathematics and Mathematical Physics|accessdate=13 October 2013}}</ref> if an external magnetic field is present, the electron may be deflected by the [[Lorentz force]].{{citation needed|date=November 2013}}<ref name=HoweTEM>{{cite book|last=Howe|first=Brent Fultz, James|title=Transmission electron microscopy and diffractometry of materials|year=2008|publisher=Springer|location=Berlin|isbn=978-3-540-73885-5|edition=3rd}}</ref><ref name=KohlTEM>{{cite book|last=Kohl|first=L. Reimer, H.|title=Transmission electron microscopy physics of image formation|year=2008|publisher=Springer|location=New York, N.Y.|isbn=978-0-387-34758-5|edition=5th ed.}}</ref> This scattering typically happens with solids such as metals, semiconductors and insulators;<ref name=MATTER>{{cite web|title=Electron scattering|url=http://www.matter.org.uk/tem/electron_scattering.htm|work=MATTER|publisher=The University of Liverpool|accessdate=13 October 2013}}</ref> and is a limiting factor in integrated circuits and transistors.<ref name=Britannica />
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| The application of electron scattering is such that it can be used as a high resolution microscope for [[hadron]]ic systems, that allows the measurement of the distribution of charges for nucleons and nuclear structure.<ref name=MTiES>{{cite book|last=Sick|first=editors, B. Frois, I.|title=Modern topics in electron scattering|year=1991|publisher=World Scientific|location=Singapore|isbn=997150975X}}</ref><ref name=IoP>{{cite journal |last=Drechsel |first=D. |last2=Giannini |first2=M. M. |title=Electron scattering off nuclei |year=1989 |volume=52 |journal=Reports on Progress in Physics |issue=9 |doi=10.1088/0034-4885/52/9/002 |pages=1083|bibcode = 1989RPPh...52.1083D }}</ref> The scattering of electrons has allowed us to understand that [[proton]]s and [[neutron]]s are made up of the smaller elementary subatomic particles called [[quark]]s.<ref name=Britannica />
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| Electrons may be scattered through a solid in several ways:
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| *'''Not at all'''; no electron scattering occurs at all and the beam passes straight through.
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| *'''Single scattering'''; when an electron is scattered just once.
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| *'''Plural scattering'''; when electron(s) scatter several times.
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| *'''Multiple scattering'''; when electron(s) scatter very many times over.
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| The likelihood of an electron scattering and the proliferance of the scattering is a probability function of the specimen thickness to the mean free path.<ref name=MATTER />
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| ==History==
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| The principle of the electron was first theorised in the period of 1838-1851 by a natural philosopher by the name of [[Richard Laming]] who speculated the existence of sub-atomic, unit charged particles; he also pictured the atom as being an 'electrosphere' of concentric shells of electrical particles surrounding a material core.<ref name=RepElec>{{cite book|last=Arabatzis|first=Theodore|title=Representing Electrons A Biographical Approach to Theoretical Entities.|year=2005|publisher=University of Chicago Press|location=Chicago|isbn=0226024210}}</ref><ref group=note>Further notes can be found in '''Laming, R.
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| (1845): "Observations on a paper by Prof. Faraday concerning electric conduction and the nature of matter", Phil. Mag. 27, 420-3''' and in '''Farrar. W. F. (1969): “Richard Laming and the coal-gas industry, with his views on the structure of matter”,
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| Annals of Science 25, 243-53'''</ref>
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| <br>
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| It is generally accepted that [[J J Thompson]] first discovered the electron in 1897, although other notable members in the development in charged particle theory are [[George Johnstone Stoney]] (who coined the term "electron"), [[Emil Wiechert]] (who was first to publish his independent discovery of the electron), [[Walter Kaufmann (physicist)|Walter Kaufmann]], [[Pieter Zeeman]] and [[Hendrik Lorentz]].<ref name=Electron100>{{cite book|last=Springford|first=ed. by Michael|title=Electron : a centenary volume|year=1997|publisher=Cambridge Univ. Press|location=Cambridge [u.a.]|isbn=0521561302|edition=1st ed.}}</ref>
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| <br>
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| Compton scattering was first observed at [[Washington University]] in 1923 by [[Arthur Holly Compton]] who earned the 1927 Nobel Prize in Physics for the discovery; his graduate student [[Y. H. Woo]] who further verified the results is also of mention. Compton scattering is usually cited in reference to the interaction involving the electrons of an atom, however nuclear Compton scattering does exist.{{citation needed|date=November 2013}}
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| <br>
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| The first electron diffraction experiment was conducted in 1927 by [[Clinton Davisson]] and [[Lester Germer]] using what would come to be a prototype for modern [[Low-energy electron diffraction|LEED]] system.<ref name=PendryLEED>{{cite book|last=Pendry|first=J.B.|title=Low energy electron diffraction : the theory and its application to determination of surface structure|year=1974|publisher=Academic Press|location=London|isbn=0125505507}}</ref> The experiment was able to demonstrate the wave-like properties of electrons,<ref group=note>Details can be found in Ritchmeyer, Kennard and Lauritsen's (1955) book on atomic physics</ref> thus confirming the [[Matter wave|de Broglie hypothesis]] that matter particles have a wave-like nature.{{citation needed|date=November 2013}} However, after this the interest in LEED diminished in favour of [[High-energy electron diffraction]] until the early 1960s when an interest in LEED was revived; of notable mention during this period is [[H. E. Farnsworth]] who continued to develop LEED techniques.<ref name=PendryLEED />
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| <br>
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| High energy electron-electron colliding beam history begins in 1956 when K. O'Neill of Princeton University became interested in high energy collisions, and introduced the idea of accelerator(s) injecting into storage ring(s). While the idea of beam-beam collisions had been around since approximately the 1920s, it was not until 1953 that a German patent for colliding beam apparatus was obtained by [[Rolf Wideroe]].<ref name=eePanofsky>{{cite journal|last=PANOFSKY|first=W.K.H.|title=SOME REMARKS ON THE EARLY HISTORY OF HIGH ENERGY ELECTRON–ELECTRON SCATTERING|journal=International Journal of Modern Physics A|date=10 June 1998|volume=13|issue=14|pages=2429–2430|doi=10.1142/S0217751X98001219}}</ref>
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| ==Phenomena==
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| {{see also|Quantum electrodynamics}}
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| Electrons can be scattered by other charged particles through the electrostatic Coulomb forces. Furthermore, if a magnetic field is present, a traveling electron will be deflected by the Lorentz force. An extremely accurate description of all electron scattering, including quantum and relativistic aspects, is given by the theory of quantum electrodynamics.
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| ===Lorentz force===
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| [[File:Action of the Lorentz force bending the path of an electron in a magnetic field.gif|thumb|right|upright=1.5|Path of an
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| '''electron''' of velocity '''''v''''' moving in a magnetic field '''''B'''''. Where the dotted circle indicates the magnetic field directed '''out''' of the plane, and the crossed circle indicates the magnetic field directed '''into''' the plane.]]
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| {{Main|Lorentz force}}
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| The Lorentz force, named after Dutch physicist [[Hendrik Lorentz]], for a charged particle ''q'' is given (in [[International System of Units|SI units]]) by the equation:<ref name=FitzpatrickTLF>{{cite web|last=Fitzpatrick|first=Richard|title=The Lorentz force|url=http://farside.ph.utexas.edu/teaching/em/lectures/node33.html|publisher=University of Texas}}</ref>
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| : <math>\mathbf{F} = q\mathbf{E} + q\mathbf{v} \times \mathbf{B}</math>
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| where ''q'''E''''' describes the '''electric force''' due to a present electric field,'''''E''''', acting on ''q''.
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| <br>And ''q'''v''' x '''B''''' describes the '''magnetic force''' due to a present magnetic field, '''''B''''', acting on ''q'' when ''q'' is moving with velocity '''''v'''''.<ref name=FitzpatrickTLF /><ref name=hyperLFL>{{cite web|last=Nave|first=R.|title=Lorentz Force Law|url=http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfor.html|work=hyperphysics|publisher=Georgia State University|accessdate=1 November 2013}}</ref>
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| <br>Which can also be written as:
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| :<math>\mathbf{F} = q[- \nabla \phi - \frac{d\mathbf{A}}{dt} + \nabla(\mathbf{A} \cdot \mathbf{v})]</math>
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| where ''ϕ'' is the '''electric potential''', and '''''A''''' is the '''magnetic vector potential'''.<ref name=WolframLF>{{cite web|last=Weisstein|first=Eric W.|title=Lorentz Force|url=http://scienceworld.wolfram.com/physics/LorentzForce.html|work=scienceworld|publisher=wolfram research|accessdate=1 November 2013}}</ref>
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| It was [[Oliver Heaviside]] who is attributed in 1885 and 1889 to first deriving the correct expression for the Lorentz force of ''q'''v''' x '''B'''''.<ref name=DarrigolED>{{cite book|last=Darrigol|first=Olivier|title=Electrodynamics from Ampère to Einstein|year=2000|publisher=Oxford Univ. Press|location=Oxford [u.a.]|isbn=0198505949|edition=Repr.}}</ref> [[Hendrik Lorentz]] derived and refined the concept in 1892 and gave it his name,<ref name=KurtusLF>{{cite web|last=Kurtus|first=Ron|title=Lorentz Force on Electrical Charges in Magnetic Field|url=http://www.school-for-champions.com/science/magnetic_force_lorentz.htm|work=Ron Kurtus' School for Champions|publisher=School for Champions|accessdate=6 November 2013}}</ref> incorporating forces due to electric fields.
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| <br>Rewriting this as the equation of motion for a free particle of charge ''q'' mass ''m'',this becomes:<ref name=FitzpatrickTLF />
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| : <math>m\frac{d\mathbf{v}}{dt} = q\mathbf{E} + q\mathbf{v} \times \mathbf{B}</math>
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| or
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| : <math>m\frac{d\gamma\mathbf{v}}{dt} = q\mathbf{E} + q\mathbf{v} \times \mathbf{B}</math>
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| in the relativistic case using [[Lorentz contraction]] where ''γ'' is:<ref name=Feynman2>{{cite book|last=Sands|first=Feynman, Leighton,|title=Mainly electromagnetism and matter|year=2010|publisher=Basic Books|location=New York|isbn=9780465024162|edition=New millenium ed.}}</ref>
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| :<math>\gamma (v) \equiv \frac{1}{\sqrt{1-v^2/c^2}}</math>
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| this equation of motion was first verified in 1897 in [[J J Thomson|J.J. Thomson's]] experiment investigating cathode rays which confirmed, through bending of the rays in a magnetic field, that these rays were a stream of charged particles now known as electrons.<ref name=Electron100 /><ref name=FitzpatrickTLF />
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| Variations on this basic formula describe the magnetic force on a current-carrying wire (sometimes called Laplace force), the electromotive force in a wire loop moving through a magnetic field (an aspect of Faraday's law of induction), and the force on a particle which might be traveling near the speed of light (relativistic form of the Lorentz force).
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| ===Electrostatic Coulomb force===
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| [[Image:CoulombsLaw.svg|thumb|right|upright=1.5|The absolute value of the force '''F''' between two [[point charge]]s ''q'' and ''Q'' relates to the distance ''r'' between the point charges and to the simple product of their charges. The diagram shows that like charges repel each other, and opposite charges attract each other.]]
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| [[Image:Coulombslaw.svg|thumb|right|upright=1.5|A graphical representation of Coulomb's law.|In the image, the vector '''''F<sub>1</sub>''''' is the force experienced by ''q<sub>1</sub>'', and the vector '''''F<sub>2</sub>''''' is the force experienced by ''q<sub>2</sub>''. When ''q<sub>1</sub>q<sub>2</sub> > 0'' the forces are repulsive (as in the image) and when ''q<sub>1</sub>q<sub>2</sub> < 0'' the forces are attractive (opposite to the image). The magnitude of the forces will always be equal.
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| In this case:
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| <math>\mathbf{F} = k \frac{q_1 q_2}{|\mathbf{r_{21}}|^2}\mathbf{\hat{r_{21}}} = \frac{q_1 q_2}{4 \pi \epsilon_0 |\mathbf{r_{21}}|^2}\mathbf{\hat{r_{21}}}</math>
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| <br>where the vector,
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| <br><math>\boldsymbol{r_{21}}=\boldsymbol{r_1-r_2}</math>
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| <br>is the vectorial distance between the charges and,
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| <math>\boldsymbol{\hat{r}_{21}}={\boldsymbol{r_{21}}/|\boldsymbol{r_{21}}|}</math>
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| <br>(a unit vector pointing from ''q<sub>2</sub>'' to ''q<sub>1</sub>'').
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| <br>The vector form of the equation above calculates the force '''F<sub>1</sub>''' applied on ''q<sub>1</sub>'' by ''q<sub>2</sub>''. If '''''r<sub>12</sub>''''' is used instead, then the effect on ''q<sub>2</sub>'' can be found. It can be also calculated using [[Newton's third law]]: '''F<sub>2</sub>''' = -'''F<sub>1</sub>.]]
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| {{Main|Coulomb's law}}
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| '''Electrostatic Coulomb force''' also known as '''Coulomb interaction''' and '''electrostatic force''', named for [[Charles-Augustin de Coulomb]] who published the result in 1785, describes the attraction or repulsion of particles due to their electric charge.<ref name=EBCoulombForce>{{cite web|title=Coulomb force|url=http://www.britannica.com/EBchecked/topic/140084/Coulomb-force|work=Encyclopædia Britannica|publisher=Encyclopædia Britannica, Inc.|accessdate=21 November 2013}}</ref>
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| Coulomb's law states that:
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| :''The magnitude of the electric [[force]] between two point [[electric charge|charge]]s is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.''<ref name=Y&FUniversityPhysics>{{cite book|last=Ford|first=Hugh D. Young, Roger A. Freedman, A. Lewis|title=Sears and Zemansy's university physics : with modern physics|year=2007|publisher=Pearson Addison Wesley|location=San Francisco|isbn=9780321501301|pages=716–719, 830|edition=12e ed.}}</ref> <ref group=note>In -- Coulomb (1785a) [http://books.google.com/books?id=by5EAAAAcAAJ&pg=PA569#v=onepage&q&f=false "Premier mémoire sur l’électricité et le magnétisme,"] ''Histoire de l’Académie Royale des Sciences'', pages 569-577 -- Coulomb studied the repulsive force between bodies having electrical charges of the same sign: <br /><blockquote>''Page 574'' : Il résulte donc de ces trois essais, que l'action répulsive que les deux balles électrifées de la même nature d'électricité exercent l'une sur l'autre, suit la raison inverse du carré des distances.</blockquote><blockquote>''Translation'' : It follows therefore from these three tests, that the repulsive force that the two balls --[that were] electrified with the same kind of electricity -- exert on each other, follows the inverse proportion of the square of the distance.</blockquote>In -- Coulomb (1785b) [http://books.google.com/books?id=by5EAAAAcAAJ&pg=PA578#v=onepage&q&f=false "Second mémoire sur l’électricité et le magnétisme,"] ''Histoire de l’Académie Royale des Sciences'', pages 578-611. -- Coulomb showed that oppositely charged bodies obey an inverse-square law of attraction.</ref>
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| The magnitude of the electrostatic force is proportional to the scalar multiple of the charge magnitudes, and inversely proportional to the square of the distance (i.e. [[Inverse square law]]), and is given by:
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| :<math>F = k \frac{|q_1 q_2|}{r^2} = \frac{|q_1 q_2|}{4 \pi \epsilon_0 r^2}</math>
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| or in vector notation:
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| :<math>\mathbf{F} = k \frac{q_1 q_2}{|\mathbf{r}|^2}\mathbf{\hat{r}} = \frac{q_1 q_2}{4 \pi \epsilon_0 |\mathbf{r}|^2}\mathbf{\hat{r}}</math>
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| where ''q<sub>1</sub>,q<sub>2</sub>'' are two signed point charges; '''''r-hat''''' being the unit vector direction of the distance '''''r''''' between charges; ''k'' is ''Coulombs constant'' and ''ε<sub>0</sub>'' is the permittivity of free space, given in SI units by:<ref name=Y&FUniversityPhysics />
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| :<math>k = \frac{1}{4 \pi \epsilon_0} \approx 8.988 \times 10^9 Nm^2{C^-}^2</math>
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| :<math>\epsilon_0 \approx 8.854 \times 10^{-12} C^2N^{-1}m^{-2}</math>
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| The directions of the forces exerted by the two charges on one another are always along the straight line joining them (the shortest distance), and are vector forces of infinite range; and obey Newtons 3rd law being of equal magnitude and opposite direction.
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| Further, when both charges ''q<sub>1</sub>'' and ''q<sub>2</sub>'' have the same sign (either both positive or both negative) the forces between them are repulsive, if they are of opposite sign then the forces are attractive.<ref name=Y&FUniversityPhysics /><ref name=hyperECF>{{cite web|last=Nave|first=R.|title=Coulomb's Law|url=http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elefor.html|work=hyperphysics|publisher=Georgia State University|accessdate=21 November 2013}}</ref> These forces obey an important property called the '''principle of superposition of forces''' which states that if a third charge were introduced then the total force acting on that charge is the ''vector sum'' of the forces that would be exerted by the other charges individually, this holds for any number of charges.<ref name=Y&FUniversityPhysics />
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| However, Coulomb's Law has been stated for charges in a ''vacuum'', if the space between point charges contains matter then the permittivity of the matter between the charges must be accounted for as follows:
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| :<math>F = k \frac{|q_1 q_2|}{\epsilon_r r^2}</math>
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| where ''ε<sub>r</sub>'' is the '''relative permittivity''' or '''dielectric constant''' of the space the force acts through, and is dimensionless.<ref name=Y&FUniversityPhysics />
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| ===Collisions===
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| If two particles interact with one another in a collision process there are four results possible after the interaction:<ref name=CTheory>{{cite book|last=Kopaleishvili|first=Teimuraz|title=Collision theory : (a short course)|year=1995|publisher=World Scientific|location=Singapore [u.a.]|isbn=9810220987}}</ref>
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| ====Elastic====
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| {{see also|Elastic scattering}}
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| Elastic scattering is when the collisions between target and incident particles have total conservation of kinetic energy.<ref name=SLAC>{{cite web|title=Elastic and Inelastic Collisions in Particle Physics|url=http://hypernews.slac.stanford.edu/slacsite/aux/HiPPP/scattering/|work=SLAC|publisher=Stanford University|accessdate=21 October 2013}}</ref> This implies that there is no breaking up of the particles or energy loss through vibrations,<ref name=SLAC /><ref name=OxPhysics>{{cite web|title=Scattering|url=http://www.physics.ox.ac.uk/documents/PUS/dis/scattering.htm|work=physics.ox|publisher=Oxford University|accessdate=21 October 2013}}</ref> that is to say that the internal states of each of the particles remains unchanged.<ref name=CTheory /> Due to the fact that there is no breaking present, elastic collisions can be modeled as occurring between point-like particles,<ref name=OxPhysics /> a principle that is very useful for an elementary particle such as the electron.<ref name=CTheory />
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| ====Inelastic====
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| {{see also|Inelastic scattering}}
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| Inelastic scattering is when the collisions do ''not'' conserve kinetic energy,<ref name=SLAC /><ref name=OxPhysics /> and as such the internal states of one or both of the particles has changed.<ref name=CTheory /> This is due to energy being converted into vibrations which can be interpreted as heat, waves (sound), or vibrations between constituent particles of either collision party.<ref name=SLAC /> Particles ''may'' also split apart, further energy can be converted into breaking the chemical bonds between components.<ref name=SLAC />
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| Furthermore, momentum is conserved in both elastic and inelastic scattering.<ref name=SLAC /> The other two results are reactions (when the structure of the interacting particles is changed producing two or more (generally complex particles)), and that new particles that are not constituent elementary particles of the interacting particles are created.<ref name=CTheory /><ref name=SLAC />
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| ==Types of scattering==
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| ===Compton scattering===
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| [[File:Compton Scattering Feynman Diagram.gif|thumb|Compton Scattering Feynman Diagram]]
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| {{Main|Compton scattering}}
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| '''Compton scattering''', so named for [[Arthur Holly Compton]] who first observed the effect in 1922 and which earned him the 1927 Nobel Prize in Physics;<ref name=hyperWPD>{{cite web|last=Nave|first=R.|title=Compton Scattering|url=http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/comptint.html|work=hyperphysics|publisher=Georgia State University|accessdate=28 November 2013}}</ref> is the '''inelastic''' scattering of a high-energy photon by a free charged particle.<ref name=ComptonASU>{{cite web|last=Neakrase|first=Jennifer|last2=Neal|first2=Jennifer|last3=Venables|first3=John|title=Photoelectrons, Compton and Inverse Compton Scattering|url=http://venables.asu.edu/quant/proj/compton.html|work=Dept of Physics and Astronomy|publisher=Arizona State University|accessdate=28 November 2013}}</ref> <ref group=note>An electron in this case. Where the notion of "free" results from considering if the energy of the photon is large compared to the binding energy of the electron; then one could make the approximation that the electron as free.</ref>
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| This was demonstrated in 1923 by firing radiation of a given wavelength (X-rays in the given case) sent through a foil (carbon target) was scattered in a manner inconsistent with classical radiation theory,<ref name=ComptonASU /><ref group=note>For example, x-ray photons have an energy value of several keV. So, both conservation of momentum and energy could be observed. To show this, Compton scattered x-ray radiation off a graphite block and measured the wavelength of the x-rays before and after they were scattered as a function of the scattering angle. He discovered that the scattered x-rays had a longer wavelength than that of the incident radiation.</ref> published
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| a paper in the ''Physical Review'' explaining the phenomenon: ''A quantum theory of the scattering of X-rays by light elements''.<ref name=AHCPhysicalReview>{{cite journal|last=Compton|first=Arthur|title=A Quantum Theory of the Scattering of X-rays by Light Elements|journal=Physical Review|date=May 1923|volume=21|issue=5|pages=483–502|doi=10.1103/PhysRev.21.483|accessdate=28 November 2013}}</ref> The Compton effect can be understood as high-energy photons scattering in-elastically off individual electrons,<ref name=ComptonASU /> when the incoming photon gives part of its energy to the electron, then the scattered photon has lower energy and lower frequency and longer wavelength according to the [[Planck relation]]:<ref name=hyperCS>{{cite web|last=Nave|first=R.|title=Compton Scattering|url=http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/compton.html|work=hyperphysics|publisher=Georgia State University|accessdate=28 November 2013}}</ref>
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| :<math> E = h \nu = h f</math>
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| which gives the energy ''E'' of the photon in terms of frequency ''f'' or ''ν'', and Planck's constant ''h'' ({{val|6.626|e=-34|u=J.s}} = {{val|4.136|e=-15|u=eV.s}}).<ref name=hyperPR>{{cite web|last=Nave|first=R.|title=The Planck Hypothesis|url=http://hyperphysics.phy-astr.gsu.edu/hbase/mod2.html#c3|work=hyperphysics|publisher=Georgia State University|accessdate=28 November 2013}}</ref>
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| The wavelength change in such scattering depends only upon the angle of scattering for a given target particle.<ref name=hyperCS /><ref name=IowaCS>{{cite web|title=Compton Scattering|url=http://www.ndt-ed.org/EducationResources/CommunityCollege/Radiography/Physics/comptonscattering.htm|work=NDT Education Resource Center|publisher=Iowa State University|accessdate=28 November 2013}}</ref>
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| This was an important discovery during the 1920s when the particle (photon) nature of light suggested by the [[Photoelectric effect]] was still being debated, the Compton experiment gave clear and independent evidence of particle-like behavior.<ref name=hyperWPD /><ref name=IowaCS />
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| The formula describing the '''Compton shift''' in the wavelength due to scattering is given by:
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| :<math>\lambda_f - \lambda_i = \frac{h}{m_ec}(1 - \cos\theta)</math>
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| where ''λ<sub>f</sub>'' is the final wavelength of the photon '''after''' scattering, ''λ<sub>i</sub>'' is the initial wavelength of the photon '''before''' scattering, ''h'' is Planck's constant, ''m<sub>e</sub>'' is the rest mass of the electron, ''c'' is the speed of light and ''θ'' is the scattering angle of the photon.<ref name=hyperWPD /><ref name=IowaCS />
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| The coefficient of ''(1 - cosθ)'' is known as the ''Compton wavelength'', but is in fact a proportionality constant for the wavelength shift.<ref name=AboutTCE>{{cite web|last=Jones|first=Andrew Zimmerman|title=The Compton Effect|url=http://physics.about.com/od/quantumphysics/a/comptoneffect.htm|work=About.com Physics|publisher=About.com|accessdate=28 November 2013}}</ref> The collision causes the photon wavelength to increase by somewhere between 0 (for a scattering angle of 0°) and twice the Compton wavelength (for a scattering angle of 180°).<ref name=BostonTCE>{{cite web|last=Duffy|first=Andrew|last2=Loewy|first2=Ali|title=The Compton Effect|url=http://physics.bu.edu/~duffy/semester2/c35_compton.html|work=Boston University's Physics department|publisher=Boston University|accessdate=28 November 2013}}</ref>
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| '''Thomson scattering''' is the classical '''elastic''' quantitative interpretation of the scattering process,<ref name=ComptonASU /> and this can be seen to happen with lower, mid-energy, photons. The classical theory of an [[electromagnetic wave]] scattered by charged particles, cannot explain low intensity shifts in wavelength.
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| '''Inverse Compton scattering''' takes place when the electron is moving, and has sufficient kinetic energy compared to the photon. In this case net energy may be transferred from the electron to the photon. The inverse Compton effect is seen in astrophysics when a low energy photon (e.g. of the cosmic microwave background) bounces off a high energy (relativistic) electron. Such electrons are produced in supernovae and active galactic nuclei.<ref name=ComptonASU />
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| ===Møller scattering===
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| [[File:Møller Scattering Feynman Diagram.gif|thumb|Møller scattering Feynman diagram]]
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| {{Main|Møller scattering}}
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| ===Mott scattering===
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| {{Main|Mott scattering}}
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| ===Bhabha scattering===
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| {{Main|Bhabha scattering}}
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| ===Bremsstrahlung scattering===
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| {{Main|Bremsstrahlung}}
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| ===Deep inelastic scattering===
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| {{Main|Deep inelastic scattering}}
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| ===Synchrotron emission===
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| {{Main|Synchrotron emission}}
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| If a charged particle such as an electron is accelerated, this can be acceleration in a straight line or motion in a curved path, electromagnetic radiation is emitted by the particle. Within electron storage rings and circular particle accelerators known as synchrotrons, electrons are bent in a circular path and emit X-rays typically. This radially emitted (<math>\mathbf{a}\perp \mathbf{v}</math>) [[electromagnetic radiation]] when charged particles are accelerated is called '''synchrotron radiation.'''<ref name=hyperSynch>{{cite web|last=Nave|first=R.|title=Synchrotron Radiation|url=http://hyperphysics.phy-astr.gsu.edu/hbase/particles/synchrotron.html|work=hyperphysics|publisher=Georgia State University|accessdate=5 December 2013}}</ref> It is produced in [[synchrotron]]s using bending magnets, [[undulator]]s and/or [[wiggler (synchrotron)|wiggler]]s.{{citation needed|date=December 2013}}
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| The first observation came at the General Electric Research Laboratory in Schenectady, New York, on April 24, 1947 in the synchrotron built by a team of Herb Pollack to test the idea of phase-stability principle for RF accelerators.<ref group=note>The mass of particles in a cyclotron grows as the energy increases into the relativistic range. The heavier particles then arrive too late at the electrodes for a radio-frequency (RF) voltage of fixed frequency to accelerate them, thereby limiting the maximum particle energy. To deal with this problem, in 1945 McMillan in the U. S. and Veksler in the Soviet Union independently proposed decreasing the frequency of the RF voltage as the energy increases to keep the voltage and the particle in synch. This was a specific application of their phase-stability principle for RF accelerators, which explains how particles that are too fast get less acceleration and slow down relative to their companions while particles that are too slow get more and speed up, thereby resulting in a stable bunch of particles that are accelerated together.</ref> When the technician was asked to look around the shielding with a large mirror to check for sparking in the tube, he saw a bright arc of light coming from the electron beam. Robert Langmuir is credited as recognizing it as synchrotron radiation or, as he called it, "Schwinger radiation" after [[Julian Schwinger]].<ref name=RobinsonSYNCH>{{cite web|last=Robinson|first=Arthur L|title=HISTORY of SYNCHROTRON RADIATION|url=http://xdb.lbl.gov/Section2/Sec_2-2.html|work=Center for X-ray Optics and Advanced Light Source|publisher=Lawrence Berkeley National Laboratory|accessdate=5 December 2013}}</ref>
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| Classically, the radiated power ''P'' from an accelerated electron is:
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| :<math>P=\frac{2 K e^2}{3 c^2} a^2</math>
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| this comes from the [[Larmor formula]]; where ''K'' is an electric permittivity constant,<ref group=note>For SI units it can be calculated as 1/4πε<sub>0</sub></ref> ''e'' is electron charge, ''c'' is the speed of light, and ''a'' is the acceleration.
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| Within a circular orbit such as a storage ring, the non-relativistic case is simply the centripetal acceleration. However within a storage ring the acceleration is highly relitivistic, and can be obtained as follows:
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| :<math> a_{non-relativistic} = \frac{v^2}{r} \rightarrow a_{relativistic} = \frac{1}{m} \frac{dp}{d\tau} = \frac{1}{m} \gamma \frac{d(\gamma m v)}{dt} = \gamma^2 \frac{dv}{dt} = \gamma^2 \frac{v^2}{r} </math>
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| where ''v'' is the circular velocity, ''r'' is the radius of the circular accelerator, ''m'' is the rest mass of the charged particle, ''p'' is the momentum, ''τ'' is the [[Proper time]] (t/γ), and ''γ'' is the [[Lorentz factor]].
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| Radiated power then becomes:
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| :<math>P=\frac{2 K e^2}{3 c^2} (\frac{\gamma^2 v^2}{r})^2 = \frac{2 K e^2}{3 c^2} \frac{\gamma^4 v^4}{r^2}</math>
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| For highly relativistic particles, such that velocity becomes nearly constant, the γ<sup>4</sup> term becomes the dominate variable in determining loss rate. This means that the loss scales as the fourth power of the particle energy γmc<sup>2</sup>; and the inverse dependence of synchrotron radiation loss on radius argues for building the accelerator as large as possible.<ref name=hyperSynch />
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| ==Facilities==
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| ===SLAC===
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| {{see also|SLAC National Accelerator Laboratory}}
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| [[Image:Stanford-linear-accelerator-usgs-ortho-kaminski-5900.jpg|thumb|750px|center|Aerial photo of the Stanford Linear Accelerator Center, with detector complex at the right (east) side]]
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| '''Stanford Linear Accelerator Center''' is located near [[Stanford university]], California.<ref name=OxSLAC>{{cite web|last=Walder|first=James|last2=O'Sullivan|first2=Jack|title=The Stanford Linear Accelerator Center (SLAC)|url=http://www.physics.ox.ac.uk/documents/PUS/dis/SLAC.htm|work=Physics Department.|publisher=University Of Oxford|accessdate=16 November 2013}}</ref> Construction began on the 2 mile long linear accelerator in 1962 and was completed in 1967, and in 1968 the first experimental evidence of quarks was discovered resulting in the 1990 Nobel Prize in Physics, shared by SLAC's Richard Taylor and Jerome I. Friedman and Henry Kendall of MIT.<ref name=SLACHist>{{cite web|title=SLAC History|url=https://www6.slac.stanford.edu/about/slac-history.aspx|work=SLAC National Accelerator Laboratory|publisher=Stanford University|accessdate=16 November 2013}}</ref> The accelerator came with a 20GeV capacity for the electron acceleration, and while similar to Rutherford's scattering experiment, that experiment operated with alpha particles at only 7MeV. In the SLAC case the incident particle was an electron and the target a proton, and due to the short wavelength of the electron (due to its high energy and momentum) it was able to probe into the proton.<ref name=OxSLAC />
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| The Stanford Positron Electron Asymmetric Ring (SPEAR) addition to the SLAC made further such discoveries possible, leading to the discovery in 1974 of the J/psi particle, which consists of a paired charm quark and anti-charm quark, and another Nobel Prize in Physics in 1976.
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| This was followed up with Martin Perl's announcement of the discovery of the tau lepton, for which he shared the 1995 Nobel Prize in Physics.<ref name=SLACHist />
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| The SLAC aims to be a premier accelerator laboratory,<ref name=SLACMiss>{{cite web|title=Our Vision and Mission|url=https://www6.slac.stanford.edu/about/vision-and-mission.aspx|work=SLAC National Accelerator Laboratory|publisher=Stanford University|accessdate=16 November 2013}}</ref> to pursue strategic programs in particle physics, particle astrophysics and cosmology, as well as the applications in discovering new drugs for healing, new materials for electronics and new ways to produce clean energy and clean up the environment.<ref name=SLACOver>{{cite web|title=SLAC Overview|url=https://www6.slac.stanford.edu/about/slac-overview.aspx|work=SLAC National Accelerator Laboratory|publisher=Stanford University|accessdate=16 November 2013}}</ref> Under the directorship of Chi-Chang Kao the SLAC's fifth director (as of November 2012), a noted X-ray scientist who came to SLAC in 2010 to serve as associate laboratory director for the Stanford Synchrotron Radiation Lightsource.<ref name=SLACOff>{{cite web|title=Director's Office|url=https://www6.slac.stanford.edu/about/directors-office.aspx|work=SLAC National Accelerator Laboratory|publisher=Stanford University|accessdate=16 November 2013}}</ref>
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| ====BaBar====
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| {{see also|BaBar experiment}}
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| ====SSRL - Stanford Synchrotron Radiation Lightsource====
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| {{see also|Stanford Synchrotron Radiation Lightsource}}
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| Other scientific programs run at SLAC include:<ref name=SLACSciProg>{{cite web|title=Scientific Programs|url=https://www6-stage.slac.stanford.edu/research/scientific-programs.aspx|work=SLAC National Accelerator Laboratory|publisher=Stanford University|accessdate=16 November 2013}}</ref>
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| *Advanced Accelerator Research
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| *ATLAS/Large Hadron Collider
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| *Elementary Particle Theory
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| *EXO - Enriched Xenon Observatory
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| *FACET - Facility for Advanced Accelerator Experimental Tests
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| *Fermi Gamma-ray Space Telescope
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| *Geant4
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| *KIPAC - Kavli Institute for Particle Astrophysics and Cosmology
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| *LCLS - Linac Coherent Light Source
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| *LSST - Large Synoptic Survey Telescope
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| *NLCTA - Next Linear Collider Test Accelerator
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| *Stanford PULSE Institute
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| *SIMES - Stanford Institute for Materials and Energy Sciences
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| *SUNCAT Center for Interface Science and Catalysis
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| *Super CDMS - Super Cryogenic Dark Matter Search
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| ===RIKEN RI Beam Factory===
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| [[RIKEN]] was founded in 1917 as a private research foundation in Tokyo, and is Japan's largest comprehensive research institution. Having grown rapidly in size and scope, it is today renowned for high-quality research in a diverse range of scientific disciplines, and encompasses a network of world-class research centers and institutes across Japan.<ref name=RIKEN>{{cite web|title=About RIKEN|url=http://www.riken.jp/en/about/|work=RIKEN|publisher=RIKEN, Japan|accessdate=11 December 2013}}</ref>
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| The '''RIKEN RI Beam Factory''', otherwise known as the RIKEN Nishina Centre (for Accelerator-Based Science), is a cyclotron-based research facility which began operating in 2007; 70 years after the first in Japanese cyclotron, from [[Yoshio Nishina|Dr. Yoshio Nishina]] whose name is given to the facility.<ref name=NishinaGreeting>{{cite web|title=About Nishina Center - Greeting|url=http://www.rarf.riken.go.jp/Eng/about/greeting.html|work=Nishina Center|publisher=RIKEN Nishina Center for Accelerator-Based Science|accessdate=11 December 2013}}</ref>
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| As of 2006, the facility has a world-class heavy-ion accelerator complex. This consists of a K540-MeV ring cyclotron (RRC) and two different injectors: a variable-frequency heavy-ion linac (RILAC) and a K70-MeV AVF cyclotron (AVF). It has a projectile-fragment separator (RIPS) which provides RI (Radioactive Isotope) beams of less than 60 amu, the world's most intense light-atomic-mass RI beams.<ref name=NishinaFacilities>{{cite web|title=Facilities - RI Beam Factory (RIBF)|url=http://www.rarf.riken.go.jp/Eng/facilities/RIBF.html|work=Nishina Center|publisher=RIKEN Nishina Center for Accelerator-Based Science|accessdate=11 December 2013}}</ref>
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| Overseen by the Nishina Centre, the RI Beam Factory is utilized by users worldwide promoting research in nuclear, particle and hadron physics. This promotion of accelerator applications research is an important mission of the Nishina Centre, and implements the use of both domestic and oversea accelerator facilities.<ref name=NishinaRG>{{cite web|title=About Nishina Center - Research Groups|url=http://www.rarf.riken.go.jp/Eng/about/group.html|work=Nishina Center|publisher=RIKEN Nishina Center for Accelerator-Based Science|accessdate=11 December 2013}}</ref>
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| ====SCRIT====
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| {{see also|SCRIT}}
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| The '''SCRIT (Self-Confining Radioactive isotope Ion Target)''' facility, is currently under construction at the RIKEN RI beam factory (RIBF) in Japan. The project aims to investigate short-lived nuclei through the use of an elastic electron scattering test of charge density distribution, with initial testing done with stable nuclei. With the first electron scattering off unstable Sn isotopes to take place in 2014.<ref name=SudaSCRIT>{{cite journal|last=Suda|first=T.|coauthors=Adachi, T.; Amagai, T.; Enokizono, A.; Hara, M.; Hori, T.; Ichikawa, S.; Kurita, K.; Miyamoto, T.; Ogawara, R.; Ohnishi, T.; Shimakura, Y.; Tamae, T.; Togasaki, M.; Wakasugi, M.; Wang, S.; Yanagi, K.|title=Nuclear physics at the SCRIT electron scattering facility|journal=Progress of Theoretical and Experimental Physics|date=17 December 2012|volume=2012|issue=1|pages=3C008–0|doi=10.1093/ptep/pts043|accessdate=19 November 2013}}</ref>
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| The investigation of short-lived radioactive nuclei (RI) by means of electron scattering has never been performed because of an inability to make these nuclei a target,<ref name=RikenSCRIT>{{cite web|last=Wakasugi|first=Masanori|title=SCRIT Team|url=http://www.riken.jp/en/research/labs/rnc/instrum_dev/scrit/|work=RIKEN Research|publisher=RIKEN Nishina Center for Accelerator-Based Science|accessdate=19 November 2013}}</ref> now the with the advent of a novel self-confining RI technique at the world’s first facility dedicated to the study of the structure of short-lived nuclei by electron scattering this research becomes possible.
| |
| The principle of the technique is based around the ion trapping phenomenon which is observed at electron storage ring facilities,<ref group=note>The residual gases in a storage ring are ionized by the circulating electron beam. Once they are ionized, they are trapped transversely by the electron beam. Since the trapped ions stay on the electron beam and kick electrons out of orbit, the results of this ion trapping are harmful for the performance of electron storage rings. This leads to shorter beam lifetime, and even beam instability when the trapping becomes severe. Thus, much effort has been paid so far to reducing the negative effects of ion trapping</ref> which has an adverse effect on the performance of electron storage rings.<ref name=SudaSCRIT />
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| The novel idea to be employed at SCRIT is to ''use'' the ion trapping to allow short-lived RI's to be made a target, as trapped ions on the electron beam, for the scattering experiments. This idea was first given a proof-of-principle study using the electron storage ring of Kyoto University, KSR; this was done using a stable nucleus of <sup>133</sup>Cs as a target in an experiment of 120MeV electron beam energy, 75mA typical stored beam current and a 100 seconds beam lifetime. The results of this study were favorable with elastically scattered electrons from the trapped Cs being clearly visible.<ref name=SudaSCRIT />
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| ==See also==
| |
| {{col-begin}}
| |
| {{col-2}}
| |
| * [[Zeeman effect]]
| |
| * [[Particle Physics]]
| |
| {{col-2}}
| |
| * [[Low-energy electron diffraction]]
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| * [[Quantum electrodynamics]]
| |
| {{col-end}}
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| | |
| ==Notes==
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| {{Reflist|group=note}}
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| | |
| ==References==
| |
| {{Reflist|30em}}
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| | |
| ==External links==
| |
| * [http://education.jlab.org/pol/electron-scattering.html Physics Out Loud: Electron Scattering] (video)
| |
| * [http://www.youtube.com/watch?v=fI2C4VlR1OM Brightstorm: Compton Scattering] (video)
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| {{DEFAULTSORT:Electron scattering}}
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| [[Category:Electron]]
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| [[Category:Scattering]]
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