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Electron Scattering
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 Secondary Electron ejected by the beam electron, emitting a characteristic photon (X-Ray) γ. BSE is a Back-Scattered Electron, an electron which is scattered backwards instead of being transmitted through the sample.
Electron ( e− , β− )
Particle	Electron
Mass	9.10938291(40)×10−31 kg 5.4857990946(22)×10−4 u [1822.8884845(14)]−1 u 0.510998928(11) MeV/c2
Electric Charge	−1 e −1.602176565(35)×10−19 C −4.80320451(10)×10−10 [[esu]]
Magnetic Moment	−1.00115965218076(27) μB
Spin	1⁄2
Scattering
Forces/Effects	Lorentz force, Electrostatic force, Gravitation, Weak interaction
Measures	Charge, Current
Categories	Elastic collision, Inelastic collision, High energy, Low energy
Interactions	e− — e− e− — γ e− — e+ e− — p e− — n e− — Nuclei
Types	Compton scattering Møller scattering Mott scattering Bhabha scattering Bremsstrahlung Deep inelastic scattering Synchrotron emission Thomson scattering

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

The application of electron scattering is such that it can be used as a high resolution microscope for hadronic systems, that allows the measurement of the distribution of charges for nucleons and nuclear structure. The scattering of electrons has allowed us to understand that protons and neutrons are made up of the smaller elementary subatomic particles quarks.

Electrons may be scattered through a solid in several ways:
-Not at all; no electron scattering occurs at all and the beam passes straight through.
-Single scattering; when an electron is scattered just once.
-Plural scattering; when electron(s) scatter several times.
-Multiple scattering; when electron(s) scatter very many times over.
The likelihood of an electron scattering and the proliference of the scattering is a probability function of the specimen thickness to the mean free path.

History

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.
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, Pieter Zeeman and Hendrik Lorentz.
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.
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 LEED system. The experiment was able to demonstrate the wave-like properties of electrons, thus confirming the de Broglie hypothesis that matter particles have a wave-like nature. 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.
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 wasnt until 1953 that a German patent for colliding beam apparatus was obtained by Rolf Wideroe.

Phenomena

See also: Quantum electrodynamics

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.

Lorentz force

Path of an 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.

The Lorentz force, named after Dutch physicist Hendrik Lorentz, for a charged particle q is given (in SI units) by the equation:

$\mathbf {F} =q\mathbf {E} +q\mathbf {v} \times \mathbf {B}$

where qE describes the electric force due to a present electric field,E, acting on q.
And qv x B describes the magnetic force due to a present magnetic field, B, acting on q when q is moving with velocity v.
Which can also be written as:

$\mathbf {F} =q[-\nabla \phi -{\frac {d\mathbf {A} }{dt}}+\nabla (\mathbf {A} \cdot \mathbf {v} )]$

where ϕ is the electric potential, and A is the magnetic vector potential.

It was Oliver Heaviside who is attributed in 1885 and 1889 to first deriving the correct expression for the Lorentz force of qv x B. Hendrik Lorentz derived and refined the concept in 1892 and gave it his name, incorporating forces due to electric fields.
Rewriting this as the equation of motion for a free particle of charge q mass m,this becomes:

$m{\frac {d\mathbf {v} }{dt}}=q\mathbf {E} +q\mathbf {v} \times \mathbf {B}$

or

$m{\frac {d\gamma \mathbf {v} }{dt}}=q\mathbf {E} +q\mathbf {v} \times \mathbf {B}$

in the relativistic case using Lorentz contraction where γ is:

$\gamma (v)\equiv {\frac {1}{\sqrt {1-v^{2}/c^{2}}}}$

this equation of motion was first verified in 1897 in 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.

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).

Electrostatic Coulomb force

The absolute value of the force F between two point charges 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.

In the image, the vector F₁ is the force experienced by q₁, and the vector F₂ is the force experienced by q₂. When q₁q₂ > 0 the forces are repulsive (as in the image) and when q₁q₂ < 0 the forces are attractive (opposite to the image). The magnitude of the forces will always be equal. In this case: $\mathbf {F} =k{\frac {q_{1}q_{2}}{|\mathbf {r_{21}} |^{2}}}\mathbf {\hat {r_{21}}} ={\frac {q_{1}q_{2}}{4\pi \epsilon _{0}|\mathbf {r_{21}} |^{2}}}\mathbf {\hat {r_{21}}}$
where the vector,
${\boldsymbol {r_{21}}}={\boldsymbol {r_{1}-r_{2}}}$
is the vectorial distance between the charges and, ${\boldsymbol {{\hat {r}}_{21}}}={{\boldsymbol {r_{21}}}/|{\boldsymbol {r_{21}}}|}$
(a unit vector pointing from q₂ to q₁).
The vector form of the equation above calculates the force F₁ applied on q₁ by q₂. If r₁₂ is used instead, then the effect on q₂ can be found. It can be also calculated using Newton's third law: F₂ = -F₁.

See also: Coulomb's law

Electrostatic Coulomb force also know 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.

Coulomb's law states that:

The magnitude of the electric force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

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:

$F=k{\frac {|q_{1}q_{2}|}{r^{2}}}={\frac {|q_{1}q_{2}|}{4\pi \epsilon _{0}r^{2}}}$

or in vector notation:

$\mathbf {F} =k{\frac {q_{1}q_{2}}{|\mathbf {r} |^{2}}}\mathbf {\hat {r}} ={\frac {q_{1}q_{2}}{4\pi \epsilon _{0}|\mathbf {r} |^{2}}}\mathbf {\hat {r}}$

where q₁,q₂ are two signed point charges; r-hat being the unit vector direction of the distance r between charges; k is Coulombs constant and ε₀ is the permittivity of free space, given in SI units by:

$k={\frac {1}{4\pi \epsilon _{0}}}\approx 8.988\times 10^{9}Nm^{2}{C^{-}}^{2}$

$\epsilon _{0}\approx 8.854\times 10^{-12}C^{2}N^{-1}m^{-2}$

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. Further, when both charges q₁ and q₂ 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. 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. 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:

$F=k{\frac {|q_{1}q_{2}|}{\epsilon _{r}r^{2}}}$

where ε_r is the relative permittivity or dielectric constant of the space the force acts through, and is dimensionless.

Collisions

If two particles interact with one another in a collision process there are four results possible after the interaction:

Elastic

See also: Elastic scattering

Elastic scattering is when the collisions between target and incident particles have total conservation of kinetic energy. This implies that there is no breaking up of the particles or energy loss through vibrations, that is to say that the internal states of each of the particles remains unchanged. Due to the fact that there is no breaking present, elastic collisions can be modeled as occurring between point-like particles, a principle that is very useful for an elementary particle such as the electron.
-Total kinetic energy is conserved
-No breaking of particles.
-Classical interpretation, i.e. can be modeled as point-like particles
-internal states unchanged

Inelastic

See also: Inelastic scattering

Inelastic scattering is when the collisions do not conserve kinetic energy, and as such the internal states of one or both of the particles has changed. 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. Particles may also split apart, further energy can be converted into breaking the chemical bonds between components.
-Total kinetic energy is NOT conserved.
-Particles MAY split apart.
-internal states changed

Furthermore, momentum is conserved in both elastic and inelastic scattering. 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.

Types of Scattering

Compton Scattering:

Compton Scattering Feynman Diagram

Main article: Compton scattering

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; is the inelastic scattering of a high-energy photon by a free charged particle. However, as both energy and momentum are conserved during the collision, the collision can be considered elastic. Described in particle physics notation as:

$\gamma e^{-}\longrightarrow \gamma 'e^{-}$

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, published a paper in the Physical Review explaining the phenomenon: A quantum theory of the scattering of X-rays by light elements. The Compton effect can be understood as high-energy photons scattering in-elastically off individual electrons, 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:

$E=h\nu =hf$

which gives the energy E of the photon in terms of frequency f or ν, and Planck's constant h (6.626×10⁻³⁴ J⋅s = 4.136×10⁻¹⁵ eV.s). The wavelength change in such scattering depends only upon the angle of scattering for a given target particle.

This was an important discovery during the 1920's 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.

The formula describing the Compton shift in the wavelength due to scattering is given by:

$\lambda _{f}-\lambda _{i}={\frac {h}{m_{e}c}}(1-\cos \theta )$

where λ_f is the final wavelength of the photon after scattering, λ_i is the initial wavelength of the photon before scattering, h is Plank's constant, m_e is the rest mass of the electron, c is the speed of light and θ is the scattering angle of the photon.

And is derived as follows:

In the classical view, Compton scattering can be simply described as a collision process between photons carrying the light and electrons in the matter. Invoking the particle – wave duality, the incident light is assimilated to a single photon of initial energy E=h-bar omega and initial momentum p=h-bar k. After the “collision”, the photon is in a final state, with energy E'=h-bar omega' and final momentum p'=h-bar k'. The initial and final wave vectors k and k' define the scattering plane, and the collision process can be reduced to a two-dimensional problem in that plane. The electron, initially at rest, acquires a final momentum p_f and a final kinetic energy E_f. By applying the conservation laws from Newtonian mechanics, one can obtain these relationships:

Conservation of momentum:

$\mathbf {p_{i}} =\hbar \mathbf {k} =\mathbf {p_{i}} +\hbar \mathbf {k'}$

Conservation of energy:

$E_{i}=\hbar \omega =E_{f}+\hbar \omega '$

De Broglie relationship:

$\omega =kc={\frac {2kc}{\lambda }}$

The coefficient of (1 - cosθ) is known as the Compton wavelength, but is in fact a proportionality constant for the wavelength shift. 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°).

"The cross section for the Compton scattering is known as the Klein-Nishina formula,derived in 1929 by Oskar Klein and Yoshio Nishina. This was one of the first results obtained in quantum electrodynamics." Compton scattering as calculated with the Klein-Nishina formula, which provides an accurate prediction of the angular distribution of x-rays and gamma-rays that are incident upon a single electron. Before this formula was derived, the electron cross section had been classically derived by the British physicist and discoverer of the electron, J.J. Thomson. However, scattering experiments showed significant deviations from the results predicted by Thomson's model. The Klein-Nishina formula incorporates the Breit-Dirac recoil factor, R, also known as radiation pressure. The formula also corrects for relativistic quantum mechanics and takes into account the interaction of the spin and magnetic moment of the electron with electromagnetic radiation. Quantum mechanics is a system of mechanics based on quantum theory to provide a consistent explanation of both electromagnetic wave and atomic structure.

Thomson scattering , named for discoverer of the electron J J Thomson,is the classical elastic quantitative interpretation of the scattering process, 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.

Nuclear Compton scattering

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. ["Radiative Processes in Astrophysics" by George B. Rybicki and Alan P. Lightman]

Møller Scattering

Main article : Møller scattering, in which two electrons scatter off of one another

Møller Scattering Feynman Diagram

"Møller scattering is the name given to electron-electron scattering in Quantum Field Theory, named after the Danish physicist Christian Møller. The electron interaction that is idealized in Møller scattering forms the theoretical basis of many familiar phenomena such as the repulsion of electrons in the Helium nucleus. While formerly many particle colliders were designed specifically for electron-electron collisions, more recently electron-positron colliders have become more common. Nevertheless Møller scattering remains a paradigmatic process within the theory of particle interactions.

We can express this process in the usual notation, often used in particle physics:

$e^{-}e^{-}\longrightarrow e^{-}e^{-}$,

In quantum electrodynamics, there are two tree-level Feynman diagrams describing the process: a t-channel diagram in which the electrons exchange a photon and a similar u-channel diagram. Crossing symmetry, one of the tricks often used to evaluate Feynman diagrams, in this case implies that Møller scattering should have the same cross section as Bhabha scattering (electron-positron scattering).

In the electroweak theory the process is instead described by four tree-level diagrams: the two from QED and an identical pair in which a Z boson is exchanged instead of a photon. The weak force is purely left-handed, but the weak and electromagnetic forces mix into the particles we observe. The photon is symmetric by construction, but the Z boson prefers left-handed particles to right-handed particles. Thus the cross sections for left-handed electrons and right-handed differ. The difference was first noticed by the Russian physicist Yakov Zel'dovich in 1959, but at the time he believed the parity violating asymmetry (a few hundred parts per billion) was too small to be observed. This parity violating asymmetry can be measured by firing a polarized beam of electrons through an unpolarized electron target (liquid hydrogen, for instance), as was done by an experiment at the Stanford Linear Accelerator Center, SLAC-E158. The asymmetry in Møller scattering is

$A_{PV}=-mE{\frac {G_{F}}{{\sqrt {2}}\pi \alpha }}{\frac {16\sin ^{2}\Theta _{\textrm {cm}}}{\left(3+\cos ^{2}\Theta _{\textrm {cm}}\right)^{2}}}\left({\frac {1}{4}}-\sin ^{2}\theta _{W}\right)$,

where m is the electron mass, E the energy of the incoming electron (in the reference frame of the other electron), $G_{F}$ is Fermi's constant, $\alpha$ is the fine structure constant, $\Theta _{\textrm {cm}}$ is the scattering angle in the center of mass frame, and $\theta _{W}$ is the weak mixing angle, also known as the Weinberg angle."

Mott Scattering

Main article : Mott scattering, Inelastic Coulomb scattering involving separation of the two spin states of an electron beam by scattering an electron off the Coulomb field of heavy atoms

"Mott scattering, also referred to as spin-coupling inelastic Coulomb scattering, is the separation of the two spin states of an electron beam by scattering the beam off the Coulomb field of heavy atoms. It is mostly used to measure the spin polarization of an electron beam.

In lay terms, Mott Scattering is similar to Rutherford Scattering but electrons are used instead of Alpha particles as they do not interact via the strong force (only weak and electromagnetic). This enables them to penetrate the atomic nucleus, giving valuable insight into the nuclear structure.

The electrons are often fired at gold foil because of gold's high atomic number (Z), because it is non-reactive (does not form an oxide layer), and because thin gold films are easy to produce. (The film should be thin to reduce multiple scattering.) The presence of a spin-orbit term in the scattering potential introduces a spin dependence in the scattering cross section. Two detectors at exactly the same scattering angle to the left and right of the foil count the number of scattered electrons. The asymmetry, A, given by:

$A={\frac {I^{right}-I^{left}}{I^{right}+I^{left}}}$

is proportional to the degree of spin polarization P according to A = SP, where S is the Sherman function.

The Mott cross section formula is the mathematical description of the scattering of a high energy electron beam from an atomic nucleus-sized positively charged point in space. The Mott scattering is the theoretical diffraction pattern produced by such a mathematical model. It is used as the beginning point in calculations in electron scattering diffraction studies.

The equation for the Mott cross section includes an inelastic scattering term to take into account the recoil of the target proton or nucleus. It also can be corrected for relativistic effects of high energy electrons, and for their magnetic moment.

When an experimentally found diffraction pattern deviates from the mathematically derived Mott scattering, it gives clues as to the size and shape of an atomic nucleus. This is because the Mott cross section assumes only point-particle Coulombic and magnetic interactions between the incoming electrons and the target. When the target is a charged sphere rather than a point (as all real protons and nuclei are), additions to the Mott cross section equation (form factor terms) can be used to probe the distribution of the charge inside the sphere.

The Born approximation of the diffraction of a beam of electrons by atomic nuclei is an extension of Mott scattering."

Bhabha Scattering

Main article :: Bhabha scattering, in which an electron and a positron scatter

"In quantum electrodynamics, Bhabha scattering is the electron-positron scattering process:

$e^{+}e^{-}\rightarrow e^{+}e^{-}$

There are two leading-order Feynman diagrams contributing to this interaction: an annihilation process and a scattering process. Bhabha scattering is named after the Indian physicist Homi J. Bhabha.

The Bhabha scattering rate is used as a luminosity monitor in electron-positron colliders."

Bremsstrahlung Scattering

Main article : Bremsstrahlung, in which an electron (most commonly, but also any other particle) passes by a heavy charged object (like a nucleus), changes energy and direction, and emits a photon

"Bremsstrahlung (German pronunciation: [ˈbʁɛmsˌʃtʁaːlʊŋ] ^ⓘ, from [bremsen] Error: {{Lang}}: text has italic markup (help) "to brake" and [Strahlung] Error: {{Lang}}: text has italic markup (help) "radiation", i.e. "braking radiation" or "deceleration radiation") is electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typically an electron by an atomic nucleus. The moving particle loses kinetic energy, which is converted into a photon because energy is conserved. The term is also used to refer to the process of producing the radiation. Bremsstrahlung has a continuous spectrum, which becomes more intense and whose peak intensity shifts toward higher frequencies as the change of the energy of the accelerated particles increases.

Strictly speaking, braking radiation is any radiation due to the acceleration of a charged particle, which includes synchrotron radiation, cyclotron radiation, and the emission of electrons and positrons during beta decay. However, the term is frequently used in the more narrow sense of radiation from electrons (from whatever source) slowing in matter.

Bremsstrahlung emitted from plasma is sometimes referred to as free-free radiation. This refers to the fact that the radiation in this case is created by charged particles that are free both before and after the deflection (acceleration) that caused the emission."

Deep Inelastic Scattering

Main article : Deep inelastic scattering, in which a high-energy electron interacts with a nucleus and breaks it up

"Deep inelastic scattering is the name given to a process used to probe the insides of hadrons (particularly the baryons, such as protons and neutrons), using electrons, muons and neutrinos. It provided the first convincing evidence of the reality of quarks, which up until that point had been considered by many to be a purely mathematical phenomenon. It is a relatively new process, first attempted in the 1960s and 1970s. It is an extension of Rutherford scattering to much higher energies of the scattering particle and thus to much smaller resolution of the components of the nuclei.

To explain each part of the terminology, ‘scattering’ refers to the lepton (electron, muon, etc.) being deflected. Measuring the angles of deflection gives information about the nature of the process. ‘lnelastic’ means that the target absorbs some kinetic energy. In fact, at the very high energies of leptons used, the target is ‘shattered’ and emits many new particles. These particles are hadrons and, to oversimplify greatly, the process is interpreted as a constituent quark of the target being ‘knocked out’ of the target hadron and due to quark confinement the quarks are not actually observed but instead produce the observable particles by hadronization. The ‘deep’ refers to the high energy of the lepton, which gives it a very short wavelength and hence the ability to probe distances that are small compared with the size of the target hadron—so it can probe ‘deep inside’ the hadron. Also, note that in the perturbative approximation it is a high-energy photon emitted from the lepton and absorbed by the target hadron which transfers energy to one of its constituent quarks, as in the diagram to the right.

History

See also: Quark#History

The Standard Model of physics, in particular the work of Murray Gell-Mann in the 1960s, had been successful in uniting much of the previously disparate concepts in particle physics into one, relatively straightforward, scheme. In essence, there were three types of particles:

• The leptons, which were light (as in not particularly massive) particles such as electrons, neutrinos and their antiparticles. They have integer electric charge.
• The gauge bosons, which were particles that exchange forces. These ranged from the massless, easy-to-detect photon (the carrier of the electro-magnetic force) to the exotic (though still massless) gluons that carry the strong nuclear force.
• The quarks, which were massive particles that carried fractional electric charges. They are the "building blocks" of the hadrons. They are also the only particles to be affected by the strong interaction.

The leptons had been detected since 1897, when J. J. Thomson had shown that electric current is a flow of electrons. Some bosons were being routinely detected, although the W⁺, W^- and Z⁰ particles of the electroweak force were only categorically seen in the early 1980s, and gluons were only firmly pinned down at DESY in Hamburg at about the same time. Quarks, however, were still elusive.

Drawing on Rutherford's groundbreaking experiments in the early years of the twentieth century, ideas for detecting quarks were formulated. Rutherford had proven that atoms had a small, massive, charged nucleus at their centre by firing alpha particles at atoms in gold. Most had gone through with little or no deviation, but a few were deflected through large angles or came right back. This suggested that atoms had internal structure, and a lot of empty space.

In order to probe the interiors of baryons, a small, penetrating and easily produced particle needed to be used. Electrons were ideal for the role, as they are abundant and easily accelerated to high energies due to their electric charge. In 1968, at the Stanford Linear Accelerator Center (SLAC), electrons were fired at protons and neutrons in atomic nuclei. Later experiments were conducted with muons and neutrinos, but the same principles apply.

The collision absorbs some kinetic energy, and as such it is inelastic. This is a contrast to Rutherford scattering, which is elastic: no loss of kinetic energy. The electron emerges from the nucleus, and its trajectory and velocity can be detected.

Analysis of the results led to the following conclusions:

• The hadrons do have internal structure.
• In baryons, there are three points of deflection (i.e. baryons consist of three quarks).
• In mesons, there are two points of deflection (i.e. mesons consist of a quark and an anti-quark).
• Quarks appear to be point charges, as electrons appear to be, with the fractional charges suggested by the Standard Model.

The experiments were important because, not only did they confirm the physical reality of quarks but also proved again that the Standard Model was the correct avenue of research for particle physicists to pursue."

Synchrotron Radiation

Main article: Synchrotron radiation

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 ($\mathbf {a} \perp \mathbf {v}$) electromagnetic radiation when charged particles are accelerated is called synchrotron radiation. It is produced in synchrotrons using bending magnets, undulators and/or wigglers.

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. 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.

Classically, the radiated power P from an accelerated electron is:

$P={\frac {2Ke^{2}}{3c^{2}}}a^{2}$

where K is ..., e is ..., c is the speed of light, and a is the acceleration. 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:

$a_{non-relativistic}={\frac {v^{2}}{r}}\rightarrow a_{relativistic}={\frac {1}{m}}{\frac {dp}{d\tau }}={\frac {1}{m}}\gamma {\frac {d(\gamma mv)}{dt}}=\gamma ^{2}{\frac {dv}{dt}}=\gamma ^{2}{\frac {v^{2}}{r}}$

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. Radiated power then becomes:

$P={\frac {2Ke^{2}}{3c^{2}}}({\frac {\gamma ^{2}v^{2}}{r}})^{2}={\frac {2Ke^{2}}{3c^{2}}}{\frac {\gamma ^{4}v^{4}}{r^{2}}}$

For highly relativistic particles, such that velocity becomes nearly constant, the γ⁴ term becomes the dominate variable in determining loss rate. This means that the loss scales as the fourth power of the particle energy γmc²; and the inverse dependence of synchrotron radiation loss on radius argues for building the accelerator as large as possible.

Facilities and Projects

SLAC

See also: SLAC National Accelerator Laboratory

Aerial photo of the Stanford Linear Accelerator Center, with detector complex at the right (east) side

Stanford Linear Accelerator Center is located near Stanford university, California. Construction began on the 2 mile long linear accelerator in 1962 and 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. 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. 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. 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.

The SLAC aims to me a premier accelerator laboratory, 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. 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.

BaBar

[1]

SSRL - Stanford Synchrotron Radiation Lightsource

[2]

Other scientific programs run at SLAC include:

• Advanced Accelerator Research
• ATLAS/Large Hadron Collider
• Elementary Particle Theory
• EXO - Enriched Xenon Observatory
• FACET - Facility for Advanced Accelerator Experimental Tests
• Fermi Gamma-ray Space Telescope
• Geant4
• KIPAC - Kavli Institute for Particle Astrophysics and Cosmology
• LCLS - Linac Coherent Light Source
• LSST - Large Synoptic Survey Telescope
• NLCTA - Next Linear Collider Test Accelerator
• Stanford PULSE Institute
• SIMES - Stanford Institute for Materials and Energy Sciences
• SUNCAT Center for Interface Science and Catalysis
• Super CDMS - Super Cryogenic Dark Matter Search

DESY

See also: DESY

ZEUS

See also: ZEUS

HERA

See also: Hadron Elektron Ring Anlage

RIKEN RI Beam Factory

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.

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 Dr. Yoshio Nishina whose name is given to the facility.

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.

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.

SCRIT

See also: SCRIT

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.

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, 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, which has an adverse effect on the performance of electron storage rings.

The novel idea to be employed at SCRIT is to use the 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. "The ions of short-lived nuclei produced at an external ion source are transported to the electron storage ring, and are kept on the electron beam by the ion-trapping phenomena. Placing a longitudinal mirror potential along the electron beam line, one can form a three-dimensionally localized target on the electron beam. By controlling the voltage applied to the electrodes for the mirror potential, one can easily control ion injection and ejection, and thereby the ion-trapping period, which is essential for targeting short-lived nuclei." 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 ¹³³Cs 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.

"The facility consists of an electron accelerator with the SCRIT system, an Isotope Seperator On-Line (ISOL) system and an electron spectrometer system. The electron accelerator consists of a 150 MeV injector racetrack microtron and a 700 MeV electron storage ring. The stored electron beam energy is variable from 150 MeV to 700 MeV. The basic configuration of the electron ring is the same as that of the SR light source facility, HiSOR, of Hiroshima University. The pulsed 150-MeV electron beam with a peak current of 0.5 mA and a pulse width of 1μs is injected with a repetition rate of 2 Hz to fill the ring. The storage beam current is over 250 mA, with a beam lifetime of over 200 minutes. An ISOL system to produce neutron-rich nuclei via the photo-fission process of uranium is under construction. The long beam lifetime of the stored electron beam, a few hours, enables us to use the microtron as a driver for the ISOL. This ISOL system makes it possible to operate the facility completely independently of the other facilities of the RI Beam Factory."

To Discuss?

Parity Violation

See also: Parity violation

Electron Storage Ring

See also: Storage ring

Astronomy

Applications

T.E.M.

See also

• Anyon
• Electride
• Electron bubble

• Exoelectron emission
• g-factor
• Periodic systems of small molecules

• Spintronics
• Stern–Gerlach experiment
• Townsend discharge

• Zeeman effect
• Particle Physics
• Low-energy electron diffraction
• Quantum electrodynamics

External links

http://education.jlab.org/pol/electron-scattering.html (video)

http://www.youtube.com/watch?v=fI2C4VlR1OM (Compton video)

Seyfert Galaxy

A lower limit to the mass of the central black hole can be calculated using the Eddington luminosity. This limit arises because light exhibits radiation pressure. Assume a simplified model where a black hole is surrounded by a disc of luminous gas. Both the attractive gravitational force acting on electron-ion pairs in the disc and the repulsive force exerted by radiation pressure follow an inverse-square law. If the gravitational force exerted by the black hole is less than the repulsive force due to radiation pressure, the disc will be blown away by radiation pressure.