Electron scattering

Not to be confused withElectron diffraction.

Types of 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/inelastically scattered electrons. SE is aSecondaryElectron ejected by the beam electron, emitting a characteristic photon (X-Ray) γ. BSE is aBack-ScatteredElectron, an electron which is scattered backwards instead of being transmitted through the sample.
Electron ( e− , β− )
Particle	Electron
Mass	9.10938291(40)×10−31kg 5.4857990946(22)×10−4u [1822.8884845(14)]−1u 0.510998928(11)MeV/c2
Electric Charge	−1e −1.602176565(35)×10−19C −4.80320451(10)×10−10esu
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 scatteringoccurs when electrons are displaced from their originaltrajectory.This is due to theelectrostatic forceswithin matter interaction or,if an external magnetic field is present, the electron may be deflected by theLorentz force.This scattering typically happens with solids such as metals, semiconductors and insulators;and is a limiting factor in integrated circuits and transistors.

Electron scattering has many applications ranging from the use of swift electron inelectron microscopesto very high energies forhadronicsystems, that allows the measurement of the distribution of charges for nucleons andnuclear structure.The scattering of electrons has allowed us to understand thatprotonsandneutronsare made up of the smaller elementary subatomic particles calledquarks.

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 many times over.

The likelihood of an electron scattering and the degree of the scattering is a probability function of the specimen thickness and 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 ofRichard Lamingwho 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 thatJ. J. Thomsonfirst discovered the electron in 1897, although other notable members in the development in charged particle theory areGeorge Johnstone Stoney(who coined the term "electron" ),Emil Wiechert(who was first to publish his independent discovery of the electron),Walter Kaufmann,Pieter ZeemanandHendrik Lorentz.

Compton scattering was first observed atWashington University in St. Louisin 1923 byArthur Comptonwho earned the 1927 Nobel Prize in Physics for the discovery; his graduate studentY. H. Woowho 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 byClinton DavissonandLester Germerusing what would come to be a prototype for modernLEEDsystem.The experiment was able to demonstrate the wave-like properties of electrons,thus confirming thede Broglie hypothesisthat matter particles have a wave-like nature.However, after this the interest in LEED diminished in favour ofhigh-energy electron diffraction

until the early 1960s when an interest in LEED was revived; of notable mention during this period isH. E. Farnsworthwho 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 was not until 1953 that a German patent for colliding beam apparatus was obtained byRolf Widerøe.

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 anelectronof velocityvmoving in a magnetic fieldB.Where the dotted circle indicates the magnetic field directedoutof the plane, and the crossed circle indicates the magnetic field directedintothe plane.

Main article:Lorentz force

The Lorentz force, named after Dutch physicistHendrik Lorentz,for a charged particleqis given (inSI units) by the equation:

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

whereqEdescribes theelectric forcedue to a present electric field,E,acting onq.
AndqvxBdescribes themagnetic forcedue to a present magnetic field,B,acting onqwhenqis moving with velocityv.
Which can also be written as:

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

where$\phi$is theelectric potential,andAis themagnetic vector potential.

It wasOliver Heavisidewho is attributed in 1885 and 1889 to first deriving the correct expression for the Lorentz force ofqvxB.Hendrik Lorentzderived 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 chargeqmassm,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 usingLorentz contractionwhereγis:

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

this equation of motion was first verified in 1897 inJ. 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 forceFbetween twopoint chargesqandQrelates to the distancerbetween 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 vectorF₁is the force experienced byq₁,and the vectorF₂is the force experienced byq₂.Whenq₁q₂> 0the forces are repulsive (as in the image) and whenq₁q₂< 0the forces are attractive (opposite to the image). The magnitude of the forces will always be equal. In this case:$\mathbf {F} =k{\frac {q_{1}q_{2}}{|\mathbf {r_{12}} |^{2}}}\mathbf {\hat {r_{12}}} ={\frac {q_{1}q_{2}}{4\pi \epsilon _{0}|\mathbf {r_{12}} |^{2}}}\mathbf {\hat {r_{12}}}$
where the vector,
${\boldsymbol {r_{12}}}={\boldsymbol {r_{1}-r_{2}}}$
is the vectorial distance between the charges and,${\boldsymbol {{\hat {r}}_{12}}}={{\boldsymbol {r_{12}}}/|{\boldsymbol {r_{12}}}|}$
(a unit vector pointing fromq₂toq₁).
The vector form of the equation above calculates the forceF₁applied onq₁byq₂.Ifr₂₁is used instead, then the effect onq₂can be found. It can be also calculated usingNewton's third law:F₂= -F₁.

Main article:Coulomb's law

Electrostatic Coulomb forcealso known asCoulomb interactionandelectrostatic force,named forCharles-Augustin de Coulombwho 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 electricforcebetween two pointchargesis 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:

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

whereq₁,q₂are two signed point charges;r-hatbeing the unit vector direction of the distancerbetween charges;kisCoulombs constantandε₀is 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 chargesq₁andq₂have 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 theprinciple of superposition of forceswhich states that if a third charge were introduced then the total force acting on that charge is thevector sumof 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 avacuum,if the space between point charges contains matter then the permittivity of the matter between the charges must be accounted for as follows:

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

whereε_ris therelative permittivityordielectric constantof the space the force acts through, and is dimensionless.

Collisions

If two particles interact with one another in a scattering process there are two 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.

Inelastic

See also:Inelastic scattering

Inelastic scattering is when the collisions donotconserve 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.Particlesmayalso split apart, further energy can be converted into breaking the chemical bonds between components.

Furthermore, momentum is conserved in both elastic and inelastic scattering.Other results than scattering are reactions, in which the structure of the interacting particles is changed producing two or more generally complex particles, and the creation of new particles that are not constituent elementary particles of the interacting particles.

Other types of scattering

Electron-molecule scattering

Electron scattering by isolated atoms and molecules occurs in the gas phase. It plays a key role in plasma physics and chemistry and it's important for such applications as semiconductor physics. Electron-molecule/atom scattering is normally treated by means of quantum mechanics. The leading approach to compute thecross sectionsis usingR-matrixmethod.

Compton scattering

Compton Scattering Feynman Diagram

Main article:Compton scattering

Compton scattering,so named forArthur Comptonwho first observed the effect in 1922 and which earned him the 1927 Nobel Prize in Physics;is theinelasticscattering of a high-energy photon by a free charged particle.

This was demonstrated in 1923 by firing radiation of a given wavelength (X-rays in the given case) through a foil (carbon target), which was scattered in a manner inconsistent with classical radiation theory.Compton published a paper in thePhysical Reviewexplaining 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 thePlanck relation:

$E=h\nu =hf$

which gives the energyEof the photon in terms of frequencyforν,and Planck's constanth(6.626×10⁻³⁴J⋅s=4.136×10⁻¹⁵eV.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 1920s when the particle (photon) nature of light suggested by thephotoelectric effectwas still being debated, the Compton experiment gave clear and independent evidence of particle-like behavior.

The formula describing theCompton shiftin the wavelength due to scattering is given by:

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

whereλ_fis the final wavelength of the photonafterscattering,λ_iis the initial wavelength of the photonbeforescattering,his Planck's constant,m_eis the rest mass of the electron,cis the speed of light andθis the scattering angle of the photon.

The coefficient of(1 - cos θ)is known as theCompton 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°).

Thomson scatteringis the classicalelasticquantitative interpretation of the scattering process,and this can be seen to happen with lower, mid-energy, photons. The classical theory of anelectromagnetic wavescattered by charged particles, cannot explain low intensity shifts in wavelength.

Inverse Compton scatteringtakes 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.

Møller scattering

Møller scattering Feynman diagram

Main article:Møller scattering

Mott scattering

Main article:Mott scattering

Bhabha scattering

Main article:Bhabha scattering

Bremsstrahlung scattering

Main article:Bremsstrahlung

Deep inelastic scattering

Main article:Deep inelastic scattering

Synchrotron emission

Main article:Synchrotron emission

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 assynchrotrons,electrons are bent in a circular path and emit X-rays typically. This radially emitted ($\mathbf {a} \perp \mathbf {v}$)electromagnetic radiationwhen charged particles are accelerated is calledsynchrotron radiation.It is produced in synchrotrons using bending magnets,undulatorsand/orwigglers.

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" afterJulian Schwinger.

Classically, the radiated powerPfrom an accelerated electron is:

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

this comes from theLarmor formula;whereKis an electric permittivity constant,eis electron charge,cis the speed of light, andais 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 relativistic, and can be obtained as follows:

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

wherevis the circular velocity,ris the radius of the circular accelerator,mis the rest mass of the charged particle,pis the momentum,τis theProper time(t/γ), andγis theLorentz 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 γ⁴term becomes the dominant variable in determining loss rate, which 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

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 Centeris located nearStanford University,California.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.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 be 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

See also:BaBar experiment

SSRL - Stanford Synchrotron Radiation Lightsource

See also:Stanford Synchrotron Radiation Lightsource

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

RIKEN RI Beam Factory

See also:Radioactive Isotope Beam Factory

RIKENwas 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.

TheRIKEN 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, fromDr. Yoshio Nishinawhose 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

TheSCRIT (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 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 tousethe 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 of¹³³Cs 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.

See also

• Zeeman effect
• Particle physics
• Low-energy electron diffraction
• Quantum electrodynamics
• R-matrix

External links

• Physics Out Loud: Electron Scattering(video)
• Brightstorm: Compton Scattering(video)