Electron scattering
Electron scattering occurs when electrons are displaced from their original trajectory. This is due to the electrostatic forces within matter 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.
Electron scattering has many applications ranging from the use of swift electron in electron microscopes to very high energies 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 many details about the atomic structure, from the ordering of atoms to that protons and neutrons are made up of the smaller elementary subatomic particles called quarks.
Electrons may be scattered through a solid in several ways:
- Not at all: no electron scattering occurs and the beam passes straight through.
- Single scattering: when an electron is scattered just once.
- Plural scattering: when electron scatter several times.
- Multiple scattering: when electron scatter many times over.
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 on 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. Thomson first discovered the electron in 1897, although other notable members in the development in charged particle theory are George Johnstone Stoney, Emil Wiechert, Walter Kaufmann, Pieter Zeeman and Hendrik Lorentz.
Compton scattering was first observed at Washington University in St. Louis in 1923 by Arthur 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 beams for collisions history begins in 1956 when Gerard K. O'Neill of Princeton University became interested in high energy collisions, and introduced the idea of accelerator injecting into storage ring. While the idea of beam-beam collisions had been around since approximately the 1920s, it was not until 1953 that a German patent for a colliding beam apparatus was obtained by Rolf Widerøe.
Phenomena
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
The Lorentz force, named after Dutch physicist Hendrik Lorentz, for a charged particle q is given by the equation:where qE describes the electric force due to a present electric field, E, acting on q.
And qv × B describes the magnetic force due to a present magnetic field, B, acting on q when q is moving with velocity v.
This can also be written as:
where is the electric potential, and A is the magnetic vector potential.
It was Oliver Heaviside who is considered to be the first in 1885 and 1889 to derive the correct expression for the Lorentz force of qv × 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:
or
in the relativistic case including the Lorentz contraction where γ is:
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, the electromotive force in a wire loop moving through a magnetic field, and the force on a particle which might be traveling near the speed of light.
Electrostatic Coulomb force
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.Coulomb's law states that:
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, and is given by:
or in vector notation:
where q1, q2 are two point charges; being the unit vector direction of the distance r between charges and ε0 is the permittivity of free space, given in SI units by:
The directions of the forces exerted by the two charges on one another are always along the straight line joining them, and are vector forces of infinite range, and they obey Newton's third law, being of equal magnitude and opposite direction. When both charges q1 and q2 have the same sign 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. 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:
where εr is the relative permittivity of 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
Elastic scattering is when the collisions between target and incident particles have total conservation of kinetic energy. This implies that there is no fragmentation of the particles or energy loss, that is to say that the internal states of each of the particles remains unchanged. Due to the fact that there is no fragmentation elastic collisions can as a first approximation be modeled as occurring between point-like particles, a principle that is very useful for an elementary particle such as the electron.Inelastic
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 heat, waves, or vibrations between constituent particles of either collision party or other excitations such as light. Particles may also split apart, and energy can be converted into breaking the chemical bonds between components.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 the cross sections is using R-matrix method.Compton scattering
Compton scattering, so named for Arthur 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.This was demonstrated in 1923 by firing radiation of a given wavelength through a foil, which was scattered in a manner inconsistent with classical radiation theory. Compton 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:
which gives the energy E of the photon in terms of frequency f or ν, and the Planck constant h.
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 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:
where λf is the final wavelength of the photon after scattering, λi is the initial wavelength of the photon before scattering, h is the Planck constant, me is the rest mass of the electron, c is the speed of light and θ is the scattering angle of the photon.
The coefficient of 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 and twice the Compton wavelength.
Thomson scattering 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.
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 bounces off a high energy electron. Such electrons are produced in supernovae and active galactic nuclei.