Mott scattering
Encyclopedia
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 particle
s as they have much lower mass (by about 4 orders of magnitude). 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:
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.
Rutherford scattering
In physics, Rutherford scattering is a phenomenon that was explained by Ernest Rutherford in 1911, and led to the development of the Rutherford model of the atom, and eventually to the Bohr model. It is now exploited by the materials analytical technique Rutherford backscattering...
, is the separation of the two spin states of an electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
beam by scattering
Scattering
Scattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of...
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
Rutherford scattering
In physics, Rutherford scattering is a phenomenon that was explained by Ernest Rutherford in 1911, and led to the development of the Rutherford model of the atom, and eventually to the Bohr model. It is now exploited by the materials analytical technique Rutherford backscattering...
but electrons are used instead of Alpha particle
Alpha particle
Alpha particles consist of two protons and two neutrons bound together into a particle identical to a helium nucleus, which is classically produced in the process of alpha decay, but may be produced also in other ways and given the same name...
s as they have much lower mass (by about 4 orders of magnitude). This enables them to penetrate the atomic nucleus
Atomic nucleus
The nucleus is the very dense region consisting of protons and neutrons at the center of an atom. It was discovered in 1911, as a result of Ernest Rutherford's interpretation of the famous 1909 Rutherford experiment performed by Hans Geiger and Ernest Marsden, under the direction of Rutherford. The...
, giving valuable insight into the nuclear structure.
The electrons are often fired at gold foil because of gold's high atomic number
Atomic number
In chemistry and physics, the atomic number is the number of protons found in the nucleus of an atom and therefore identical to the charge number of the nucleus. It is conventionally represented by the symbol Z. The atomic number uniquely identifies a chemical element...
(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:
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
Atomic form factor
In physics, the atomic form factor, or atomic scattering factor, is a measure of the scattering amplitude of a wave by an isolated atom. The atomic form factor depends on the type of scattering, which in turn depends on the nature of the incident radiation, typically X-ray, electron or neutron...
terms) can be used to probe the distribution of the charge inside the sphere.
The Born approximation
Born approximation
In scattering theory and, in particular in quantum mechanics, the Born approximation consists of taking the incident field in place of the total field as the driving field at each point in the scatterer. Born approximation is named after Max Born, winner of the 1954 Nobel Prize for physics.It is...
of the diffraction of a beam of electrons by atomic nuclei is an extension of Mott scattering.