Mott scattering in physics, also referred to as spin-coupling inelastic

Coulomb scattering In particle physics, Rutherford scattering is the elastic scattering of charged particles by the Coulomb interaction. It is a physical phenomenon explained by Ernest Rutherford in 1911 that led to the development of the planetary Rutherford model ...

, is the separation of the two spin states of an

electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have n ...

beam by

scattering Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including ...

the beam off the Coulomb field of heavy atoms. It is named after

Nevill Francis Mott Sir Nevill Francis Mott (30 September 1905 – 8 August 1996) was a British physicist who won the Nobel Prize for Physics in 1977 for his work on the electronic structure of magnetic and disordered systems, especially amorphous semiconductor ...

, who first developed the theory. It is mostly used to measure the spin polarization of an electron beam. In lay terms, Mott scattering is similar to

Rutherford scattering In particle physics, Rutherford scattering is the elastic scattering of charged particles by the Coulomb interaction. It is a physical phenomenon explained by Ernest Rutherford in 1911 that led to the development of the planetary Rutherford model ...

but

electrons The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have n ...

are used instead of

alpha particle Alpha particles, also called alpha rays or alpha radiation, consist of two protons and two neutrons bound together into a particle identical to a helium-4 nucleus. They are generally produced in the process of alpha decay, but may also be prod ...

s as they do not interact via the strong force (only weak and electromagnetic). This enables them to penetrate the

atomic nucleus The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger–Marsden gold foil experiment. After the discovery of the neutron ...

, giving valuable insight into the nuclear structure. The electrons are often fired at gold foil because gold has a high

atomic number The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of an atomic nucleus. For ordinary nuclei, this is equal to the proton number (''n''p) or the number of protons found in the nucleus of ever ...

(Z), is non-reactive (does not form an oxide layer), and can be easily made into a thin film (reducing 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

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

Sherman function The Sherman function describes the dependence of electron-atom scattering events on the spin of the scattered electrons. It was first evaluated theoretically by the physicist Noah Sherman and it allows the measurement of polarization of an elec ...

. 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, 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 Generally 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. The Born approximation is named a ...

of the diffraction of a beam of electrons by atomic nuclei is an extension of Mott scattering.

References

* * {{DEFAULTSORT:Mott Scattering Electron beam Foundational quantum physics Scattering