Definitions

Mott scattering

Mott scattering, also referred to as spin-coupling in elastic 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 are much (around 4 orders of magnitude) smaller. 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:

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

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

Mott scattering is the mathematical description of the scattering of an electron beam from an atomic nucleus-sized positively charged sphere 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. 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 (see: ME Rose 1948 The Charge Distribution in Nuclei and the Scattering of High Energy Electrons Physical Review 73 #4 p279-84). The Born approximation of the diffraction of a beam of electrons by atomic nuclei is an extension of Mott scattering. (see: NF Mott and HSW Massey 1965 The Theory of Atomic Collisions, Third Edition (Oxford: Oxford University Press).

References

• J. Stohr & H.C. Siegmann, Magnetism – From Fundamentals to Nanoscale Dynamics (Springer, 2006)
• T.J. Gay & F.B. Dunning, Rev. Sci. Instrum. 63, 1635-1651 (1992)
• Hyperphysics

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