Mott scattering

Template:More citations needed In physics, Mott scattering is elastic electron scattering from nuclei. It is a form of Coulomb scattering that requires treatment of spin-coupling. It is named after Nevill Francis Mott, who first developed the theory in 1929.

Mott scattering is similar to Rutherford scattering but electrons are used instead of alpha particles as they do not interact via the strong interaction (only through weak interaction and electromagnetism), which enable electrons to penetrate the atomic nucleus, giving valuable insight into the nuclear structure.

History

Mott scattering derives from a 1929 paper by Nevill Mott which proposed a mechanism for experimentally verifying free electron spin quantization. Samuel Goudsmit and George Eugene Uhlenbeck had proposed electron spin and spin-orbit coupling to explain line splitting in atomic spectra in 1925 and by 1928 Paul Dirac had a relativistic quantum theory incorporating these ideas. As Mott details in the first part of his paper, direct obsevation of free electron spin was thought to be impossible due to issues with the uncertainty principle. Mott proposed double scattering of a high energy beam of electrons from atomic nuclei. The first backscattering event would polarize the beam transverse to the scattering plane; the second scattering event above or below the plane would then have measurable intensity differences to the left or right in a amounts according to the degree of polarization.Template:Rp The predicted effect was finally observed experimentally 1942.

During the 1950s, Noah Sherman analyzed detailed relativistic electron scattering calculations of the intensity asymmetry in terms of a function later called the Sherman function. This concept became the basis for Mott electron polarimetry. The first successful measurement of the electron g factor in 1954, used this technique.

Description

The electrons are often fired at gold foil because gold has a high atomic number (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:

$A=\frac{I^{\mathrm{r}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}}-I^{\mathrm{l}\mathrm{e}\mathrm{f}\mathrm{t}}}{I^{\mathrm{r}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}}+I^{\mathrm{l}\mathrm{e}\mathrm{f}\mathrm{t}}}$

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

References

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