User:Macumba/Sandbox/Mott scattering

User:Macumba/Sandbox/Mott scattering

Mott scattering is a phenomenon in particle physics and nuclear physics. It is named after Neville Mott who first described it in 1929. It is similar to elastic Rutherford scattering but additionally shows spin-coupling effects.

Experiment
Mott scattering occurs, when point-like spin-1/2 particles (fermions) are scattered by heavy atomic nuclei with total spin zero. A typical example is the scattering of electrons on gold nuclei. The electrons are fired at gold foil because of gold's high atomic number (Z), because it does not form an oxide layer, and because thin gold films are easy to produce. The film should be thin to reduce multiple scattering.

It is mostly used to measure the spin polarization of an electron beam.

Mott differential cross section
The Mott cross section corresponds to the Rutherford scattering with an additional term accounting for the spin coupling. Because one of the particles has a non-zero spin


 * $$\left( \frac{d \sigma}{d \Omega} \right)_{\text{Mott}} = \left(\frac{\alpha \hbar c}{2mv_0^2} \right)^2 \frac{1}{\sin^4 (\frac{\theta}{2})} \times \left(1- \beta^2 sin^2 \left(\frac{\theta}{2}\right) \right) $$

The presence of a spin-orbit term in the scattering potential introduces a spin dependence in the scattering cross section.

Scattering asymmetry
Two detectors at exactly the same scattering angle to the left and right of the foil count different numbers of scattered electrons. The asymmetry, A, given by

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

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