User:Macumba/Sandbox/Mott scattering

Mott scattering is a phenomenon in

Neville Mott who first described it in 1929^{[citation needed]}. It is similar to elastic Rutherford scattering

but additionally shows spin-coupling effects.

Experiment

Mott scattering occurs, when point-like spin-1/2 particles (

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^[citation needed].

Theory

Mott differential cross section

The Mott cross section corresponds to 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 ^[1]. The Born approximation of the diffraction of a beam of electrons by atomic nuclei is an extension of Mott scattering ^[2].

References

Mott, N. F. “The scattering of fast electrons by atomic nuclei”. 1929. Proc. R. Soc. Lond. A

124: 425-442. http://rspa.royalsocietypublishing.org/content/124/794/425.full.pdf+html?ijkey=dbd72838cad1c11e3457f4e0652eff734028babe&keytype2=tf_ipsecsha

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 [1]

^ ME Rose 1948 The Charge Distribution in Nuclei and the Scattering of High Energy Electrons Physical Review 73 #4 p279-84)
^ NF Mott and HSW Massey 1965 The Theory of Atomic Collisions, Third Edition (Oxford: Oxford University Press)

[[Category:Scattering]] [[Category:Foundational quantum physics]]

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[1] ME Rose 1948 The Charge Distribution in Nuclei and the Scattering of High Energy Electrons Physical Review 73 #4 p279-84)

[2] NF Mott and HSW Massey 1965 The Theory of Atomic Collisions, Third Edition (Oxford: Oxford University Press)

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