Mott scatter

The Mott scattering (according to Nevill F. Mott ) is the elastic scattering of a spin- 1/2 particle ( fermion ) that is considered point-like , e.g. B. an electron , on a static, point-like charge without spin. It is used in nuclear and particle physics to examine the structures of nucleons ( protons and neutrons ) or their components, the quarks .

This scattering mechanism is similar to Rutherford scattering , in which a spinless particle is scattered on a charge. However, the magnetic moment associated with the spin results in an additional spin-orbit interaction .

The elastic scattering of two point-like particles that both have a spin is called Dirac scattering .

The differential cross section of the Mott scattering, the Mott cross section , is:

${\displaystyle \left({\frac {\mathrm {d} \sigma }{\mathrm {d} \Omega }}\right)_{\textrm {Mott}}=\left({\frac {2ZZ'e^{2}}{4\pi \varepsilon _{0}}}\right)^{2}\cdot {\frac {E^{2}}{(qc)^{4}}}\cdot \left[1-\left({\frac {v}{c}}\right)^{2}\cdot \sin ^{2}\left({\frac {\theta }{2}}\right)\right]}$

With

• ${\displaystyle Z,Z'}$: Ordinal numbers or charges (as multiples of the elementary charge) of the two particles involved
• e : elementary charge
• ${\displaystyle \varepsilon _{0}}$: electric field constant
• E : relativistic total energy of the fermion after the scattering: ${\displaystyle E^{2}=(pc)^{2}+(mc^{2})^{2}}$
  • p : momentum
  • c : speed of light
  • m : mass of the fermion
• q : momentum transfer: ${\displaystyle q=2\gamma mv\sin \left({\frac {\theta }{2}}\right)}$
  • Lorentz factor ${\displaystyle \gamma ={\frac {1}{\sqrt {1-\left({\frac {v}{c}}\right)^{2}}}}}$
  • v : speed
  • ${\displaystyle \theta }$: Scattering angle .

The dependence on the scattering angle can be understood in such a way that the backward scattering ( ) is suppressed. This would correspond to a spin flip ; this is not possible with a spinless target particle . ${\displaystyle \theta }$ ${\displaystyle \theta =\pi }$

In the non-relativistic borderline case (i.e. neglecting the spin ), the Mott scattering cross section merges into the Rutherford scattering cross section. ${\displaystyle \beta ={\frac {v}{c}}\ll 1}$

The Mott scattering forms the basis for the Mott detector , with which the direction of the spin of electrons can be determined.

See also

• Form factor