# 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:${\ displaystyle E ^ {2} = (pc) ^ {2} + (mc ^ {2}) ^ {2}}$
• 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.