text: When an electron beam is polarized, an unbalance between spin-up, , and spin-down electrons, , exists. The unbalance can be evaluated through the polarization   defined as
  It is known that, when an electron collides against a nucleus, the scattering event is governed by Coulomb interaction. This is the leading term in the Hamiltonian, but a correction due to spin-orbit coupling can be taken into account and the effect on the Hamiltonian can be evaluated with the perturbation theory. Spin orbit interaction can be evaluated, in the rest reference frame of the electron, as the result of the interaction of the spin magnetic moment of the electron
  with the magnetic field that the electron sees, due to its orbital motion around the nucleus, whose expression in the non-relativistic limit is:
  In these expressions  is the spin angular-momentum,  is the Bohr magneton,  is the g-factor,  is the reduced Planck constant,  is the electron mass,  is the elementary charge,  is the speed of light,  is the potential energy of the electron and  is the angular momentum.
  Due to spin orbit coupling, a new term will appear in the Hamiltonian, whose expression is
  Due to this effect, electrons will be scattered with different probabilities at different angles. Since the spin-orbit coupling is enhanced when the involved nuclei possess a high atomic number Z, the target is usually made of heavy metals, such as mercury, gold and thorium.