The self-polarization occurs through the emission of spin-flip synchrotron radiation.
The effect was predicted by Igor Ternov and the prediction rigorously justified by Arseny Sokolov using exact solutions to the Dirac equation.
The polarization arises due to the fact that the rate of transition through emission of synchrotron radiation to the "spin down" state is slightly greater than the probability of transition to the "spin up" state.
As a result, an initially unpolarized beam of high-energy electrons circulating in a storage ring after sufficiently long time will have spins oriented in the direction opposite to the magnetic field.
is less than one due to the existence of spin–orbital energy exchange, which allows transitions to the "spin up" state (with probability 25.25 times less than to the "spin down" state).
Typical relaxation time is on the order of minutes and hours.
Thus producing a highly polarized beam requires a long enough time and the use of storage rings.
The self-polarization effect for positrons is similar, with the only difference that positrons will tend to have spins oriented in the direction parallel to the direction of the magnetic field.
[4] The Sokolov–Ternov effect was experimentally observed in the USSR, France, Germany, United States, Japan, and Switzerland in storage rings with electrons of energy 1–50 GeV.
[3][5] The effect of radiative polarization provides a unique capability for creating polarized beams of high-energy electrons and positrons that can be used for various experiments.
The equilibrium polarization given by the Sokolov and Ternov has corrections when the orbit is not perfectly planar.