Single-Particle Electrodynamics - Assassination Science

to the precession and orbital periods, but nevertheless within the domain of
experimental practicality.
The analysis of the Sokolov–Ternov effect was further generalised to the
case of arbitrary magnetic field configurations by Baier and Katkov [17]; they
found that the spin-flip transition probability per unit time for relativistic
electrons or positrons is given, in the general case, by
w = 5√ 3 e 2¯h {
16 m 2 γ5 | ˙v| 3 1 − 2 9 (σ·ˆv)2 + 8√ }
3
15 σ·ˆv׈˙v , (6.135)
where ˆv and ˆ˙v are unit vectors in the direction of v and ˙v respectively. For a
circular orbit in a uniform magnetic field, the Baier–Katkov equation (6.135)
reduces to the Sokolov–Ternov results (6.132), (6.133) and (6.134).
As an extension of this work, Baier, Katkov and Strakhovenko [18] derived
a general equation of motion for the polarisation vector, incorporating the
Thomas–Bargmann–Michel–Telegdi and Baier–Katkov equations:
˙σ = σ×Ω TBMT − 1 {
σ − 2 τ ST 9 (σ·ˆv)ˆv + 8 }
5 √ 3 ˆv׈˙v , (6.136)
where Ω TBMT is the Thomas–Bargmann–Michel–Telegdi spin precession frequency
vector.
In making any connection with classical physics, we should of course use
the Baier–Katkov–Strakhovenko equation, (6.136), as the general expression
encompassing the Sokolov–Ternov effect, for electrons and positrons in arbitrary
relativistic motion. However, for the purposes of this simplified analysis,
we shall consider only the simplified Sokolov–Ternov configuration.
We shall also refrain, here, from discussing the many exciting advances
being made in polarised beam physics in high energy storage rings, but will
instead refer the interested reader to some entry points in the literature:
[155, 21, 22, 23, 15, 123].
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