Single-Particle Electrodynamics - Assassination Science

coëfficient is 2/3, not 5 √ 3/8. As to the asymptotic polarisation, the rough
analysis would probably hazard a guess of simply the neutron result (6.137),
namely, 100%; this is close to, but not quite the Sokolov–Ternov result of
∼ 92.4%.
Considering the approximations made, this rather heuristic explanation
stacks up quite well.
6.10.4 Jackson’s comments
In his review article, Jackson [114] describes the Lyuboshitz elementary description
of the Ternov–Bagrov–Khapaev effect, and examines in detail why
it cannot be pushed too far for charged particles.
Firstly, it is noted by Jackson that, for g = 2, the Thomas–Bargmann–
Michel–Telegdi precession frequency and the orbital revolution frequency are
equal; but if g is widely different from 2, then in ultra-relativistic motion
the precession frequency is much higher than the orbital frequency. Making
the quantum-mechanical connection between frequencies and energies, one
can then already see that the characteristic energy of the orbital motion is
negligible compared to that of the magnetic field interaction energy for large
g, but is of the same magnitude when g ∼ 2. Since a naïve application of the
Lyuboshitz result essentially considers the magnetic energy levels as isolated,
we should expect it to fail when g ∼ 2.
Secondly, it is noted by Jackson that the Derbenev–Kondratenko [67]
results for the Sokolov–Ternov effect for arbitrary g show a very sensitive
dependence on the value of g—indeed, the direction of polarisation is reversed
for 0 < g < 1.2. A naïve application of the Lyuboshitz result (6.144), on
the other hand, yields simply a |g| 5 dependence. But Jackson notes that,
for large |g|, the Derbenev–Kondratenko results do indeed approach the |g| 5
dependence of (6.144).
The remainder of Jackson’s paper considers the Sokolov–Ternov effect in
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