Single-Particle Electrodynamics - Assassination Science

Now, in this first attack on the problem, we shall simply ignore the contribution
of Thomas precession terms, due to the radiation reaction force equation;
from Jackson’s discussion [114], we expect that this decoupling of the
orbital degrees of freedom will lead to approximate, not exact, results. The
calculation of Ω RR from (6.158), using the electron’s Thomas–Bargmann–
Michel–Telegdi motion as the zeroth approximation, is rather lengthy, and
has been relegated to the computer program kinemats, in Section G.4.12;
after some manipulation of the results, one finds that the evolution of the
transverse polarisation P t (t) is functionally identical to (6.154), with the
classical characteristic polarisation time now given by
⎧
⎨
2
g
3 ( ⎫
∣ ∣∣∣ g
2
τ cl. =
⎩ ∣ ∣ ∣ +v
2) e2¯hγ 5 v 3 −1 ⎬
. (6.159)
3 2 2 4πm 2 R 3 ⎭
If we take the limit of large |g|, use expressions (6.143) to convert the circular
orbit back into a linear one, and trivially boost back to the rest frame, we are
returned to the result (6.155) for the classical stationary neutron, as would
be expected [114].
We now compare these completely classical results to those of the previous
sections. Firstly, we note that for spin-half particles,
s = 1 2¯h,
the characteristic time, τ cl. , of (6.155) becomes
τ cl. | s=
1
2 ¯h = { 32
3
µ 5 B 3 } −1
4π¯h 4 .
This is exactly half of the Ternov–Bagrov–Khapaev result (6.142). It may
be thought that the missing factor of 2 could simply be due to an algebraic
oversight on the part of the author; it will shortly be clear that this is not
the case. Moreover, this factor of 2 is, in fact, the least of our concerns: more
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