Single-Particle Electrodynamics - Assassination Science

detail, for arbitrary values of g, by starting with a review of the elementary
second-quantisation of the electromagnetic field. The spin-flip synchrotron
radiation expressions are obtained, as are the spin-flip rates themselves; the
results are in accord with those of Derbenev and Kondratenko. We shall not
go into the details here, but merely refer the interested reader to the review
article [114].
6.10.5 Classical analysis
Clearly, if one wishes to change the direction of the spin of a particle—
classically—then one must do so through the torque equation of motion. An
examination of the result (6.130) of Section 6.8.9 reveals that there are not,
in fact, any terms in N self dependent on both q and µ, apart from the spin
renormalisation term; but there are terms involving µ 2 . The finite terms are,
in the instantaneous rest frame, given by
N self = 1 3
µ 2
4π σ×{ 2 ... σ − σ×( ˙vרv) } . (6.146)
Let us first concentrate on the Ternov–Bagrov–Khapaev effect. In the rest
frame of the neutron, its acceleration and jerk are completely negligible (they
would be exactly zero, but for the forces of Chapter 4, and those of radiation
reaction itself), and hence we may ignore the second term in (6.146). We are
therefore left with
N RR = 2 3 4π σ×... σ. (6.147)
Now, from the Thomas–Bargmann–Michel–Telegdi spin precession equation,
we have, in the rest frame
hence, we successively find
µ 2
N TBMT = µ×B;
˙σ = µB s σ× ˆB, (6.148)
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