Single-Particle Electrodynamics - Assassination Science

where the characteristic polarisation time, in the rest frame of the neutron,
is
{ 64
τ rest =
3
|µ| 5 B 3
4π¯h 4 } −1
, (6.142)
To boost this result to the case of arbitrary velocity, one simply needs to recall
that time-derivatives (and hence probability rates) are reduced by a factor of
γ, and the transverse magnetic field is increased by a factor of γ; substituting
these results into (6.142) thus yields an overall factor of γ 3 /γ = γ 2 , and hence
the Ternov–Bagrov–Khapaev result (6.138) is reproduced exactly.
Lyuboshitz further noted that, if one wished to apply his argument to
the case of charged particles with magnetic dipole moments, then one faces
the difficulty that the appropriate “rest frame” is, in fact, accelerated, and is
hence not a Lorentz frame. Clearly, a more general method of attack would
be required.
However, if one ignored this complication, to see, as a rough guide, what
the Ternov–Bagrov–Khapaev results would look like if naïvely applied to an
electron, then one may simply replace µ and B by means of the relations
one then obtains
|µ| = ge¯h
4m ,
For the pure Dirac electron, of g = 2, one finds
|B| = mγ
eR ; (6.143)
{ 2 g
5
e 2¯hγ τ ∼
5 } −1
∣ ∣ . (6.144)
3 2 4πm 2 R 3
{ 2
τ electron ∼
3
e 2¯hγ5
} −1
. (6.145)
4πm 2 R 3
The rough result (6.145) gives the same dependence on all physical quantities
as the Sokolov–Ternov result (6.134); the only difference is that the numerical
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