Single-Particle Electrodynamics - Assassination Science

P TBK , is, in fact, given by
P TBK = 100% (6.137)
(antiparallel to the field in the case of a neutron), and the characteristic
polarisation time is given, for motion transverse to the field, by
{ 64 |µ| 5 B 3 γ 2 } −1
τ TBK =
3 4π¯h 4 , (6.138)
where µ is the magnitude of the magnetic dipole moment, which is positive
(negative) if µ is parallel (antiparallel) to σ.
6.10.3 Lyuboshitz’s simple derivation
Shortly after the work of Ternov, Bagrov and Khapaev was published, Lyuboshitz
[141] noted that the results (6.137) and (6.138) did not require a long
a cumbersome derivation at all, but rather could be obtained on extremely
elementary grounds. His argument was as follows: In a magnetic field, the
neutron has an interaction energy, in its rest frame, of
−µ·B.
The probability per unit time of a spontaneous M1 transition from the upper
to the lower energy state is
w = 1
4π
4
3¯h ω3 ↑↓
∣
∣〈↓|µ|↑〉 ∣ 2
∣, (6.139)
where the states |↑〉 and |↓〉 are parallel and antiparallel to the magnetic
field respectively (if µ < 0 is negative, as is usually the case; these states are
reversed if µ > 0), and where
Using (6.140) in (6.139), Lyuboshitz thus found
¯hω ↑↓ ≡ ∆E ↑↓ = |2µB| . (6.140)
P t (t) = − ( 1 − e −t/τ rest)
, (6.141)
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