Développement et optimisation d'un système de polarisation de ...

tel-00726870, version 1 - 31 Aug 2012
34 1.2. Ultracold neutrons
Using the fact that W ≪ V (Table 1.2), the probability of reflection R is:
R = 1 − 2 W
V
E⊥
V − E⊥
= 1 − µ(E⊥) (1.19)
where µ(E⊥) is the wall loss probability per bounce. This probability increases if the incident
energy is close to V .
Weak interaction
The β − decay of the free neutron is governed by the weak interaction via the reaction:
n → p + e − + νe
(1.20)
In that case, a d quark is changed in a u quark with a W − boson emission. It is shown in
Fig. 1.7.
u u
d
d
d
u
W −
Figure 1.7: Feynman diagram of the neutron beta decay. A down quark turns to a up quark with an
emission of a W − boson, which disintegrates into an electron plus an antineutrino.
Electromagnetic interaction
Interaction with a magnetic field
Due to its magnetic moment µn = −9.6623641(23) · 10 −27 J/T [46], the neutron interacts with
magnetic fields. The magnetic potential energy is defined as:
In term of Pauli matrices σ, the potential energy can be rewritten:
e −
¯νe
Vm = −µn · B (1.21)
¯h
Vm = −γn
2 σ · B (1.22)
where γn = 2µn/¯h is the gyromagnetic ratio of the neutron. There is a direct coupling between
the magnetic field and the spin of the neutron. Indeed, the magnetic field exerts a torque on
the spin:
Γ = γn S × B (1.23)
This torque leads to the evolution of the spin with time: