Neutron Scattering - JUWEL - Forschungszentrum Jülich

4 W. Häußler
Figure 1: Basic principle of a NSE instrument (P: polariser, B1,2: static, homogeneous magnetic fields, A:
analyzer). The arrows indicate the neutron spins, which precess with the Larmor frequency. The region
around the sample is located in a zero magnetic field region.
figure 1 the magnetic field points in z-direction, whereas the neutron spin points in xdirection).
Then, the neutron spin precesses inside the magnetic field with the Larmor
frequency ωLar = γB, where γ = 2.916 kHz/Gauss is the neutron’s gyromagnetic ratio.
The total precession phase of the neutron after passing through B1 is proportional to the
time t the neutron spends in the magnetic field. t only depends on the neutron’s velocity
v and the length of the magnetic field L1. The phase of the neutron spin φ1(v) after the
first magnetic field can be written as:
ϕ 1 (v) = ω Lar t = γ L 1 B 1
v
. (2)
Figure 2: Polarization Px after the first magnetic field as a function of the length of the magnetic field L1. The
positions 1 to 4 (1ʼ to 4ʼ) correspond to the positions 1 to 4 (1ʼ to 4ʼ) in figure 1.
The polarization is analyzed in x-direction. It is calculated from the average over all
neutrons as follows:
Px = cosϕ = ∫ dvf
(v)cos γ L1B ⎛ 1 ⎞
⎝
⎜
v ⎠
⎟
(3)
with a distribution of neutron velocities f(v). Due to different neutron velocities, the
envelope of the polarization decreases, if φ increases (figure 2). The shape of the
measured polarization Px is called „spin rotation group“. As equation (10) shows, φ can
be varied either by scanning through B1 or by varying L1. In figure 2, Px is shown at