Neutron Scattering - JUWEL - Forschungszentrum Jülich

RESEDA 7
In this expression, a normalization is applied to account for possible changes of the
neutron polarization by the scattering process itself. Equation (10) shows that the NSE
signal PNSE is proportional to the cosine fourier transformation of the scattering function
S(q,ω). In order to obtain full information about S(q,ω), PNSE has to be measured at
several values of τ. In general, quasi-elastic processes lead to a decrease of polarization.
We note here that, in practice, the determination of the polarization in the spin echo
point is accomplished by slight variation of the field integrals B1 and B2 and fitting of an
appropriate theoretical expression to the measured values.
2.3 Example
Imagine moving particles inside a liquid sample. Each scattered neutron loses or gains
energy through the interaction with such a particle. This will result in different
velocities for the incoming and outgoing neutrons. The strength of the NSE technique is
to detect small energy changes of individual neutrons. To illustrate this fact, imagine a
velocity distribution symmetric around the mean velocity v1, with only two kinds of
neutrons namely one sort with speed v1 −Δv and a second sort with speed v1 + Δv with
Δv < v1 representing an arbitrary momentum transfer. If we now have a sample inside of
which the first sort is scattered with the probability of 100 % into the other sort and vice
versa, the measured polarization at the end of the spectrometer will differ from 1, since
only the wrong number of precessions for each neutron takes place. The first sort is too
fast and the second one too slow to precess back to the initial position.
Our assumption will be that S(q,ω) corresponds to a Lorentzian line
S(q,ω ) =
Γ
Γ 2 + ω 2
which then, using equation (10), gives for the measured polarization signal an
exponential decay :
(11)
P NSE = cosϕ = e −Γτ ≡ e −τ /τ 0 (12)
From the τ dependence of PNSE(τ) it is possible to determine the linewidth parameter Γ
of the scattering process and its lifetime τ 0 =Γ −1 .
3 Neutron Resonance Spin Echo
3.1 NRSE coils
In the Neutron Resonance Spin Echo (NRSE) method each precession coil of NSE is
replaced by a setup of two so-called neutron resonance spin flipper coils (NRSE coils)
and the field free space in between. Each of the two NRSE coils is actually housing two
different coils. The outer coil (“B0 coil“) creates a static magnetic field Bz in z-direction.
The second coil inserted in the B0 coil creates a rotating magnetic field Brf and is called