Neutron Scattering

affecting application are caused by the fact that the "spin-stop watch" can only be read
up to an unknown integer number of complete precession turns .
The reading is performed
by the cosine type transmission function of an analyzer and yields only ensemble averages
and not individual rotation angles .
The intensity at the detector is modulated accordingly.
In addition inelastic scattering does not produce only one defined velocity change but Av
is distributed according to S(Q, w ~~ kAv) . The detector signal is then proportional to
the integral of intensity contributions modulated by the cosine of the precession angle and
weighted according to the Ov of S(Q, w) .
Therefore, the signal of the NSE spectrometeras
explained in this chapter-is completely different from the TOF histograms of classical
TOF-spectrometers (chapter 11) .
Instead it is proportional to the cosine Fourier transform
of S(Q, cv), i .e . the intermediate scattering function S(Q, t) . A detailed derivation and
discussion is given below . But first of all the actual setup of an NSE spectrometer is
presented .
11 .2 Setup and Function
Figure 11 .1 shows the schematic setup of a NSE spectrometer (upper part) together with
the propagation of the neutron spin in the instrument (lower part) .
Longitudinally polarized neutrons2 (i .e . spin expectation value parallel to the beam diconcerning
its precession in the magnetic field . As long as the kinetic energy of the
neutrons is much bigger than the magnetic level splitting the classical picture is completely
sufficient . It is much easier to understand the NSE spectrometer in this way than a
quantum mechanical treatment .
2 The polarized neutron beam is obtained by reflection by a magnetic multilayer mirror .
The layer stack consists of alternating nonmagnetic (e .g . Fe, Si or Ti) and magnetic (Fe or
Co) layers .
The effective index of refraction of the magnetic layers depends on the relative
orientation of magnetization and spins of the neutrons such that there is a modulation
of index of refraction for neutrons in one spin state only.
Those neutrons are reflected,
the others are transmitted . For layer distances of 5 . . . 10 nm reflection angles of a few
degrees result for wavelengths around 10 A .
Both the reflected and the transmitted beam
are polarized (with opposite spin directions)-
11- 2