Neutron Scattering

proportional to the current throught the main precession solenoids . This current usually
is the parameter used to stepwise scan the Fourier time during an experiment to get a
table of S (Q, t) vs . t .
11.3 .2 Mastic Scattering of a Finite Width Wavelength Distribution
For a transmitted beam or elastically scattered neutrons from a reference sample w = 0
holds, i .e S(Q, w) = S(w) . With that equation 11 .8 becomes
I = 1
f [1 ~- cos(A -Y(m,/h){J2 - Jl})] w a (A)dA (11 .11)
For this case the intensity is proportional to the Fourier transform of the wavelength
distribution . Here, the underbraced part is the external control parameter . It contains
the difference between the field integrals along the primary and secondary paths JZ - Jl .
This difference can be easily controlled by sending a current through an auxiliary coil
of a few windings around one of the precession solenoids . For a Gaussian wavelength
distribution the envelope of the Fourier transform is again a Gaussian whose width is
inversely proportional to the width of the wavelength distribution . Since wA is centered
at a finite nominal wavelength \o the envelope is multiplied by a cosine with a period
oc I/A o . This function follows immediately from equation 11 .11 if wA = ô(,\) is assumed .
Figure 11 .4 displays the results of an extensive measurement using the attenuated direct
beam with a central wavelength of \o = 0.7nm and O,\Fwxm/,\o = 0 .1 compared to a
calculation (fit) assuming a Gaussian wavelength distribution .
At the echo point (i .e . a phase coil current close to 1 .5 A creating perfect symmetry) the
count rate has a minimum . Ideally the count rate should be zero there, but because all
elements that contribute to the polarization manipulation and analysis are imperfect a
residual intensity is left that has to be determined by calibration measurements . From the
the functional dependence of the intensity on the phase current it is possible to determine
the wavelength distribution .