Neutron Scattering

11 .3 The detector signal
As mentioned above the detector signal results from the transmission function of the analyzer
shaped as the cosine of the net precession angle in combination with the distribution
of net precession angles due to the distribution of velocity changes during scattering . The
velocity distribution is proportional to the spectral part of S(Q, W) . In the following this
is derived in terms of mathematical expressions . First the field integrals along the primary
and secondary paths of precession are defined :
I(Z)
1 IBldl (11 .2)
l((7r/2)1)
J2 =
l((z/2)z)
IB I dl (11 .3)
for a symmetric setup J 1 = J2 ; l(7r, (7r/2) 1, 2 ) denotes the positions of the corresponding
flippers . The precession angle accumulated on a path i is
v
where v is the neutron velocity (typically several 100 m/s) .
the sign of ~P 1, a total precession angle of
Because the 7r-flipper inverts
lyii
v
+
'Y j2
v + Ov
results, where Av is the velocity change of the neutron due to inelastic scattering . The
transmission function of an (assumedly ideal) analyzer is
Ta =
From that the detector intensity
'Y J2
2 1+cos(-`Yv1
~ + v+Av
I = 77S(Q) fi 1 + cos --Yv 1 + w,,(Av)wA(v) dAv A (l1 .7)
2 ~ ( v +JOv )]
the flipper or by a tiny extra component of the external field in direction of the flipper
axis the ideal function may be restored .
internal field
The condition to be fulfilled is that the resulting
is orthogonal to the embedding field which may be slightly tilted from its
horizontal orientation by the added small extra field component .
11- 8