Neutron Scattering

where QBG denotes the background .
Hence, the magnetic cross-section is separated by
dQ dor NSF d07 NSF dor SF dor SF
2 2
d9 mag (de L d9 ) (de I I de i
(4 .18)
and all nuclear scattering contributions and the background cancel in the differences of
Eq . (4.18), since they are independent of the magnetic field[11 ] .
For a multi-detector instrument it is possible to fulfill the condition P L Q wich P = Pz
perpendicular to the scattering plane, however, P I j Q cannot be realized simultaneously
for all different scattering angles . However, a similar expression lias been obtained for
paramagnetic scattering [12] . Therefore, two measurements are required with the two
polarizations P x and P y lying in the scattering plane perpendicular to eacli other . Using
(MxMx ) _ (MyM y ) _ (MzMz) and COS2 a + sine a = l, we may substitute (valid for both
spin-flip and non-spin flip term)
dQ dQ _ dQ dQ
d9 I I + d9 L d9 x + dQ y
4 .19
(trivial, if x lies in direction of Q) . Hence, the paramagnetic scattering is given by [12] :
d2 or
dQdW paramagnetic
d2a SF d2o SF d2a SF
2 (df2dwx + iS2dwy - 2 df2dwz )
-2 ( d2, NSF + d2, NSF - 2 d2, NSF
d9dwx d2dwy dQdwz )
(4 .20)
Furthermore, the coherent scattering and the spin-incoherent scattering can be separated
from each other and from paramagnetic scattering by the following useful combinations
[12] :
d207 NSF
dQdwcolterent
d9dwz
1 d 2 07 1 d2 07
2 dQdwparamagnetic 3 dQdwspin-incolterent
(4 .21)
d 2 07
dQd~jspin-incoherent
_
One may note, however, that - different from the Separation for (para-)magnetic scattering
- the above relations do not compensate for possible background contributions .
Furthermore, the above equations hold for ideal experimental conditions for polarization
and flipping ratio .
3 d207 SF d2Q SF d20r SF\
- - .
2 13 dS2dWz dPdwx dS2dW y I (4 .22)
In general, depolarizing effects may occur at all experimental devices,
and appropriate corrections need to be taken into account . Fig . 4 .5 illustrates that the
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