Neutron Scattering

Therefore the non-spin flip matrix elements equal to A, arid (as derived before) the coherent
nuclear scattering is proportional to the square of b ol ,, identifying A = b = bcoh .
dQ (±-± ,NSF )
dS2 coherent
- b2 L e.`i- r-)
r,r,
(4 .12)
The non-spin flip matrix elements vanish, however, for the incoherent scattering, which
is proportional to bz - b 2 , and we have to consider the thermal average of the squares of
the matrix elements . Since
(Ix) (Iy) (Iz) = 3I(II + 1)
(4 .13)
from Eq . (4 .l0) one obtains the spin-incoherent scattering (per atom) :
dQ (± - :±,NSF) - (b2 _ b2)NSF - 1 (B 2 I(I + 1))
d9 spin-incoherent 3
(4 .14)
du (+~-' -- + - SF)
(b2 - b2 )SF - 2 (B 2 I(I + 1))
dP spin-incolterent 3
(4 .15)
113 of the spin-incoherent part of the nuclear scattering is non-spin flip scattering and
213 of it is spin-flip scattering independent of the (direction) of an external field H .
In arialogy to the coherent scattering amplitude bcoh, orie may define the (spin-) incoherent
scattering amplitude bin , \ B 2 I(I + 1) .
4 .3.4 Rules for separation
From the preceding discussion we cari summarize some useful rules for separating different
scattering contributions .
If we may neglect magnetic scattering, the coherent and spinincoherent
scattering is obtained from the spin-flip and non-spin flip scattering :
du du NSF 1 du SF (4 .16)
d9 coherent d9 2 d9
If a part of the scattering is of magnetic origin, a field variation is required (perpendicular
and parallel to Q) to separate the magnetic cross-section :
dor 3 du SF (4 .17)
d9 spin-incoherent 2 d9
field/polarization spin-flip intensities non-spin flip intensities
H I I Q umag + 5Qinc + QBG 07coh + ()umag + 3Qinc + 07BG
2Umag + 3Qinc + QBG
(Tcoh + 2Umag + 3(Tinc + QBG
4-9