Neutron Scattering

It follows that the nuclear scattering for nuclei wich zero spin is purely "non-spin-flip"
scattering, i . e . there are no scattering processes that turn the neutron spin around . In
particular this is valid for all isotopic-incoherent scattering and coherent nuclear scattering
. Silice the coherent scattering amplitude represents the average non-fluctuating part
of the total actual scattering amplitude, it is the part that is also independent even of
any possibly existing nuclear spin.
4 .3 .2 Magnetic scattering
The matrix element of the interaction potential for pure magnetic scattering between the
states k and k' has already been introduced in the previous chapter 3 . The scattering
amplitude results to
A(Q) - (Sz
-`ynro
ML(Q)IS,)
. - -(Szior,I sz) MLa (Q) .
2Ms 2Ps a
-`ynro _
Here y, -1 .913 denotes the magnetic dipole moment of the neutron expressed in
nuclear magnetons PN = 5 .051 . 10 -27 JIT, and ro = 2 Z
is the classical electron radius .
Q , denotes the Pauli-spin matrices :
(4 .5)
0 1 0 -i
i1 0 )
1 1 y, (
0
(4 .6)
Writing briefly the spin-up and down states as 1+) - (
we obtain the following relations :
1
0
~ and 1-) _ (
0 1 ~
respectively,
or X l +) = H , = W
or Y.H = i H , Or YH = - i H
(4 .7)
Or 'M - W , - -H .
Inserting there relations into Eq. (4 .5) we obtain the matrix elements (scattering amplitudes)
for spin-flip and non-spin flip scattering :
+ + (NSF)
A(Q)
-ynro
2/IB
-MLZ (Q)
(Mlm(Q) - i VIL I (Q))
for
- (NSF)
+ - (SF)
(4 .8)
(L ~, (Q) + i M L1(Q))
- + (SF)
4-7