Neutron Scattering

Different to the coherent nuclear scattering now we cari also observe "spin-flip" processes
that reverse the neutron spin direction . Recall that ML (Q) is the perpendicular
component of VI with respect to the scattering vector Q, and the neutron polarization
has been chosen parallel to an external field H z . We obtain two rules for the magnetic
scattering :
The "spin-flip" processes are observed for the component 1!I+ (Q) that is perpendicular to
the neutron polarization . The "non-spin flip" processes are observed for the composent
of ML(Q) that is parallel to the neutron polarization .
4 .3 .3 Nuclear spin-dependent scattering
If the neutron is scattered from a nucleus wich non-zero spin the compound may form
a singulett or triplett state where the neutron spin Q is asti-parallel or parallel to the
nuclear spin 1 with different scattering lengths b_ and b+ respectively. The case of nuclear
spin-dependent scattering cari be formally treated in analogy to the magnetic scattering
by introducing the scattering length operator
b=A+Bu-I (4 .9)
with A = (I+1)b + +Ib- b+ - b-
and B
21+1
= 21+1 '
where I and o- denote the nuclear spin operator and the neutron spin operator respectively.
The scattering amplitude A(Q) will have the came form as given in Eq . (4 .8) only
VIL (Q) has to be replaced by the nuclear spin operator I .
A-BI,
A(Q) = (S (Z) JA+B or - I I s(z) )
B (l x - il,)
--+
SF
While in Eq . (4 .5) M1 is assumed to represent the thermodynamic expectation value, the
thermal average has te, be calculated now for the different nuclear spin orientations and
for the firnt matrix element in Eq . (4 .10) . Except for some unusual cases, we may expect
that the orientation of nuclear spins is given by a random distribution, i . e .
(IX ) _ (I,,) _ (IZ) = 0
4-8