Neutron Scattering

Here, the magnetic moment ofthe neutron is given by :
IU n =-YnuN'6
(3 .44)
a denotes the spin operator, gN the nuclear magneton and yN = -1 .913 the gyromagnetic factor
ofthe neutron . The magnetic field B of an electron is due to a spin- and orbital- part B = Bs +
BI, The dipole field of the spin moment is given by :
As =0x R 3
> 'ue = -2jUB 'S (3 .45)
The field due to the movement ofthe electron is given according to Biot-Savart :
-e v e x R
B L
=
c R3
(3 .46)
The magnetic scattering cross section for a process, where the neutron changes its wave
vector from k to k' and the projection of its spin moment to a quantisation axis z from az to az
can be expressed within the first Born approximation :
du(_
2
mn I/k~6 _
) ,IVmIk6_)I2
2zh 2
(3 .47)
As mentioned, we only consider the single differential cross section for elastic scattering .
Introducing the interaction potential from (3 .43) to (3 .46) in (3 .47), we obtain aller a lot of
algebra [4, 5] :
_d6 _ ( )2 - 1
YnrO 6_ , 6
dS2-
~ 2
-
f~B (
(3 .48)
The pre-factor ynro has the value ynro = 0.539 - 10-12 cm = 5 .39 fin . Here, M 1(Q) denotes the
component of the Fourier transform of the sample magnetisation, which is peipendicular to
the scattering vector Q :
3-22