Neutron Scattering

E
ô
ô
x
z
w
0
z
_w
U
N
Figure 2 .7 : Scattering length of nuclei for thermal neutrons as a function of atomic weight .
2 .6 .2 Coherent and incoherent scattering
The scattering of neutrons depends on the isotope as well as on the relative spin orientations .
We now will look into the consequences in regarding the elastic scattering from an ensemble
of isotopes with the coordinates and scattering lengths {R, , b, } . The pseudo potential of this
ensemble has the form
V (L) - 2z b z Y, b, 8(r - R ) (2 .23)
ni,
l
with Eq . [2 .l8] we may calculate the matrix element of Vbetween k and k' as
~k' IVI k) = 2z b z b f e>k'r ä (r _ R, ) e>~ d3 r (2 .24)
m
2zb 2
m
b, eiQnr Q - k_ k'
The matrix element is just a Fourier surr over the atomic positions decorated with the
appropriate scattering length bi. The scattering cross section is obtained following Eq .[2.19] .
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