An Introduction to Neutron Scattering - Spallation Neutron Source

Coherent and Incoherent Scattering
The scattering length, b i , depends on the nuclear isotope, spin relative to the
neutron & nuclear eigenstate. For a single nucleus:
b
i
b b
i
=
but
j
δb
2
i
=
dσ
∴
dΩ
b
δb
=
=
+ δb
b
2
=
b
i
b
0
i
+
−
2
b
where δb
averages to zero
and
b
∑
i,
j
( δb
e
2
i
+ δb
δb
δb
=
i
b
2
r r r
−iQ.(
R −R
Coherent Scattering
(scattering depends on the
direction of Q)
i
j
j
j
)
) + δbδb
vanishes
−
+ (
b
b
2
i
2
j
−
unless
b
2
) N
Note: N = number of atoms in scattering system
i
=
Incoherent Scattering
(scattering is uniform in all directions)
j