An Introduction to Neutron Scattering - Spallation Neutron Source

SANS Measures Particle Shapes and Inter-particle Correlations
dσ
dΩ
=
=
b
3
∫ d R ∫
space space
2 3
∫ d r ∫
space space
d
3
R'
n
P
d
3
r'
n
r
( R)
n
N
P
r
( r ) n
r
( R')
dσ
= ( ρ − ρ
dΩ
0
)
2
N
e
v
F(
Q)
r
( r ').
e
r r r
iQ.(
R−
R')
r
F(
Q)
2
r r r
iQ.(
r −r
')
2
where G P is the particle - particle correlation
function (the probability
that the re
r
v 2
is a particle at R if there's
one at the origin) and F( Q)
is the particle form factor
=
∫
( ρ − ρ
N
d
particle
3
∫
P
space
x.
e
d
0
3
)
r v
iQ.
x
R.
G
2
∫
d
particle
P
3
x.
e
r v
iQ.
x
r
( R).
e
These expressions are the same as those for nuclear scattering except for the addition
of a form factor that arises because the scattering is no longer from point-like particles
2
r r
iQ.
R
: