An Introduction to Neutron Scattering - Spallation Neutron Source

Scattering for Spherical Particles
particles.
of
number
the
times
volume
particle
the
of
square
the
to
al
proportion
is
)]
r
(
)
r
G(
when
[i.e.
particles
spherical
ed
uncorrelat
of
assembly
an
from
scattering
total
the
0,
Q
as
Thus,
0
Q
at
)
(
3
)
(
cos
sin
3
)
(
:
Q
of
magnitude
on the
depends
only
F(Q)
R,
radius
of
sphere
a
For
shape.
particle
by the
determined
is
)
(
factor
form
particle
The
0
1
0
3
0
2
.
2
v
r
r
r r
r
δ
→
→
=
→
≡
⎥
⎦
⎤
⎢
⎣
⎡ −
=
= ∫
V
QR
j
QR
V
QR
QR
QR
QR
V
Q
F
e
r
d
Q
F
sphere
V
r
Q
i
2 4 6 8 10
0.2
0.4
0.6
0.8
1
3j 1 (x)/x
x
Q
and
(a)
axis
major
the
between
angle
the
is
where
)
cos
sin
(
:
by
R
replace
particles
elliptical
For
2
/
1
2
2
2
2
r
ϑ
ϑ
ϑ b
a
R +
→