Neutron Scattering

2 .5 Scattering amplitude and cross section, the Born approximation
We now consider the scattering event by a fixed nucleus . The geometry for such a scattering
process is sketched in Fig .2 .6 . The incoming neutrons are described by plane waves e'krr
travelling in z -direction . At the target this plane wave interacts with a nucleus and is scattered
into a solid angle S2 df.
e ikr
Incident
neutrons
r = (0, 0, Z)
Figure 2.6 : Scattering geometiy for an incident plane wave scattered at a target .
The partial cross section is defmed by
_d6 _ current of scattered neutrons into (52,
A2
current of incident neutrons
dÇ2)
(2 .5)
Quantum mechanically the current is given by
2mi (Y/*V y/-VvV/ *)
(2 .6)
For an incident plane wave yr= ezkr Eq.[2 .6] leads immediately to j = h~ , where V is
n
the normalization volume . The scattered spherical wave has the form 1 f(Ç2)e"" therej(~
r
2-9