Neutron Scattering

2 .7 Comparison between X-ray and neutron scattering
Other than neutrons, X-rays are scattered by the electrons, which are distributed in space
around the respective nucleus . This spatial distribution leads to an atomic form factor which is
the Fourier transformed ofthe electron density distribution pi(! :). It depends in principle on the
degree of ionisation of a nucleus but not on the isotope .
fi (Q) = f pi (r) exp (iQr) dV (2 .32)
Since the atomic radii (about 10 4 times larger than the radius of a nucleus) are comparable
with the wavelength, the scattering amplitude f(Q) depends strongly on Q . Thus, with
increasing scattering angle the scattering intensity drops significantly . Furthermore, the atom
formfactor depends on the number of electrons Z and is given by
f; (Q=o)=Z
(2 .33)
Thereby, Z is the number of electrons of an atom or of an ion .
the atomic formfactor normalized to one as a function of sin B
Fig .2 .8 displays schematically
t
sin 9
Figure 2.8 :
Schematic representation of normalized X-ray and magnetic neutron scattering
form factors as a function of sin BQ.
2- 18