Neutron Scattering

For a spherical electron distribution pj(r), f(r) depend only on the absolute value of Q. For
neutral atoms and possible ionic states they bas been calculated by Hartree-Fock calculations
and may be found tabulated .
Since the atomic form factors depend on the atomic number, the scattering contributions of
light atoms for X-rays are only weak . Therefore, in structure determinations the precision of
the localization of such important atoms like hydrogen, carbon or oxygen is limited in the
presence of heavy atoms . Neutrons do not suffer from this problem since the scattering length
for all atoms are about equal .
In particular important is the case of hydrogen . In the bound state the density distribution of
the only electron is typically shifted with respect to the proton position and an X-ray structure
analysis in principle cannot give the precise hydrogen positions . On the other hand, bonding
effects which are important for the understanding of the chemistry, may be precisely studied
by X-ray electron density distributions .
Atoms or ions with slightly different atom number like neighbouring elements in the periodic
table are difficult to distinguish in X-ray experiments. Again, neutron scattering experiments
also by the use ofthe proper isotope allow a by far better contrast creation . Such effects are in
particular important for e .g . the 3d-elements .
The paramagnetic moment of an atom or ion fcj results form the unpaired electrons . The
density distribution of these electrons oj,n (r) is also named magnetization density or spin
density and is a partial electron density compared to the total electron density pj(r) . Because
of the magnetic dipole interaction, the amplitude of the magnetic neutron scattering is given
in analogy to Eq.[2 .32] as the Fourier transformed of the magnetization density pjM (r) . The
normalized scattering amplitude
(Q) 1
fjM
rI
--
J
pjM (r) exp
(iQr
dV
(2 .34)
2- 19