[For info only]
Electron scattering is the tool of choice for determining the density distributions of nuclei. A schematic introduction is given here. This ignores all relativistic effects and spin interactions, but illustrates the importance of the form factor and its relation to the scattering potential. It is also a quick introduction to scattering.
Consider a plane wave 
incident
on a target nucleus fixed at the coordinate origin. This wave is scattered
to 
by the potential V(r). We use
perturbation theory (first Born approximation) in order to find the
amplitude for finding 
. The probability for finding a
particle is given by the square of the amplitude which is also
proportional to the differential cross section, i.e.
We can evaluate this integral (with 
):
Now, if the charge distribution is not pointlike, the potential can be written
The above matrix element M then becomes
This can be split into two independent integrals by means of the
substitutions 
and 
Then
The function 
is known as the form factor and is the Fourier
transform of the charge density.