  Atomic form factors are widely used for the characterization of targets and
specimens, from crystallography to biology. By using recent mathematical
results, here we derive an analytical expression for the atomic form factor
within the independent particle model constructed from nonrelativistic screened
hydrogenic wavefunctions. The range of validity of this analytical expression
is checked by comparing the analytically obtained form factors with the ones
obtained within the Hartee-Fock method. As an example, we apply our analytical
expression for the atomic form factor to evaluate the differential cross
section for Rayleigh scattering off neutral atoms.
