  Properties and different representations of the Uehling potential are
investigated. Based on these properties and by using our formulas for the
Fourier transform of the Uehling potential we have developed the new
analytical, logically closed and physically transparent procedure which can be
used to evaluate the lowest-order vacuum polarization correction to the cross
sections of a number of QED processes, including the Mott electron scattering,
bremsstrahlung, creation and/or annihilation of the $(e^{-}, e^{+})-$pair in
the field of a heavy Coulomb center, e.g., atomic nucleus.
