Atom as a "Dressed" Nucleus
  It is shown that the electrostatic potential of atomic nucleus "seen" by a fast charged projectile at short distances is smeared quantum mechanically due to nucleus motion around the atomic center of inertia. For example, the "positive charge cloud" size in the Hydrogen ground state is much larger than the proper proton size. It is even bigger for the target atoms in excited initial states. The elastic scattering at large angles is generally weaker than the Rutherford one since the effective potential at short distances is softer than the Colombian one due to a natural "cutoff". In addition, the large angle scattering leads to the target atom excitations due to pushing the nucleus (=> inelastic processes). The Rutherford cross section is in fact the inclusive rather than the elastic one. These results are analogous to the QED ones. The difference and the value of presented below non relativistic atomic calculations is in non perturbatively (exact) nucleus "dressing" that immediately leads to correct physical results and to significant technical simplifications. In these respects the nucleus bound in an atom is a simple but a rather realistic model of a "dressed" charge in the QFT. This idea is briefly demonstrated on the real electron model (electronium) that is made free from infinities. 
Vladimir Kalitvianski