Inside the Hydrogen Atom
  We apply the non-linear Euler-Heisenberg theory to calculate the electric field inside the hydrogen atom. We will demonstrate that the electric field calculated in the Euler-Heisenberg theory can be much smaller than the corresponding field emerging from the Maxwellian theory. In the hydrogen atom this happens only at very small distances. This effect reduces the large electric field inside the hydrogen atom calculated from the electromagnetic form-factors via the Maxwell equations. The energy content of the field is below the pair production threshold. 
M. Nowakowski, N. G. Kelkar, D. Bedoya Fierro, A. D. Bermudez   Manjarres
hep-ph physics.atom-ph