  In calculating the energy corrections to the hydrogen levels we can identify
two different types of modifications of the Coulomb potential $V_{C}$, with one
of them being the standard quantum electrodynamics corrections, $\delta V$,
satisfying $\left|\delta V\right|\ll\left|V_{C}\right|$ over the whole range of
the radial variable $r$. The other possible addition to $V_{C}$ is a potential
arising due to the finite size of the atomic nucleus and as a matter of fact,
can be larger than $V_{C}$ in a very short range. We focus here on the latter
and show that the electric potential of the proton displays some undesirable
features. Among others, the energy content of the electric field associated
with this potential is very close to the threshold of $e^+e^-$ pair production.
We contrast this large electric field of the Maxwell theory with one emerging
from the non-linear Euler-Heisenberg theory and show how in this theory the
short range electric field becomes smaller and is well below the pair
production threshold.
