Why there is no electron-positron production inside the, let say, Hydrogen atom?. I know that the electric field near nucleus get modified by some form factors making it not as big as the Coulomb field, but still i think is still very big.
Where should the energy come from? Which process would not violate energy conservation?
A theoretical nucleus with something like 150+ protons without any electrons might be able to make pair production because the electron ground state would be so deeply bound its binding energy would be sufficient to make a positron, but those nuclei don't exist. You can still get pair production if two lead nuclei pass very close to each other, mimicing such a heavy nucleus. This is studied at the LHC.
My confusions is that above the Schwinger limit it is supposed to be pair productions. Due to the form of the coulomb field electric fields above the Schwinger limit can be found, why in this case that limit seems to not matter?.