Inside the Hydrogen Atom

TL;DR

This paper applies the non-linear Euler-Heisenberg theory to calculate the electric field inside the hydrogen atom, showing it can be significantly smaller than the Maxwellian prediction at very small distances, with implications for field energy and pair production.

Contribution

It demonstrates how non-linear quantum electrodynamics modifies the electric field inside the hydrogen atom compared to classical Maxwell theory.

Findings

Electric field inside hydrogen is reduced at small distances.

Field energy remains below pair production threshold.

Non-linear effects are significant only at very small scales.

Abstract

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.