Short Range Interactions in the Hydrogen Atom

TL;DR

This paper examines the effects of finite nuclear size on the hydrogen atom's potential, revealing issues with classical models and demonstrating how non-linear quantum electrodynamics can mitigate these problems.

Contribution

It analyzes the short-range modifications to the Coulomb potential due to nuclear size and shows how non-linear QED reduces problematic electric fields.

Findings

Classical finite-size potential leads to near-threshold electric fields.

Non-linear Euler-Heisenberg theory lowers electric field strength.

Standard Coulomb potential issues are mitigated by non-linear effects.

Abstract

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.