Force Density Balance inside the Hydrogen Atom

TL;DR

This paper investigates the internal force balance within the hydrogen atom, demonstrating that Coulomb attraction is locally balanced by a confinement force, and extends this concept to the stability of charged particles in quantum electrodynamics.

Contribution

It provides a detailed local analysis of force densities inside the hydrogen atom using a classical Dirac field framework, revealing a point-by-point force balance.

Findings

Coulomb and confinement forces balance exactly at every point in the hydrogen atom.

The local force balance concept extends to charged particles in vacuum polarization.

The analysis goes beyond traditional global stability criteria for atoms.

Abstract

Motivated by the long-debated question about the internal stability of the electron, the force densities acting on the charge density of the 1s electron in the H atom are investigated. The problem is mapped onto the canonical formalism for a classical Dirac field coupled to the electric field of an external point charge. An explicit calculation shows that the attractive Coulomb force density is balanced exactly at every point in space by the repulsive confinement force density. The latter requires evaluating the divergence of the stress tensor for the 1s solution of the Dirac equation. Such a local force balance goes beyond the global stability criteria that are usually given for the H atom. This concept is extended to the internal stability of any charged particle by investigating the force densities acting on its surrounding vacuum polarization. At large distances one has to consider only the charge density of virtual electrons and positrons, induced by a point charge in the vacuum of quantum electrodynamics.