On the stability of classical orbits of the hydrogen ground state in Stochastic Electrodynamics

TL;DR

This paper investigates the stability of classical hydrogen orbits in Stochastic Electrodynamics, extending previous work to elliptical orbits and showing that certain conditions lead to self-ionisation, while adding a potential can stabilize the ground state.

Contribution

It extends the analysis of orbit stability in Stochastic Electrodynamics to elliptical orbits and introduces a modified potential that can stabilize the hydrogen ground state.

Findings

Elliptic orbits with high eccentricity tend to self-ionise due to energy gain.

Adding a repulsive $1/r^2$ potential can stabilize the hydrogen ground state.

The results also apply to positronium under similar conditions.

Abstract

de la Pe\~na 1980 and Puthoff 1987 show that circular orbits in the hydrogen problem of Stochastic Electrodynamics are stable. Though the Cole-Zou 2003 simulations support the stability, our recent numerics always lead to self-ionisation. Here the de la Pe\~na-Puthoff argument is extended to elliptic orbits. For very eccentric orbits with energy close to zero and angular momentum below some not-small value, there is on the average a net gain in energy for each revolution, which explains the self-ionisation. Next, an $1/r^2$ potential is added, which could stem from a dipolar deformation of the nuclear charge by the electron at its moving position. This shape retains the analytical solvability. When it is enough repulsive, the ground state of this modified hydrogen problem is predicted to be stable. The same conclusions hold for positronium.