Effect of a relativistic correction to the Coulomb potential on the energy levels of hydrogen atom

TL;DR

This paper proposes a relativistic correction to the Coulomb potential in the hydrogen atom, which affects energy levels and spectral degeneracies, challenging existing theoretical and experimental agreements.

Contribution

It introduces a relativistic correction based on retarded potentials, altering the hydrogen atom energy spectrum and questioning the current understanding of atomic spectra.

Findings

Correction lifts the l-degeneracy in hydrogen spectra

Results are of the same order as fine structure corrections

Suggests need for re-examination of hydrogen spectral theory

Abstract

Based on classical electrodynamics, it is argued that the Coulomb potential (which is strictly valid for two point charges at rest), commonly used in the study of energy levels of hydrogen atom is not the correct one, because the electron in the hydrogen atom moves with relativistic speeds with respect to the nucleus. Retardation effect has to be considered in accordance with Li\'{e}nard-Wiechert (or retarded) potential of a moving charge or the relativistic electrodynamics. However, such a consideration introduces a correction to the Coulomb potential, whose quantum mechanical expectation value is estimated at $E_{ret} = - \frac{mc^2\alpha ^4}{2n^3(l+1/2)}$, which is of the same order as the fine structure of hydrogen atom and hence added to the standard energy eigenvalue values of H-atom. This correction lifts the $l$-degeneracy in the spectra of H-atom and hence modifies the standard result. The result disturbs the existing agreement between the theory and experiments on H-atom and hence requires further theoretical and experimental re-examination. The implications of this result for the Kepler-problem in general is also discussed in the context of Heaviside's gravity, which seems to offer an alternative explanation for the non-Newtonian perihelion advance of Mercury without invoking the space-time curvature formalism of Einstein's general theory of relativity.