Going from Classical to Quantum Description of Bound Charged Particles Part 2: Implications for the light hydrogenic atoms

TL;DR

This paper extends a novel bound field theory to hydrogenic atoms, showing it yields energy levels consistent with standard theory but introduces corrections that improve agreement with experimental data, including proton radius measurements.

Contribution

It introduces a modified energy level calculation for hydrogenic atoms based on a bound field theory, aligning theory more closely with experimental results, especially for proton radius.

Findings

Corrected energy levels match gross and fine structures.

Reduces discrepancy in 1S-2S interval and hyperfine splitting.

Proton radius estimate aligns with muonic hydrogen measurements.

Abstract

This paper continues the analysis of bound quantum systems started in (T. Yarman, A.L. Kholmetskii and O.V. Missevitch. Going from classical to quantum description of bound charged particles. Part 1: basic concepts and assertions), based on a novel approach, involving the requirement of energy-momentum conservation for the bound electromagnetic (EM) field, when the EM radiation is forbidden. It has been shown that the modified expression for the energy levels of hydrogenic atoms within such a pure bound field theory (PBFT) provides the same gross and fine structure of energy levels, like in the standard theory. At the scale of hyperfine interactions our approach, in general, evokes important corrections to the energy levels. Part of such corrections, like the spin-spin splitting in hydrogen, is less than the present theoretical uncertainty in the evaluation of hyperfine contributions into the atomic levels. But the most interesting result is the appearance of a number of significant corrections, which improve the convergence between theory and experiment. In particular, the corrected 1S-2S interval and 1S spin-spin splitting in positronium reduce the existing up to date discrepancy between theoretical and experimental data. The re-estimated classic 2S-2P Lamb shift in the hydrogen atom lead to the proton charge radius rp=0.841(6) fm, which perfectly agrees with the latest estimation of proton size via the measurement of 2S-2P Lamb shift in muonic hydrogen, i.e. rp=0.84184(67) fm.