A New Relation between Lamb Shift Energies

TL;DR

This paper derives a new formula relating the Lamb shift energies of hydrogen and muonium, based on non-relativistic QED and reduced mass considerations, which aligns well with experimental data and offers a cutoff-free test of QED.

Contribution

It introduces a novel relation between hydrogen and muonium Lamb shifts derived from non-relativistic QED and reduced mass treatment, improving theoretical-experimental agreement.

Findings

The new relation matches experimental data accurately.

It provides a cutoff-free test of QED.

The formula emphasizes the role of reduced mass in Lamb shift calculations.

Abstract

We derive a new relation between the observed Lamb shift energies of hydrogen and muonium atoms. The relation is based on the non-relativistic description of the Lamb shift, and the proper treatment of the reduced mass of electron and target particles (proton and muon) leads to the new formula which is expressed as $\displaystyle{{\Delta E^{(H)}_{2s_{1/2}}\over \Delta E^{(\mu)}_{2s_{1/2}}} =({1+{m_e\over m_\mu}\over 1+{m_e\over M_p}})^3}$. This relation achieves an excellent agreement with experiment and presents an important QED test free from the cutoff momentum $\Lambda$.