Brownian motion of the electron and the Lamb shift at finite temperature

TL;DR

This paper investigates how finite temperature electromagnetic radiation influences electron fluctuations in a hydrogen atom, leading to measurable shifts in the Lamb effect and potential insights into proton size.

Contribution

It introduces a model for electron fluctuation effects at finite temperature and quantifies their impact on the Lamb shift, especially for weakly bound states.

Findings

2% correction to Bethe's Lamb shift at weak fluctuations

Order of magnitude larger effects at strong fluctuations

Potential to measure proton diameter directly

Abstract

By enhancing electron position fluctuations, equilibrium electromagnetic radiation modifies the potential for an electron in a Hydrogen atom. This can have significant effects for weakly bound states and especially at finite temperature. This implies a 2% correction to Bethe's value for 2S-2P Lamb shift for weak fluctuations, but the effect is an order of magnitude larger for strong fluctuations where it provides direct measure of the proton diameter.