Non-perturbative evaluation of some QED contributions to the muonic hydrogen $\bm{n=2}$ Lamb shift and hyperfine structure

TL;DR

This paper performs exact numerical evaluations of the Dirac equation to calculate key QED contributions to the muonic hydrogen n=2 Lamb shift and hyperfine structure, confirming previous perturbative results and analyzing nuclear size effects.

Contribution

It introduces a non-perturbative numerical approach to evaluate QED effects in muonic hydrogen, improving accuracy over traditional perturbation methods.

Findings

Confirmed validity of perturbation expansion for light elements

Quantified nuclear size and model dependence of effects

Provided precise non-perturbative calculations of Lamb shift and hyperfine structure

Abstract

The largest contributions to the $n=2$ Lamb-shift, fine structure interval and $2s$ hyperfine structure of muonic hydrogen are calculated by exact numerical evaluations of the Dirac equation, rather than by a perturbation expansion in powers of $1/c$, in the framework of non-relativistic quantum electrodynamics. Previous calculations and the validity of the perturbation expansion for light elements are confirmed. The dependence of the various effects on the nuclear size and model are studied