Radiative corrections of the order $\alpha\,(Z\,\alpha)^6$ for rotational states of two-body systems

TL;DR

This paper analytically calculates the complete one-loop radiative correction of order  to the energies of two-body systems with angular momentum greater than zero, applicable to systems like hydrogen and muonium.

Contribution

It provides the first analytical derivation of  order radiative corrections for two-body systems with arbitrary masses and spin 1/2, extending previous work to a broader class of systems.

Findings

Derived analytical formulas for  order corrections

Applicable to hydrogen, muonium, positronium, and antiprotonic atoms

Enhances precision in theoretical energy level calculations

Abstract

The analytical calculation of the complete $\alpha\,(Z\,\alpha)^6$ one-loop radiative correction to energies of two-body systems with the angular momenta $l>0$, consisting of a pointlike particle and an extended-size nucleus with arbitrary masses and spin 1/2, is presented. The obtained results apply to a wide variety of two-body systems, such as hydrogen, muonium, positronium, and antiprotonic atoms.