Two-loop QED corrections with closed fermion loops

TL;DR

This paper presents a comprehensive calculation of two-loop QED corrections with closed fermion loops for hydrogen-like ions across a wide range of nuclear charges, improving accuracy over previous methods.

Contribution

It provides all-order in Zα calculations of two-loop QED corrections with closed fermion loops for n=1 and n=2 states, including comparison with previous expansion results.

Findings

Agreement with previous (Z α)-expansion calculations

Identification of higher-order remainder terms

Extension of calculations to all orders in Zα

Abstract

We report a calculation of all two-loop QED corrections with closed fermion loops for the n=1 and n=2 states of H-like ions and for a wide range of the nuclear charge numbers Z=1-100. The calculation is performed to all orders in the binding-strength parameter (Z \alpha), with the exception that in a few cases the free-loop approximation is employed in the treatment of the fermion loops. Detailed comparison is made with previous (Z \alpha)-expansion calculations and the higher-order remainder term to order \alpha^2 (Z \alpha)^6 is identified.