The two-loop self-energy for the ground state of medium-Z hydrogen-like ions

TL;DR

This paper calculates the two-loop self-energy correction to the Lamb shift in medium-Z hydrogen-like ions using a novel numerical method, improving accuracy and providing insights into hydrogen's higher-order effects.

Contribution

It introduces a new calculational technique for Feynman diagrams in mixed coordinate-momentum space, enhancing numerical precision in two-loop self-energy calculations.

Findings

Improved numerical accuracy over previous results.

Extrapolated data towards Z=1 for hydrogen.

Reduced discrepancy between all-order and perturbative approaches.

Abstract

The two-loop self-energy correction to the ground state Lamb shift is calculated for hydrogen-like ions with the nuclear charge Z=10-30 without any expansion in the binding field of the nucleus. A calculational technique is reported for treatment of Feynman diagrams in the mixed coordinate-momentum representation, which yields significant improvement in numerical accuracy as compared to previous results. An extrapolation of the all-order numerical data towards Z=1 yields a result for the higher-order remainder function for hydrogen. The previously reported disagreement between the all-order and the perturbative approaches is reduced to the marginal agreement.