Fundamental constants and tests of theory in Rydberg states of one-electron ions

TL;DR

This paper discusses high-precision theoretical predictions for circular Rydberg states of hydrogenlike ions, highlighting their potential for testing fundamental physics and refining constants through quantum electrodynamics calculations and frequency measurements.

Contribution

It introduces a new nonperturbative QED result for Rydberg states, enhancing the accuracy of energy level predictions and enabling more stringent tests of fundamental theories.

Findings

Negligible nuclear size correction uncertainties for high angular-momentum states

Development of a nonperturbative QED calculation method

Potential for improved Rydberg constant determination through frequency measurements

Abstract

The nature of the theory of circular Rydberg states of hydrogenlike ions allows highly-accurate predictions to be made for energy levels. In particular, uncertainties arising from the problematic nuclear size correction which beset low angular-momentum states are negligibly small for the high angular-momentum states. The largest remaining source of uncertainty can be addressed with the help of quantum electrodynamics (QED) calculations, including a new nonperturbative result reported here. More stringent tests of theory and an improved determination of the Rydberg constant may be possible if predictions can be compared with precision frequency measurements in this regime. The diversity of information can be increased by utilizing a variety of combinations of ions and Ryberg states to determine fundamental constants and test theory.