Proposal for the determination of nuclear masses by high-precision spectroscopy of Rydberg states

TL;DR

This paper proposes using high-precision spectroscopy of Rydberg states in one-electron ions to accurately determine nuclear masses, leveraging the minimal nuclear-size correction and detailed QED calculations for specific states.

Contribution

It introduces a novel method to deduce nuclear masses from Rydberg state spectroscopy and provides detailed theoretical calculations to support this approach.

Findings

Nuclear mass can be precisely deduced from Rydberg transition measurements.

QED self-energy calculations for high-n states are provided.

Application potential for hydrogen, deuterium, and light ions is demonstrated.

Abstract

The theoretical treatment of Rydberg states in one-electron ions is facilitated by the virtual absence of the nuclear-size correction, and fundamental constants like the Rydberg constant may be in the reach of planned high-precision spectroscopic experiments. The dominant nuclear effect that shifts transition energies among Rydberg states therefore is due to the nuclear mass. As a consequence, spectroscopic measurements of Rydberg transitions can be used in order to precisely deduce nuclear masses. A possible application of this approach to the hydrogen and deuterium, and hydrogen-like lithium and carbon is explored in detail. In order to complete the analysis, numerical and analytic calculations of the quantum electrodynamic (QED) self-energy remainder function for states with principal quantum number n=5,...,8 and with angular momentum L=n-1 and L=n-2 are described (j = L +/- 1/2).