Influence of ion movement on the bound electron g-factor

TL;DR

This paper investigates how the motion of ions in traps affects the relativistic measurements of the electron g-factor, finding that the effects are negligible at current measurement precisions.

Contribution

It provides a detailed calculation of the relativistic shifts in the g-factor caused by ion motion in different trapping environments, showing these effects are minimal.

Findings

Relativistic shift of the g-factor due to ion motion is negligible at current precision.

Energy shift in a Paul trap vanishes in leading order.

Ion motion influences measurements but is currently insignificant.

Abstract

In the relativistic description of atomic systems in external fields the total momentum and the external electric field couple to the angular momentum of the individual particles. Therefore, the motional state of an ion in a particle trap influences measurements of internal observables like energy levels or the g-factor. We calculate the resulting relativistic shift of the Larmor frequency and the corresponding g-factor correction for a bound electron in a hydrogen-like ion in the 1S state due to the ion moving in a Penning trap and show that it is negligible at the current precision of measurements. We also show that the analogous energy shift for measurements with an ion in the ground state of a Paul trap vanishes in leading order.