The electron mass from $g$-factor measurements on hydrogen-like carbon $^{12}$C$^{5+}$

TL;DR

This paper reports a highly precise measurement of the electron mass using $g$-factor measurements on hydrogen-like carbon ions, significantly improving the accuracy of previous values.

Contribution

It introduces a novel combination of high-precision frequency ratio measurements and advanced $g$-factor calculations to determine the electron mass with unprecedented accuracy.

Findings

Electron mass determined with a relative uncertainty of 2.8×10^{-11}

13-fold improvement over 2010 CODATA value

Detailed analysis of systematic shifts and phase jitters

Abstract

The electron mass in atomic mass units has been determined with a relative uncertainty of $2.8\cdot 10^{-11}$, which represents a 13-fold improvement of the 2010 CODATA value. The underlying measurement principle combines a high-precision measurement of the Larmor-to-cyclotron frequency ratio on a single hydrogen-like carbon ion in a Penning trap with a corresponding very accurate $g$-factor calculation. Here, we present the measurement results in detail, including a comprehensive discussion of the systematic shifts and their uncertainties. A special focus is set on the various sources of phase jitters, which are essential for the understanding of the applied line-shape model for the $g$-factor resonance.