The $g$-factor of light ions for an improved determination of the fine-structure constant

TL;DR

This paper proposes a method using weighted differences of $g$-factors of light ions to accurately determine the fine-structure constant, minimizing nuclear effects and enhancing experimental precision.

Contribution

It introduces an optimized weighted difference approach for $g$-factors of light ions to improve the extraction accuracy of the fine-structure constant.

Findings

Weighted difference effectively cancels nuclear effects.

Method achieves accuracy comparable or superior to current literature.

Potential for near-future experiments to refine fundamental constants.

Abstract

A weighted difference of the $g$-factors of the H- and Li-like ions of the same element is theoretically studied and optimized in order to maximize the cancelation of nuclear effects between the two charge states. We show that this weighted difference and its combination for two different elements can be used to extract a value for the fine-structure constant from near-future bound-electron $g$-factor experiments with an accuracy competitive with or better than the present literature value.