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

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.