Weighted difference ofgfactors of light Li-like and H-like ions for an improved determination of the fine-structure constant

Abstract

A weighted difference of the g-factors of the Li-and H-like ion of the same element is studied and optimized in order to maximize the cancellation of nuclear effects. To this end, a detailed theoretical investigation is performed for the finite nuclear size correction to the one-electron g-factor, the one-and two-photon exchange effects, and the QED effects. The coefficients of the Zα expansion of these corrections are determined, which allows us to set up the optimal definition of the weighted difference. It is demonstrated that, for moderately light elements, such weighted difference is nearly free from uncertainties associated with nuclear effects and can be utilized to extract the fine-structure constant from bound-electron g-factor experiments with an accuracy competitive with or better than its current literature value.

QED corrections to the g factor of Li- and B-like ions

“…The extension of experiments to the heaviest ions, including Pb 81+ and U 91+ , is expected in the forthcoming years by the use of the ALPHATRAP Penning-trap setup [22] and the HITRAP facility [23,24]. Measurements with these systems are anticipated to provide an alternative determination of the value of α [25][26][27]. In Ref.…”

“…In Refs. [26,27] a specific difference of the g factors of low-Z H-and Li-like ions was proposed, for which an even stronger suppression of nuclear effects and their uncertainties can be achieved, leading to an accuracy competitive with the current value of α. A calculation of the nuclear polarization effect extended to Li-and B-like ions showed that these terms can also be largely suppressed in a specific difference of the g factors for two different charge states of the same element [28].…”

g Factor of Lithiumlike Silicon and Calcium: Resolving the Disagreement between Theory and Experiment

“…In Ref. [28], the most accurate at that time theoretical g-factor value for 28 Si 11+ was obtained, g th,2019 = 2.000 889 894 4 (34), and it was found to be 1.7σ away from the experimental value, g exp,2019 = 2.000 889 888 45 (14), presented ibid. The improvement was achieved mainly due to the accurate treatment of the higherorder effects within the perturbation theory.…”

“…For example, the measurement of the g-factor isotope shift with Li-like calcium ions [27] has opened a possibility to test the relativistic nuclear recoil theory in the presence of magnetic field and paved the way to probe boundstate QED effects beyond the Furry picture in the strong-field regime [30,31]. The high-precision bound-electron g-factor experiments combined with theoretical studies are expected to provide an independent determination of the fine structure constant α [32][33][34]. Moreover, one can search for the effects beyond the Standard Model [35].…”

The $g$ factor of bound electrons as a test for physics beyond the Standard Model

“…A relatively direct method consists in comparing the best available theoretical and experimental results, the largest difference between which allowed by the uncertainties, provides a bound for the NP contribution to the g factor. With this method, we also use data on weighted differences of g factors of ions in different charge states [28][29][30][31]. Another method is centered on the isotope shift.…”