Nuclear recoil effect on $g$ factor of heavy ions: prospects for tests of quantum electrodynamics in a new region

TL;DR

This paper evaluates the nuclear recoil effect on the g factor of heavy ions, reducing theoretical uncertainties and proposing a way to test quantum electrodynamics in strong fields beyond the Furry picture.

Contribution

It provides an all-order calculation of the recoil effect, including nuclear size and electron-electron interactions, enabling new tests of QED in heavy ions.

Findings

Recoil effect calculations are improved with reduced uncertainties.

QED recoil effects can be probed at a few-percent level in specific g-factor differences.

Potential to test QED in strong-coupling regimes beyond traditional approaches.

Abstract

The nuclear recoil effect on the $g$ factor of H- and Li-like heavy ions is evaluated to all orders in $\alpha Z$. The calculations include an approximate treatment of the nuclear size and the electron-electron interaction corrections to the recoil effect. As the result, the second largest contribution to the theoretical uncertainty of the $g$-factor values of $^{208}$Pb$^{79+}$ and $^{238}$U$^{89+}$ is strongly reduced. Special attention is paid to tests of the QED recoil effect on the $g$ factor in experiments with heavy ions. It is found that, while the QED recoil effect on the $g$-factor value is masked by the uncertainties of the nuclear size and nuclear polarization contributions, it can be probed on a few-percent level in the specific difference of the $g$ factors of H- and Li-like heavy ions. This provides a unique opportunity to test QED in a new region --- strong-coupling regime beyond the Furry picture.