Higher-order corrections to the field shift in atomic systems

Differences in nuclear charge distributions between isotopes lead to small changes in atomic spectra known as the field shift. While largely proportional to the change in the mean-square nuclear radius, the field shift also contains higher-order contributions with different dependencies on nuclear moments. Their knowledge is required in searches for new physics using King plots, as they can induce deviations from King-plot linearity. We present a systematic expansion of the field-shift energies in terms of nuclear parameters and test its validity against direct numerical calculations for H-like ions. We also compute leading-and higher-order field-shift corrections for alkali-like systems from Li-like to Rb-like ions, and find that their ratio is nearly independent of the ionic charge state, agreeing with the corresponding hydrogenic 1s ratios on a sub-percent level. Motivated by this observation, we introduce an approximation in which these fractional contributions are assumed to be independent of the electronic configuration. We show that within this approximation, higherorder field-shift corrections do not contribute to King-plot nonlinearities.