Higher-order corrections to the field shift in atomic systems
Abstract
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, since they contribute to deviations from King-plot linearity observed experimentally in recent studies. 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 ratios are nearly independent of the ionic charge state, agreeing with the corresponding hydrogenic 1s ratios on a sub-percent level. Motivated by these findings, we introduce an approximation in which these ratios are assumed to be independent of the electronic configuration. It is shown that, within this approximation, higher-order field-shift corrections do not induce King-plot nonlinearities. We conclude that only the small contributions beyond this approximation can contribute to the nonlinearities observed experimentally.
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BibTeX
@misc{yerokhin2026higherorder,
title = {{Higher-order corrections to the field shift in atomic systems}},
author = {V. A. Yerokhin and Z. Harman and C. H. Keitel},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.26902},
eprint = {2607.26902},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.26902},
}
RIS
TY - UNPB
TI - Higher-order corrections to the field shift in atomic systems
AU - V. A. Yerokhin
AU - Z. Harman
AU - C. H. Keitel
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2607.26902
UR - https://arxiv.org/abs/2607.26902
AB - 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, since they contribute to deviations from King-plot linearity observed experimentally in recent studies. 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 ratios are nearly independent of the ionic charge state, agreeing with the corresponding hydrogenic 1s ratios on a sub-percent level. Motivated by these findings, we introduce an approximation in which these ratios are assumed to be independent of the electronic configuration. It is shown that, within this approximation, higher-order field-shift corrections do not induce King-plot nonlinearities. We conclude that only the small contributions beyond this approximation can contribute to the nonlinearities observed experimentally.
ER -