Exact Results in Quantum Theory

The isotope shifts (IS) of atomic spectra can be measured with high accuracy and are widely used for extracting differences of the nuclear mean-square charge radii of isotopes. Detailed understanding of higher-order IS effects becomes essential at the level of precision of modern radius determinations. Another motivation has recently emerged in the context of new-physics searches based on King plots [1-4]. A King plot is a graphical representation of IS’s for at least two transitions across several isotope pairs. Since it is expected to be linear, it has been proposed [5] that a hypothetical new-physics boson coupling electrons and neutrons could manifest itself as a small deviation from its linearity. However, a number of “old-physics” effects also contribute to King-plot nonlinearities. Reliable theoretical understanding of these effects is therefore essential for interpreting observed deviations from linearity in King plots [1-4]. In my talk I discuss the theory of the higher-order field-shift and mass-shift effects in atomic spectra, which are required for interpretation of King-plot nonlinearities.References [1] I. Counts et al., Phys. Rev. Lett. 125, 123002 (2020) [2] J. Hur et al., Phys. Rev. Lett. 128, 163201 (2022) [3] A. Wilzewski et al. Phys. Rev. Lett. 134, 233002 (2025) [4] M. Door et al. Phys. Rev. Lett. 134, 063002 (2025) [5] J. Berengut et al. Phys. Rev. Lett. 120, 091801 (2018)