Investigations of isotope shifts of atomic spectral lines provide insights into nuclear properties. Deviations from the linear dependence of the isotope shifts of two atomic transitions on nuclear parameters, leading to a nonlinearity of the so-called King plot, are actively studied as a possible way of searching for new physics. In the present Letter we calculate the King-plot nonlinearities originating from the standard-model atomic theory. The calculation is performed both analytically, for a model example applicable for an arbitrary atom, and numerically, for one-electron ions. It is demonstrated that the standard-model predictions of the King-plot nonlinearities are hypersensitive to experimental errors of nuclear charge radii. This effect significantly complicates identifications of possible King-plot nonlinearities originating from the new physics.

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• Electronic structure of atoms & molecules
• Relativistic & quantum electrodynamic effects in atoms, molecules,& ions