Nonlinearities of King's plot and their dependence on nuclear radii

TL;DR

This paper analyzes the nonlinearities in King plots caused by nuclear radii and demonstrates that Standard-Model predictions are highly sensitive to experimental errors, complicating searches for new physics.

Contribution

It provides both analytical and numerical calculations of King-plot nonlinearities within the Standard Model, highlighting their sensitivity to nuclear charge radius uncertainties.

Findings

Standard-Model predicts King-plot nonlinearities are highly sensitive to nuclear radius errors

Analytical model applicable to arbitrary atoms

Numerical calculations performed for one-electron ions

Abstract

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 the new physics. In the present work 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.