Nuclear polarisation and relativistic effects contributions to King plot non-linearity

TL;DR

This paper investigates how nuclear polarisation and relativistic effects influence the non-linearity of King plots in isotope shift measurements of Ca+, Sr+, and Yb+ ions, relevant for new physics searches.

Contribution

It introduces a method to separate electronic and nuclear variables using relativistic calculations and shows relativistic effects are minimal in spherical nuclei.

Findings

Nuclear polarisation has a small impact on King plot non-linearity.

Relativistic effects contribute negligibly to non-linearity in spherical nuclei.

The proposed method effectively isolates electronic and nuclear contributions.

Abstract

The effect of nuclear polarisation on the non-linearities of King plot for isotope shift in Ca$^+$, Sr$^+$ and Yb$^+$ ions is studied. These ions are currently used in search for the manifestation of new interaction via non-linearities of King plot. The role of relativistic effects is also studied. The best way to achieve separation of electronic and nuclear variables (which is necessary for the linearity) is to present the field shift as $F"\delta \langle r^{\lambda} \rangle$, where the value of $\lambda$ is the result of numerical relativistic calculations ($2\gamma < \lambda <2$, $\gamma = \sqrt{1-(Z/137.036)^2}$). Using this ansatz we demonstrated that the contribution of the relativistic effects to the non-linearity in spherical nuclei is very small.