Nuclear polarization and the contributions of relativistic effects to King plot nonlinearity

Abstract

The effect of nuclear polarization on the nonlinearities of a King plot for isotope shift in ${\mathrm{Ca}}^{+},$ ${\mathrm{Sr}}^{+},$ and ${\mathrm{Yb}}^{+}$ ions is studied. These ions are currently used in search for the manifestation of new interaction via nonlinearities of the 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 ${F}^{\ensuremath{''}}\ensuremath{\delta}\ensuremath{\langle}{r}^{\ensuremath{\lambda}}\ensuremath{\rangle},$ where the value of $\ensuremath{\lambda}$ is the result of numerical relativistic calculations $[2\ensuremath{\gamma}<\ensuremath{\lambda}<2,$ $\ensuremath{\gamma}=\sqrt{1\ensuremath{-}{(Z/137.036)}^{2}}]$. Using this ansatz, we demonstrate that the contribution of the relativistic effects to the nonlinearity in spherical nuclei is very small.