King plots constructed from combinations of mass-weighted atomic isotope shifts provide a sensitive technique to search for electron-neutron interactions beyond the standard model mediated by a light boson. Using high-precision variational wave functions in Hylleraas coordinates, we present a comprehensive survey of all possible King plots arising from states of ${\mathrm{Li}}^{+}$ up to principal quantum number $n=10$ and angular momentum $L=7$ in order to identify the ones most sensitive to new physics. A major limitation in previous work due to second-order mass polarization is eliminated by the introduction of a second-King plot defined in terms of second differences. The residual theoretical uncertainty is then of the order of ${\alpha }^2{(\mu /M)}^3\sim 0.4$ Hz, where $\alpha$ is the fine-structure constant and $\mu$ is the reduced electron mass for a nucleus of mass $M$. Test results are presented for the ${}^A{\mathrm{Li}}^{+}$ isotope sequence with $A=6,7,8,9,11$ and are compared with other methods, including the ${\mathrm{Yb}}^{+}$ case recently studied both experimentally and theoretically. It is shown that the second-King plots for ${\mathrm{Li}}^{+}$ have about the same sensitivity to new physics as the ${\mathrm{Yb}}^{+}$ case for boson masses up to about 10 keV, and nuclear size uncertainties (including nuclear polarization) are suppressed. This greatly extends the sensitivity to new physics for light two-electron systems.

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• Atomic spectra
• Electron correlation calculations for atoms & ions
• Exotic atoms & molecules