Diamagnetic susceptibility of neon and argon including leading relativistic effects

We report theoretical calculations of the static diamagnetic susceptibility, ${\chi }_0$, of neon and argon atoms. The calculations were performed using a hierarchy coupled-cluster methods combined with application of both the Gaussian and Slater orbital basis sets. We included the complete relativistic correction of order of ${\alpha }^4$, where $\alpha$ is the fine structure constant, and obtained an estimate of the quantum electrodynamics (QED) contributions. The finite nuclear mass and size corrections were also considered but are found to be small. The final results are ${\chi }_0=-8.4786(7)\cdot {10}^{-5}$ $a_0^3$ for the neon and ${\chi }_0=-22.9545(32)\cdot {10}^{-5}$ $a_0^3$ for the argon atom, where $a_0$ is the Bohr radius. The uncertainties in the last digits, shown in the parentheses, are primarily due to the errors in the non-relativistic electronic wavefunction, as well as due to the neglected quantum electrodynamics corrections.