Relativistic treatment of diamagnetic susceptibility of helium

We report theoretical calculations of the diamagnetic susceptibility, ${\chi }_0$, of helium atom. We determined the complete relativistic correction to ${\chi }_0$ of the order of ${\alpha }^4$, where $\alpha$ is the fine structure constant, by including all ${\alpha }^4$ terms originating from the Dirac and Breit equations for a helium atom in a static magnetic field. Finite nuclear mass corrections to ${\chi }_0$ was also evaluated. To obtain very accurate results and reliable uncertainty estimates we used a sequence of explicitly correlated basis sets of fully optimized Slater geminals. We found that ${\chi }_0=-2.119106(34)\cdot {10}^{-5}$ $a_0^3$ and ${\chi }_0=-2.119400(34)\cdot {10}^{-5}$ $a_0^3$ for ${}^4$He and ${}^3$He isotopes, respectively, where $a_0$ is the Bohr radius and the uncertainties shown in the parentheses are due entirely to the very conservative estimate of the neglected QED corrections of the order of ${\alpha }^5$. Our results are compared with the available experimental data and with previous, incomplete theoretical determinations of the ${\alpha }^4$ contributions to the diamagnetic susceptibility of helium.