Relativistic treatment of diamagnetic susceptibility of helium

Abstract

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 $\chi_0=-2.119\,106(34)\cdot10^{-5}$ $a_0^3$ and $\chi_0=-2.119\,400(34)\cdot10^{-5}$ $a_0^3$ 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.