Relativistic, QED, and nuclear mass effects in the magnetic shielding of $^3$He

Abstract

The magnetic shielding $\sigma$ of $^3$He is studied. The complete relativistic corrections of order $O(\alpha^2)$, leading QED corrections of order $O(\alpha^3 \ln\alpha)$, and finite nuclear mass effects of order $O(m/m_{\rm N})$ are calculated with high numerical precision. The resulting theoretical predictions for $\sigma = 59.967~43(10)\cdot 10^{-6}$ are the most accurate to date among all elements and support the use of $^3$He as a NMR standard.