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

TL;DR

This paper provides highly precise theoretical calculations of the magnetic shielding in helium-3, incorporating relativistic, quantum electrodynamics, and nuclear mass effects, confirming its suitability as an NMR standard.

Contribution

The study presents the most accurate theoretical predictions for helium-3's magnetic shielding, including comprehensive relativistic, QED, and nuclear mass corrections.

Findings

Calculated magnetic shielding: 59.96743(10)×10^{-6}

Inclusion of relativistic and QED corrections improves accuracy

Supports helium-3 as a reliable NMR standard.

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.