New Nuclear Magnetic Moment of $^{209}$Bi - Resolving the Bismuth Hyperfine Puzzle

TL;DR

This paper resolves the hyperfine puzzle for $^{209}$Bi by demonstrating that the previously tabulated nuclear magnetic moment was inaccurate, and providing a new, smaller value that aligns theory with experimental measurements.

Contribution

The study presents a new, more accurate value for the nuclear magnetic moment of $^{209}$Bi, resolving discrepancies between experimental hyperfine splitting measurements and theoretical predictions.

Findings

The tabulated nuclear magnetic moment of $^{209}$Bi was significantly overestimated.

Using the new magnetic moment aligns theoretical predictions with experimental results.

Relativistic calculations and NMR measurements were combined to determine the magnetic moment.

Abstract

A recent measurement of the hyperfine splitting in the ground state of Li-like $^{209}$Bi$^{80+}$ has established a "hyperfine puzzle" -- the experimental result exhibits a 7$\sigma$ deviation from the theoretical prediction [J. Ullmann et al., Nat. Commun. 8, 15484 (2017); J. P. Karr, Nat. Phys. 13, 533 (2017)]. We provide evidence that the discrepancy is caused by an inaccurate value of the tabulated nuclear magnetic moment ($\mu_I$) of $^{209}$Bi. We perform relativistic density functional theory and relativistic coupled cluster calculations of the shielding constant that should be used to extract the value of $\mu_I(^{209}{\rm Bi})$ and combine it with nuclear magnetic resonance measurements of Bi(NO$_3$)$_3$ in nitric acid solutions and of the hexafluoridobismuthate(V) BiF$_6^-$ ion in acetonitrile. The result clearly reveals that $\mu_I(^{209}{\rm Bi})$ is much smaller than the tabulated value used previously. Applying the new magnetic moment shifts the theoretical prediction into agreement with experiment and resolves the hyperfine puzzle.