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

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 ${\mu }_I{(}^{209}\mathrm{Bi})$ 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 ${\mu }_I{(}^{209}\mathrm{Bi})$ 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.

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