New Nuclear Magnetic Moment of Bi209 : Resolving the Bismuth Hyperfine Puzzle

A recent measurement of the hyperfine splitting in the ground state of Li-like ${^{208}\mathrm{Bi}}^{80+}$ has established a ``hyperfine puzzle''---the experimental result exhibits a $7\ensuremath{\sigma}$ 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 (${\ensuremath{\mu}}_{I}$) of $^{209}\mathrm{Bi}$. We perform relativistic density functional theory and relativistic coupled cluster calculations of the shielding constant that should be used to extract the value of ${\ensuremath{\mu}}_{I}(^{209…