Magnetic moment of ${}^{207}\mathrm{Pb}$ and the hyperfine splitting of ${}^{207}\mathrm{Pb}^{81+}$

We performed nuclear magnetic resonance measurements on lead(II) nitrate $\mathrm{Pb}{\left({\mathrm{NO}}_3\right)}_2$ in aqueous solution and on the hexafluoridoplumbate(IV) ${\left[{\mathrm{PbF}}_6\right]}^{2-}$ ion in acetonitrile. Combined with new relativistic coupled cluster and relativistic density functional theory calculations of the shielding constant, we obtained a magnetic moment of $\mu {(}^{207}\mathrm{Pb})=0.59102\left(18\right){\mu }_N$ that is in clear disagreement with the tabulated value of $+0.592583\left(9\right){\mu }_N$. Similarly as in the case of ${}^{209}\mathrm{Bi}$ this might be caused by an underestimated chemical shift in the aqueous solution of the nitrate. The consequences for a test of QED in strong magnetic fields by laser spectroscopy of the hyperfine splitting in ${\mathrm{Pb}}^{81+}$ and for the magnetic moments of short-lived lead isotopes are discussed.

Figure 1

${}^{207}\mathrm{Pb}$ NMR spectra obtained for (a) lead(II) nitrate in an aqueous solution and (b) for hexafluorido-plumbate(IV) ions in acetonitrile. The outermost satellites of the ${\left[{\mathrm{PbF}}_6\right]}^{2-}$-septett are barely visible.

Figure 2

Temperature dependence of the resonance frequencies for the two sample types. Below the axis break the temperature-dependent frequency ratios ${\nu }_{\mathrm{Pb}}/{\nu }_{\mathrm{H}}$ (H in TMS) for aqueous $\mathrm{Pb}{\left({\mathrm{NO}}_3\right)}_2$ solutions are shown for three sample concentrations. The ratio shifts by more than 160 ppm across a temperature range of 100 K. In the case of ${\left[{\mathrm{PbF}}_6\right]}^{2-}$, plotted above the axis break, the shift is less than 5 ppm/80 K.

Figure 3

NMR spectra obtained for ${\left[\mathrm{N}{\left({\mathrm{C}}_2{\mathrm{H}}_5\right)}_4\right]}_2\left[{\mathrm{PbF}}_6\right]$ in acetonitrile with (a) ${}^1\mathrm{H}$ NMR and (b) ${}^{19}\mathrm{F}$ NMR after synthesis.