Precision measurement of the Ca+43 nuclear magnetic moment

We report precision measurements of the nuclear magnetic moment of $^{43}\mathrm{Ca}^{+}$, made by microwave spectroscopy of the $4s\phantom{\rule{0.16em}{0ex}}^{2}S_{1/2}|F=4,\phantom{\rule{0.28em}{0ex}}M=0\ensuremath{\rangle}\ensuremath{\rightarrow}|F=3,\phantom{\rule{0.28em}{0ex}}M=1\ensuremath{\rangle}$ ground level hyperfine clock transition at a magnetic field of $\ensuremath{\approx}146\phantom{\rule{0.16em}{0ex}}\mathrm{G}$, using a single laser-cooled ion in a Paul trap. We measure a clock-transition frequency of $f=3\phantom{\rule{0.16em}{0ex}}199\phantom{\rule{0.16em}{0ex}}941\phantom{\rule{0.16em}{0ex}}076.920(46)\phantom{\rule{0.28em}{0ex}}\mathrm{Hz}$ from which we determine ${\ensuremath{\mu}}_{I}/{\ensuremath{\mu}}_{N}=\ensuremath{-}1.315\phantom{\rule{0.16em}{0ex}}350(9)(1)$ where the uncertainty (9) arises from uncertainty in the hyperfine $A$ constant, and the (1) arises from the uncertainty in our measurement. This measurement is not corrected for diamagnetic shielding due to the bound electrons. We make a second measurement which is less precise but agrees with the first. We use our ${\ensuremath{\mu}}_{I}$ value in combination with previous NMR results to extract the change in shielding constant of calcium ions due to solvation in ${\mathrm{D}}_{2}\mathrm{O}\text{:}\phantom{\rule{0.16em}{0ex}}\mathrm{\ensuremath{\Delta}}\ensuremath{\sigma}=\ensuremath{-}0.000\phantom{\rule{0.16em}{0ex}}22(1)$.