Precision measurement of the ${}^{43}$Ca${}^{+}$ nuclear magnetic moment

Abstract

We report precision measurements of the nuclear magnetic moment of \textsuperscript{43}Ca\textsuperscript{+}, made by microwave spectroscopy of the 4s ${}^2$S${}_{1/2}$ $|F=4,M=0⟩\to |F=3,M=1⟩$ ground level hyperfine clock transition at a magnetic field of $\approx$ 146 G, using a single laser-cooled ion in a Paul trap. We measure a clock transition frequency of $f=3199941076.920\pm 0.046$ Hz, from which we determine ${\mu }_I/{\mu }_{\mathrm{N}}=-1.315350(9)(1)$, 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 ${\mu }_I$ value, in combination with previous NMR results, to extract the change in shielding constant of calcium ions due to solvation in D${}_2$O: $\Delta \sigma =-0.00022(1)$.

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