Determination of the magnetic moment of a $^{23}$Na nucleus using an NMR spectrometer with simultaneous detection of signals from two nuclei

Experimental results on measuring the resonance frequency ratio of the protons of water and of $^{23}$Na nuclei in NaCl solutions with concentrations from 0.1 to 0.5 g per 100 g H$_2$O are presented. Signals of water protons and sodium nuclei were acquired simultaneously, which allowed minimizing random and systematic uncertainties in measurements of the ratio of resonance frequencies $f$(H$_2$O)/$f$($^{23}$Na$^+$) to the level of one billionth. Extrapolation of the content of NaCl in water to zero for individual ions in water yielded the value $f$(H$_2$O)/$f$($^{23}$Na$^+$) = 3.780463993(25). Using the known data on the magnetic moment of proton and on the shielding of protons and sodium ions in water, the magnetic moment of sodium nuclei was found to be $\mu$($^{23}$Na) = 2.2175065(55). The new result is discussed in the light of data obtained by other authors.