A gaseous $^{\mathrm{3}}$He NMR probe at 4.2K for precision measurements of electron and positron magnetic moments

A 4.2 K cold bore magnet is used in the new electron's and positron's magnetic moments experiment. In order to optimize the homogeneity of the magnet at 5 Tesla, a gaseous $^{\mathrm{3}}$He NMR probe based on a two-volume method is developed. A high signal-to-noise ratio comparable to a room temperature water NMR probe is achieved, and the relaxation time constants T$_{\mathrm{1}}$, T$_{\mathrm{2}}$, and T$_{\mathrm{2}}^{\mathrm{\ast }}$ have been measured. We also discuss the stability and the homogeneity of the cold bore magnet studied with the $^{\mathrm{3}}$He probe.