Direct measurement of the 3 He + magnetic moments.

Helium-3 has nowadays become one of the most important candidates for studies in fundamental physics 1-3 , nuclear and atomic structure 4,5 , magnetometry and metrology 6 , as well as chemistry and medicine 7,8 . In particular, 3 He nuclear magnetic resonance (NMR) probes have been proposed as a new standard for absolute magnetometry 6,9 . This requires a high-accuracy value for the 3 He nuclear magnetic moment, which, however, has so far been determined only indirectly and with a relative precision of 12 parts per billon 10,11 . Here we investigate the 3 He + ground-state hyperfine structure in a Penning trap to directly measure the nuclear g-factor of 3 He + [Formula: see text], the zero-field hyperfine splitting [Formula: see text] Hz and the bound electron g-factor [Formula: see text]. The latter is consistent with our theoretical value [Formula: see text] based on parameters and fundamental constants from ref. 12 . Our measured value for the 3 He + nuclear g-factor enables determination of the g-factor of the bare nucleus [Formula: see text] via our accurate calculation of the diamagnetic shielding constant 13 [Formula: see text]. This constitutes a direct calibration for 3 He NMR probes and an improvement of the precision by one order of magnitude compared to previous indirect results. The measured zero-field hyperfine splitting improves the precision by two orders of magnitude compared to the previous most precise value 14 and enables us to determine the Zemach radius 15 to [Formula: see text] fm.