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.