Direct measurement of the 3He+ magnetic moments

Helium-3 has nowadays become one of the most important candidates for studies in fundamental physics1–3, nuclear and atomic structure4,5, magnetometry and metrology6, as well as chemistry and medicine7,8. In particular, 3He nuclear magnetic resonance (NMR) probes have been proposed as a new standard for absolute magnetometry6,9. This requires a high-accuracy value for the 3He nuclear magnetic moment, which, however, has so far been determined only indirectly and with a relative precision of 12 parts per billon10,11. Here we investigate the 3He+ ground-state hyperfine structure in a Penning trap to directly measure the nuclear g-factor of 3He+ $${g}_{I}^{{\prime} }=-\,4.2550996069(30{)}_{{\rm{stat}}}(17{)}_{{\rm{sys}}}$$ g I ′ = − 4.2550996069 ( 30 ) stat ( 17 ) sys , the zero-field hyperfine splitting $${E}_{{\rm{HFS}}}^{\exp }=-\,8,\,665,\,649,\,865.77{(26)}_{{\rm{stat}}}{(1)}_{{\rm{sys}}}$$ E HFS exp = − 8 , 665 , 649 , 865.77 ( 26 ) stat ( 1 ) sys Hz and the bound electron g-factor $${g}_{e}^{{\rm{\exp }}}=-\,2.00217741579(34{)}_{{\rm{stat}}}(30{)}_{{\rm{sys}}}$$ g e exp = − 2.00217741579 ( 34 ) stat ( 30 ) sys . The latter is consistent with our theoretical value $${g}_{e}^{{\rm{theo}}}=-\,2.00217741625223(39)$$ g e theo = − 2.00217741625223 ( 39 ) based on parameters and fundamental constants from ref. 12. Our measured value for the 3He+ nuclear g-factor enables determination of the g-factor of the bare nucleus $${g}_{I}=-\,4.2552506997(30{)}_{{\rm{stat}}}(17{)}_{{\rm{sys}}}(1{)}_{{\rm{theo}}}$$ g I = − 4.2552506997 ( 30 ) stat ( 17 ) sys ( 1 ) theo via our accurate calculation of the diamagnetic shielding constant13 $${\sigma }_{{}^{3}{\mathrm{He}}^{+}}=0.00003550738(3)$$ σ 3 He + = 0.00003550738 ( 3 ) . This constitutes a direct calibration for 3He 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 value14 and enables us to determine the Zemach radius15 to $${r}_{Z}=2.608(24)$$ r Z = 2.608 ( 24 ) fm.