Magnetic Moment of the Proton in Bohr Magnetons

The magnetic moment of the proton has been measured by observing simultaneously an electronic and a nuclear magnetic transition in atomic hydrogen. Observations were made with a hydrogen maser operating in a 3500-G field. A theory is presented for the transient response of a three-level system under conditions of double resonance including effects of cavity pulling, spin-exchange collisions, and frequency shifts due to motional field narrowing. The electron-proton $g$-factor ratio in hydrogen is found to be $\frac{{g}_{j}(\mathrm{H})}{{g}_{p}(\mathrm{H})}=\frac{{\ensuremath{\mu}}_{j}(\mathrm{H})}{{\ensuremath{\mu}}_{p}(\mathrm{H})}=\ensuremath{-}658.210706(6)$. This leads to a value of the proton moment in Bohr magnetons of $\frac{{\ensuremath{\mu}}_{p}}{{\ensuremath{\mu}}_{B}}=1.521032181(15)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$.