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 $\frac{g_j\left(\mathrm{H}\right)}{g_p\left(\mathrm{H}\right)}=\frac{{\mu }_j\left(\mathrm{H}\right)}{{\mu }_p\left(\mathrm{H}\right)}=-658.210\mathrm{}706\left(6\right)\mathrm{}$. This leads to a value of the proton moment in Bohr magnetons of $\frac{{\mu }_p}{{\mu }_B}=1.521\mathrm{}032181\left(15\right)\mathrm{}\times {10}^{-3\mathrm{}}$.