Precision Measurement of the Magnetic Moment of the Muon

A determination of the ratio of the muon to the proton magnetic moment, $\frac{{\mu }_{\mu }}{{\mu }_p}$, is described. The precession rate of positive muons was compared to that of protons in the same magnetic field and chemical environment. Attention is given to the points which bear on the accuracy of the result: timing, magnetic field, many systematic checks, and particularly the question of the chemical environment of the ${\mu }^{+}$. It is shown experimentally that the so-called "Ruderman correction"-the ionic state in water once tentatively proposed by Ruderman-does not occur. A physical effect which excludes the possibility of the ionic state is pointed out. Consistent results were obtained in three different media: water, NaOH solution, and an organic liquid. Chemical corrections were ≤ 2 ppm. The result, including residual uncertainties in the chemical corrections, is $\frac{{\mu }_{\mu }}{{\mu }_p}=3.1833467\mathrm{}\pm 0.0000082$ (2.6 ppm); in terms of the muon mass this implies $\frac{m_{\mu }}{m_e}=206.7682\mathrm{}\pm 0.0005$, or $m_{\mu }=105.6594\mathrm{}\pm 0.0004$ MeV. The new value for the muon moment, used with the most recent measurements of the muonium hyperfine interval, yields a value for the fine-structure constant of ${\alpha }^{-1\mathrm{}}=137.03632\mathrm{}\pm 0.00019$, an accuracy comparable with that of the current recommended value which depends primarily on the Josephson effect. The two numbers differ by 2.2 ppm, while the standard deviation of the difference is 2.1 ppm, which is satisfactory agreement.