Precision Experiments on Muonium. III. Ramsey Resonance in Zero Field

A novel method for measuring the hyperfine interval $\Delta \nu$ of muonium in zero magnetic field is described. It consists in applying two successive coherent microwave pulses (lengths $\tau$, separation $T+\tau$) to muonium, and observing the change in muon polarization at $t>T+2\mathrm{}\tau$. By linearly extrapolating two low-pressure runs in Kr together with earlier Chicago data, we obtain $\Delta \nu \mathrm{}\left(0\right)=4463301.2\mathrm{}\left(2.3\right)\mathrm{}$ kHz (0.5 ppm). A joint fit of all available data in Ar and Kr yields $\Delta \nu \mathrm{}\left(0\right)=4463304.4\mathrm{}\left(2.3\right)\mathrm{}$ kHz. With $\frac{{\mu }_{\mu }}{{\mu }_p}=3.183349\mathrm{}\left(15\right)\mathrm{}$ the latter implies (a) ${\alpha }^{-1\mathrm{}}-137=0.03631\mathrm{}\left(32\right)\left(2.4\mathrm{} \mathrm{ppm}\right)$, and (b) a proton polarizability ${\delta }_p^{\prime }=5.4\mathrm{}\left(4.8\right)\mathrm{}$ ppm.