Precision experiments on muonium. III. Ramsey resonance in zero field

A novel method for measuring the hyperfine interval $\ensuremath{\Delta}\ensuremath{\nu}$ of muonium in zero magnetic field is described. It consists in applying two successive coherent microwave pulses (lengths $\ensuremath{\tau}$, separation $T+\ensuremath{\tau}$) to muonium, and observing the change in muon polarization at $tgT+2\ensuremath{\tau}$. By linearly extrapolating two low-pressure runs in Kr together with earlier Chicago data, we obtain $\ensuremath{\Delta}\ensuremath{\nu}(0)=4463301.2(2.3)$ kHz (0.5 ppm). A joint fit of all available data in Ar and Kr yields $\ensuremath{\Delta}\ensuremath{\nu}(0)=4463304.4(2.3)$ kHz. With $\frac{{\ensuremath{\mu}}_{\ensuremath{\mu}}}{{\ensuremath{\mu}}_{p}}=3.183349(15)$ the latter implies (a) ${\ensuremath{\alpha}}^{\ensuremath{-}1}\ensuremath{-}137=0.03631(32)(2.4 \mathrm{ppm})$, and (b) a proton polarizability ${\ensuremath{\delta}}_{p}^{\ensuremath{'}}=5.4(4.8)$ ppm.