Precision Measurement of the Hyperfine Interval of Muonium by a Novel Technique: 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 $T$) to muonium, and observing the change in muon polarization at $t>T+2\mathrm{}\tau$. By extrapolating two low-pressure runs in Kr we obtain $\Delta \nu \mathrm{}\left(0\right)=4463.3013\mathrm{}\left(40\right)\mathrm{}$ MHz, while a joint fit with earlier Chicago Kr data gives $\Delta \nu \mathrm{}\left(0\right)=4463.3012\mathrm{}\left(23\right)\mathrm{}$ (0.5 ppm). With $\frac{f_{\mu }}{f_p}=3.183\mathrm{}338\left(13\right)\mathrm{}$ this implies (a) ${\alpha }^{-1}-137=0.036\mathrm{}19\left(30\right)\mathrm{}$ (2.2 ppm) and (b) a proton polarizability ${{\delta }_N}^{\mathrm{}\left(2\right)\mathrm{}}=-(4\mathrm{}\pm 4)$ ppm.