Precision Measurement of the Hyperfine Interval of Muonium by a Novel Technique: Ramsey Resonance in Zero Field

Abstract

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 $T$) to muonium, and observing the change in muon polarization at $t>T+2\ensuremath{\tau}$. By extrapolating two low-pressure runs in Kr we obtain $\ensuremath{\Delta}\ensuremath{\nu}(0)=4463.3013(40)$ MHz, while a joint fit with earlier Chicago Kr data gives $\ensuremath{\Delta}\ensuremath{\nu}(0)=4463.3012(23)$ (0.5 ppm). With $\frac{{f}_{\ensuremath{\mu}}}{{f}_{p}}=3.183338(13)$ this implies (a) ${\ensuremath{\alpha}}^{\ensuremath{-}1}\ensuremath{-}137=0.03619(30)$ (2.2 ppm) and (b) a proton polarizability ${{\ensuremath{\delta}}_{N}}^{(2)}=\ensuremath{-}(4\ifmmode\pm\else\textpm\fi{}4)$ ppm.