Muonium. IV. Precision Measurement of the Muonium Hyperfine-Structure Interval at Weak and Very Weak Magnetic Fields

A complete discussion is given of our precision measurement of the hyperfine-structure interval $\Delta \nu$ of the ground state of muonium at a weak magnetic field ($\sim 3$ G) using the resolved transitions $(F,M_F)=(1,\pm 1)\to \mathrm{}(0,0)\mathrm{}$, and at a very weak magnetic field ($\sim 10$ mG) using unresolved transitions $\Delta F=\pm 1$. The method of magnetic resonance studies of muonium is used, where a single oscillatory field is employed and the resonance line is swept by varying the applied frequency. This research yielded values for the coefficients of the linear hfs density shifts for muonium in argon and krypton at a temperature of approximately 20°C: ${}_{a\mathrm{M}-\mathrm{A}\mathrm{r}}=-5.00\mathrm{}\left(22\right)\mathrm{}\times \frac{{10}^{-9\mathrm{}}}{\mathrm{torr}}$, $a_{\mathrm{M}-\mathrm{K}\mathrm{r}}=-10.57\mathrm{}\left(39\right)\mathrm{}\times \frac{{10}^{-9\mathrm{}}}{\mathrm{torr}}$, and also for the quadratic hfs pressure-shift coefficients: $b_{\mathrm{M}-\mathrm{A}\mathrm{r}}=8.1\mathrm{}\left(2.5\right)\mathrm{}\times \frac{{10}^{-15\mathrm{}}}{{\left(\mathrm{torr}\right)}^2}$, $b_{\mathrm{M}-\mathrm{K}\mathrm{r}}=8.6\mathrm{}\left(5.9\right)\mathrm{}\times \frac{{10}^{-15\mathrm{}}}{{\left(\mathrm{torr}\right)}^2}$. The value obtained for $\Delta \nu$ is $\Delta \nu =4463.308\mathrm{}\left(11\right)\mathrm{}$ MHz (2.5 ppm), where the 1-standard-deviation error is principally a statistical counting error. Our result for $\Delta \nu$ is in good agreement with other measurements of $\Delta \nu$ and also with the current theoretical value.