Muonium. III. Precision Measurement of the Muonium Hyperfine-Structure Interval at Strong Magnetic Field

A complete discussion is given of our precision measurement of the hyperfine-structure interval $\Delta \nu$ of the ground state of muonium at a strong magnetic field of 5000 G. Particular emphasis is placed on refinements to the theory of the resonance line shape and on a detailed discussion of the sources of error and of the capability of our method. The final result for $\Delta \nu$ is $\Delta \nu =4463.24\mathrm{}\pm 0.12$ MHz (27 ppm), in which the 1-standard-deviation error is caused principally by the statistical counting error and magnetic field inhomogeneity. Allowance is included for a quadratic as well as a linear dependence of $\Delta \nu$ on pressure. This result is in good agreement with other, more precise, experimental values and with the current theoretical value $\Delta \nu =4463.326\mathrm{}\pm 0.019$ MHz (4.2 ppm).