High Precision Measurements of the Ground State Hyperfine Structure Interval of Muonium and of the Muon Magnetic Moment

High precision measurements of two Zeeman hyperfine transitions in the ground state of muonium in a strong magnetic field have been made at LAMPF using microwave magnetic resonance spectroscopy and a resonance line narrowing technique. These determine the most precise values of the ground state hyperfine structure interval of muonium $\ensuremath{\Delta}\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4463302765(53)\mathrm{Hz}$ $(12\mathrm{ppb})$, and of the ratio of magnetic moments ${\ensuremath{\mu}}_{\ensuremath{\mu}}/{\ensuremath{\mu}}_{p}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3.18334513(39)$ $(120\mathrm{ppb})$, representing a factor of 3 improvement. Values of the mass ratio ${m}_{\ensuremath{\mu}}/{m}_{e}$ and the fine structure constant $\ensuremath{\alpha}$ are derived from these results.