Precision Experiments on Muonium. I. Determination of the Muonium Hyperfine Splitting in Low-Pressure Argon from a Field-Independent Zeeman Transition

The ground-state hyperfine interval $\ensuremath{\Delta}\ensuremath{\nu}$ of muonium has been redetermined in argon by measuring the (1, 1) \ensuremath{\leftrightarrow} (1, 0) Zeeman frequency ${\ensuremath{\nu}}_{1}$ at that external field value where $\frac{\ensuremath{\partial}{\ensuremath{\nu}}_{1}}{\ensuremath{\partial}B}=0$. The measurements were performed with good statistics at much lower pressures than heretofore, greatly reducing uncertainties in extrapolating to zero pressure. Our value, $\ensuremath{\Delta}\ensuremath{\nu}(0)=4463.313(18)$, disagrees with the linearly extrapolated values found in higher-pressure Ar and Kr by Crane et al. However, a new interpretation, namely, a pressure extrapolation based on a quadratic function with the linear coefficient fixed at the "atomic" value (i.e., assumption of no isotope dependence in the linear pressure shift), results in consistency between all present (data published before April, 1971) determinations of $\ensuremath{\Delta}\ensuremath{\nu}$.