Determination of the Atomic-Hydrogen Fine Structure by Level Crossing in the $2P$ States of Hydrogen, a Measurement of the Fine-Structure Constant

The Sommerfeld fine-structure constant $\alpha$ has been determined from a direct measurement of the fine-structure separation in the $2P$ states of atomic hydrogen using the level-crossing technique. From the changes in resonance fluorescence caused by level crossing at 3484 G, we obtain a value for the fine-structure separation $E\left({}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\right)-E\left({}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}\right)=10\mathrm{}969.13\left(0.10\right)\mathrm{}$ MHz and ${\alpha }^{-1\mathrm{}}=137.0354\mathrm{}\left(6\right)\mathrm{}$. The quoted uncertainty represents our estimate of 70% confidence from the analysis of 84 separate runs.