Remeasurement of the2S122−2P322Splitting in Atomic Hydrogen

We have completed a remeasurement of the $2{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}-2\mathrm{}{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ energy separation in atomic hydrogen, using an atomic beam microwave technique. The final result obtained from measurements on four resonances is 9911.173 ± 0.042 MHz. When this is combined with the recent remeasurement by Robiscoe of the $2{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}-2\mathrm{}{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ energy separation, we obtain a value for the fine-structure splitting $\Delta E$ and the fine-structure constant ${\alpha }^{-1\mathrm{}}=137.035\mathrm{}8\left(5\right)\mathrm{}$.