Remeasurement ofΔE−Sin Atomic Hydrogen

Abstract

The $2{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}-2\mathrm{}{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ separation $\Delta E-\mathcal{S}$ in hydrogen has been measured by a microwave atomic-beam technique. The result obtained from four independent transitions is $\Delta E-\mathcal{S}=9911.173\mathrm{}\pm 0.042$ MHz. We combine this result with the recent determination of the Lamb shift $\mathcal{S}$ by Robiscoe to obtain a value for the fine-structure splitting $\Delta E$ and a value for the fine-structure constant ${\alpha }^{-1\mathrm{}}=137.0358\mathrm{}\left(5\right)\mathrm{}$.