Determination of the Atomic-Hydrogen Fine Structure by Level Crossing in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>2</mml:mn><mml:mi>P</mml:mi></mml:math>States of Hydrogen, a Measurement of the Fine-Structure Constant

Abstract

The Sommerfeld fine-structure constant $\ensuremath{\alpha}$ 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 $E(^{2}P_{\frac{3}{2}})\ensuremath{-}E(^{2}P_{\frac{1}{2}})=10969.13(0.10)$ MHz and ${\ensuremath{\alpha}}^{\ensuremath{-}1}=137.0354(6)$. The quoted uncertainty represents our estimate of 70% confidence from the analysis of 84 separate runs.