Fine Structure of the Hydrogen Atom. VI

Abstract

Measurements of improved accuracy of transition frequencies from the $2^{2}S_{\frac{1}{2}}(m=+\frac{1}{2})$ state to several of the $2^{2}P_{\frac{3}{2}}$ magnetic sub-states in deuterium are presented and analyzed. The shape of the observed resonance curves is discussed and compared with theory.The experimental result is given for the $2^{2}P_{\frac{3}{2}}\ensuremath{-}2^{2}S_{\frac{1}{2}}$ separation, $\ensuremath{\Delta}{E}_{\mathrm{D}}\ensuremath{-}{\mathcal{S}}_{\mathrm{D}}=9912.59\ifmmode\pm\else\textpm\fi{}0.10$ Mc/sec, for deuterium. This is combined with the result for ${\mathcal{S}}_{\mathrm{D}}$ from the preceding article to obtain the $2^{2}P_{\frac{3}{2}}\ensuremath{-}2^{2}P_{\frac{1}{2}}$ separation, $\ensuremath{\Delta}{E}_{\mathrm{D}}=10,971.59\ifmmode\pm\else\textpm\fi{}0.20$ Mc/sec for deuterium. From $\ensuremath{\Delta}{E}_{\mathrm{D}}$ and the auxiliary constants ${R}_{\mathrm{D}}$ and $c$ a new value is computed for the fine structure constant $\ensuremath{\alpha}=\frac{1}{(137.0365\ifmmode\pm\else\textpm\fi{}0.0012)}$. The uncertainty stated is considered to be a limit of error for our experimental procedure without allowance for the uncertainty of the auxiliary constants.