Fine Structure of the Hydrogen Atom. IV

Abstract

The fourth paper of this series contains an analysis of measurements made in 1950 on the fine structure of hydrogen and deuterium. After application of numerous experimental and theoretical corrections the following results are obtained. The displacement $2^{2}S_{\frac{1}{2}}\ensuremath{-}2^{2}P_{\frac{1}{2}}$ is 1058.27 Mc/sec for hydrogen and 1059.71 Mc/sec for deuterium, each with a limit of error \ifmmode\pm\else\textpm\fi{}1.0 Mc/sec. There seems to be satisfactory agreement between these and the most recently calculated values. The difference of 1.44 Mc/sec between deuterium and hydrogen is compatible with an explanation based on reduced mass effects and the finite extension of the deuteron.The $2^{2}P_{\frac{3}{2}}\ensuremath{-}2^{2}P_{\frac{1}{2}}$ separation for deuterium is 10,972.11 Mc/sec (limit of error \ifmmode\pm\else\textpm\fi{}1.0 Mc/sec). With assumption of a well-justified theoretical formula for the doublet splitting, one may calculate a value for the fine structure constant $\ensuremath{\alpha}$. The result for $\frac{1}{\ensuremath{\alpha}}=137.033$ (limit of error \ifmmode\pm\else\textpm\fi{}0.006) is in distinct disagreement with the value $\frac{1}{\ensuremath{\alpha}}=137.0429\ifmmode\pm\else\textpm\fi{}0.0009$ derived from the hyperfine splitting of the ground state of hydrogen. The formula used for this was in error due to neglect of corrections of relative order $Z{\ensuremath{\alpha}}^{2}$, and is still in doubt because of reduced mass effects and spatial extent of nuclear magnetism.