Fine Structure of the Hydrogen Atom. IV

Phys. Rev. 86, 1014 – Published 15 June 1952
Willis E. Lamb, Jr. and Robert C. Retherford


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 2S122-2P122 is 1058.27 Mc/sec for hydrogen and 1059.71 Mc/sec for deuterium, each with a limit of error ±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 2P322-2P122 separation for deuterium is 10,972.11 Mc/sec (limit of error ±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 α. The result for 1α=137.033 (limit of error ±0.006) is in distinct disagreement with the value 1α=137.0429±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 Zα2, and is still in doubt because of reduced mass effects and spatial extent of nuclear magnetism.


  • Received 29 February 1952
  • Published in the issue dated June 1952

© 1952 The American Physical Society

Authors & Affiliations

Willis E. Lamb, Jr.* and Robert C. Retherford

  • Radiation Laboratory, Columbia University, New York, New York

  • *Present address. Department of Physics, Stanford University, Stanford, California. This author is responsible for the calculation of theoretical and experimental corrections.
  • Present address: Department of Electrical Engineering, University of Wisconsin, Madison, Wisconsin.

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