Bethe, H.A.; The Electromagnetic Shift of Energy Levels
Phys. Rev. 72 (1947) 339;
Reprinted in The Physical Review - the First Hundred Years, AIP Press (1995) 949.
Selected Papers on Quantum Electrodynamics, editor J. Schwinger, Dover Publications, Inc., New York (1958) 139.
The reported difference of energy of the 2s and 2p levels of H, in contradiction to the Dirac theory, is explained as an interaction energy of the electron with the radiation field. The calculated and observed values are in good agreement. The correction used is the difference of the interaction energies of the bound electron with the field, and that of a free electron with the same kinetic energy, since the latter is interpreted as part of the electronic mass. Calculation using
non-relativistic radiation theory shows that this difference is still logarithmically divergent and infty. A finite value is obtained by cutting off the spectrum at an upper energy limit of mc2, since a relativistic calculation using hole theory is likely to give a finite result not differing essentially from this value. (Science Abstracts, 1947, 3608. G. J. K.).
Related references See also E. A. Uehling, Phys. Rev. 48 (1935) 55;
Analyse data from W. V. Houston, Phys. Rev. 51 (1937) 446;
E. C. Kemble and R. D. Present, Phys. Rev. 44 (1933) 1031;
S. Pasternack, Phys. Rev. 54 (1938) 113;
W. E. Lamb and R. C. Retherford, Phys. Rev. 72 (1947) 241;
R. C. Williams, Phys. Rev. 54 (1938) 558;
First theoretical calculation of the Lamb shift in non-relativistic QED.