Lamb shift comparison between theoretical

Prom the theoretical point of view the accuracy of calculations is limited by the magnitude of the yet uncalculated contributions to the Lamb shift. Corrections to the P levels are known now with a higher accuracy than the corrections to the S levels, and do not limit the results of the comparison between theory and experiment. 

This experimental development was matched by rapid theoretical progress, and the comparison and interplay between theory and experiment has been important in the field of metrology, leading to higher precision in the determination of the fundamental constants. We feel that now is a good time to review modern bound state theory. The theory of hydrogenic bound states is widely described in the literature. The basics of nonrelativistic theory are contained in any textbook on quantum mechanics, and the relativistic Dirac equation and the Lamb shift are discussed in any textbook on quantum electrodynamics and quantum field theory. An excellent source for the early results is the classic book by Bethe and Salpeter [6]. A number of excellent reviews contain more recent theoretical results, and a representative, but far from exhaustive, list of these reviews includes [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]. 

The above does not mean that the subject has become boring and moribund. On the contrary, great theoretical issues are at stake. For the earlier Born approximations did not really test the deeper field-theoretic aspects of the theory, whereas the present comparisons between theory and experiment are sensitive to these elements. They play a role almost like that of the Lamb shift in establishing the validity of quantum electrodynamics (QED). 

Comparison between scaled theoretical and experimental one-electron Lamb shifts, expressed as deviations from the theoretical mjjn. The upper horizontal line for each ion is Erij son s theory and the lower horizontal line is Mohr s theory and S is the average of the two. The experimental data are labelled by the method of measurement according to (0) microwave resonance (a) anisotropy measurement (+) quench-rate measurement ( ) laser resonance. The dashed lines are the Borie corrections to the theoretical values. (From Drake )... 

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