Theoretical Accuracy of P-State Lamb Shifts

The Lamb shift theory of P-states is in a better shape than the theory of P-states. Corrections of order a(Za) are now known with uncertainty about 1 Hz for 2P states [10, 11, 12, 13]. 

State-independent contributions to the Lamb shift scale as 1/n and vanish in the difference Z = n Pi(nP) — EL nS), which may be calculated more 

Many experiments on the precise measurement of the classic Lamb shift were performed since its experimental discovery in 1947. We have collected modern post 1979 experimental results in Table 12.2. Two entries in this Table are changed compared to the original published experimental results [16, 15]. These alterations reflect recent improvements of the theory used for extraction of the Lamb shift value from the raw experimental data. 

Accuracy of the radiofrequency measurements of the classic 2S — 2P Lamb shift [15, 16, 23, 24, 25] is limited by the large (about 100 MHz) natural width of the 2P state, and cannot be significantly improved. New perspectives in reducing the experimental error bars of the classic 2S — 2P Lamb shift were opened with the development of the Doppler-free two-photon laser spectroscopy for measurements of the transitions between the energy levels with different principal quantum numbers. Narrow linewidth of such transi- 

Both the theoretical and experimental data for the classic 2S i/2 — 2Pi/2 Lamb shift are collected in Table 12.2. Theoretical results for the energy shifts in this Table contain errors in the parenthesis where the first error is determined by the yet uncalculated contributions to the Lamb shift, discussed above, and the second reflects the experimental uncertainty in the measurement of the proton rms charge radius. We see that the uncertainty of the proton rms radius is the largest source of error in the theoretical prediction of the classical Lamb shift. An immediate conclusion from the data in Table 12.2 is that the value of the proton radius [27] recently derived form the analysis of the world data on the electron-proton scattering seems compatible with the experimental data on the Lamb shift, while the values of the rms proton radius popular earlier [28, 29] are clearly too small to accommodate the experimental data on the Lamb shift. Unfortunately, these experimental results are rather widely scattered and have rather large experimental errors. Their internal consistency leaves much to be desired. 

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