Abstract
The Lamb shift in the light hydrogenlike atoms is evaluated for the state-dependent part of the S states (n(3) Delta E-n - Delta E-1)/n(3) and P-1/2 states by means of a recently proposed relativistic generalization of multipole expansion. We obtain the results for Z = 1-5 and n = 2-10, where Z is the charge of the nucleus and n is the principal quantum number of the state under consideration.
The results are in an excellent agreement with the results obtained by means of Z alpha expansion truncated after the alpha(Z alpha)(6) term. The state-dependent part of the S states for n = 2-4 is evaluated also for the case of moderately strong Coulomb fields, Z = 10-50.
It is argued that the present results for the state-dependent part of the S states for low Z are the most accurate results given so far in the literature. In the case of hydrogen the uncertainty is significantly less than 1 Hz.
Finally, the extrapolation of the results to infinite n is performed.