Bethe logarithm relativistic

The closest theoretical result, the Unified theory [68], differs by more than 300 times the experimental uncertainty. This discrepancy should be partially removed by analysis including an estimate of the order (Za)4a2mec2 relativistic term and a complete calculation of the two-electron Bethe-logarithm [92]. The 14,i5N5+ 21S o — 23Pi isotope shift was measured to be —1.6623(10) cm-1, in fair agreement with an estimate based on [68]. The hyperfine corrected 3Pq —3Pi... 

The total relativistic and QED energy shift for many-electron atoms consists of two parts. The first part contains the Bethe logarithm and the other is the average value of some effective potential. Throughout the exact nonrelativistic (Schrddinger) wave functions for the many-electron atom are used. The energy shift is [50] ... 

This paper reviews progress in the application of atomic isotope shift measurements, together with high precision atomic theory, to the determination of nuclear radii from the nuclear volume effect. The theory involves obtaining essentially exact solutions to the nonrelativistic three- and four-body problems for helium and lithium by variational methods. The calculation of relativistic and quantum electrodynamic corrections by perturbation theory is discussed, and in particular, methods for the accurate calculation of the Bethe logarithm part of the electron self energy are presented. The results are applied to the calculation of isotope shifts for the short-... 

The principle message of this paper is that few-body atomic systems such as helium and lithium can be solved essentially exactly for all practical purposes in the nonrelativistic limit, and there is a systematic procedure for calculating the relativistic and other higher-order QED corrections as perturbations. The solution of the problem of calculating Bethe logarithms means that the theoretical energy levels are complete up to and including terms of order Ry. 

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