Two-loop self-energy correction in H-like ions

Abstract

A part of the two-loop self-energy correction, the so-called P term, is evaluated numerically for the 1s state to all orders in Zα. Our calculation, combined with the previous investigation [S. Mallampalli and J. Sapirstein, Phys.Rev. A 57, 1548 (1998)], yields the total answer for the two-loop self-energy correction in H-like uranium and bismuth. As a result, the major uncertainty is eliminated from the theoretical prediction for the Lamb shift in these systems. The total value of the ground-state Lamb shift in H-like uranium is found to be 463.93(50) eV.

Improved theoretical prediction for the 2s hyperfine interval in helium ion

“…It is of approximately the same value as contributions to the error budget in [3] from the two-loop corrections and the higher-order nuclear-size effects. A conclusion of the present investigation is that it was originally underestimated [5] and actually it is approximately four times larger and thus gives the dominant effect to the uncertainty.…”

“…Since we consider logarithmic coefficients of order of unity in the natural units, any more accurate result may be achieved only on base of additional information and we consider the uncertainty in [5] as unappropriate.…”

“…in the range of the input data for the extrapolation. The data [5] for Z below 10 look correlated and uncertain and we do not use them for the fitting. The same was done in [5].…”

“…The natural values of the unknown coefficients are pretty large and their underestimation should lead to a serious overestimation of the accuracy of the extrapolation C(Z) to Z = 1, 2 (cf. [5]). …”

“…The results of [5] and this paper were obtained by fitting the numerical data obtained in [5] for a medium Z region, while the value of interest is related to Z = 1, 2 . The calculation itself is a complicated problem, in fact much more complicated than the extrapolation.…”