Heidelberg 1999 – wissenschaftliches Programm

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A: Atomphysik

A 3: Spektroskopie II

A 3.4: Vortrag

Montag, 15. März 1999, 17:15–17:30, TE2

Numerische Berechnung der Lamb Shift für kleine Kernladung — •Ulrich Jentschura¹, Peter Mohr², and Gerhard Soff¹ — ¹Institut für Theroretische Physik, TU Dresden, 01062 Dresden — ²National Institute of Standards and Technology, Gaithersburg MD20899, USA

We present a high-precision numerical evaluation of the self energy in hydrogenlike ions with the low nuclear charge numbers Z = 1-5. The difference between the sum of the analytically evaluated terms up to the order of α (Zα)⁶ and our all-order numerical result is 28 kHz for atomic hydrogen and 3200 kHz for He⁺. The numerical calculation is non-perturbative in the external binding field, and we obtain results for the self-energy remainder function G_SE(Zα) with a precision of roughly 0.8 Hz for hydrogen and 13 Hz for ionized helium. Resummation and convergence acceleration techniques are used in the calculation. The numerical techniques lead to a reduction in computer time by three orders of magnitude and thereby remove the principal numerical difficulties associated with the singularity of the relativistic propagators for nearly equal radial arguments.