Three-Loop Slope of the Dirac Form Factor and the 1S Lamb Shift in Hydrogen

The last unknown contribution to hydrogen energy levels at order mα^{7}, due to the slope of the Dirac form factor at three loops, is evaluated in a closed analytical form. The resulting shift of the hydrogen nS energy level is found to be 3.016/n^{3} kHz. Using the QED calculations of the 1S Lamb s...

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Bibliographic Details
Published in:Physical review letters 2000-02, Vol.84 (8), p.1673
Main Authors: Melnikov, K, van Ritbergen, T
Format: Article
Language:English
Online Access:Get full text
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Summary:The last unknown contribution to hydrogen energy levels at order mα^{7}, due to the slope of the Dirac form factor at three loops, is evaluated in a closed analytical form. The resulting shift of the hydrogen nS energy level is found to be 3.016/n^{3} kHz. Using the QED calculations of the 1S Lamb shift, we extract a precise value of the proton charge radius r_{p}=0.883±0.014 fm.
ISSN:0031-9007