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

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The Hydrogen Atom

Part of the book series: Lecture Notes in Physics ((LNP,volume 570))

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Abstract

The calculation of the last unknown contribution to hydrogen energy levels at order mα7, due to the three loop slope of the Dirac form factor, is described. The resulting shift of the nS energy level is found to be 3.16/n 3 kHz. Adding this result to many known contributions to the 1S Lamb shift and comparing with experimental value, we derive the value of the proton charge radius \( r_p = 0.883 \pm 0.014 \) fm.

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Author information

Authors and Affiliations

  1. Stanford Linear Accelerator Center, Stanford University, 94309, CA, USA

    Kirill Melnikov

  2. Institut für Theoretische Teilchenphysik, Universität Karlsruhe, D-76128, Karlsruhe, Germany

    Timo van Ritbergen

Authors
  1. Kirill Melnikov
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  2. Timo van Ritbergen
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Editor information

Editors and Affiliations

  1. D.I. Mendeleev Institute for Metrology, 198005, St. Petersburg, Russia

    Savely G. Karshenboim

  2. MPI for Quantum Optics, 85748, Garching, Germany

    Savely G. Karshenboim  & T.W. Hänsch  & 

  3. Scuola Normale Superiore, Piazza dei Cavalieri, Pisa, Italy

    F. Bassani

  4. Dept.of Physics, University of Perugia, Perugia, Italy

    F.S. Pavone

  5. LENS and INFM, University of Florence, 50125, Florence, Italy

    F.S. Pavone

  6. Dept. of Physics and LENS, University of Florence, Florence, Italy

    M. Inguscio

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© 2001 Springer-Verlag Berlin Heidelberg

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Melnikov, K., van Ritbergen, T. (2001). Three-Loop Slope of the Dirac Form Factor and the 1S Lamb Shift in Hydrogen. In: Karshenboim, S.G., Bassani, F., Pavone, F., Inguscio, M., Hänsch, T. (eds) The Hydrogen Atom. Lecture Notes in Physics, vol 570. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45395-4_18

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  • DOI: https://doi.org/10.1007/3-540-45395-4_18

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41935-8

  • Online ISBN: 978-3-540-45395-6

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