Quantum electrodynamics and fundamental constants

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Wundt, Benedikt J.
Missouri University of Science and Technology
thesis / dissertation description
"The unprecedented precision achieved both in the experimental measurements as well as in the theoretical description of atomic bound states make them an ideal study object for fundamental physics and the determination of fundamental constants. This requires a careful study of the effects from quantum electrodynamics (QED) on the interaction between the electron and the nucleus.The two theoretical approaches for the evaluation of QED corrections are presented and discussed. Due to the presence of two energy scales from the binding potential and the radiation field, an overlapping parameter has to be used in both the approaches in order to separate the energy scales. The different choices for the overlapping parameter in the two methods are further illustrated in a model example.With the nonrelativistic theory, relativistic corrections in order (Zα)² to the two-photon decay rate of ionic states are calculated, as well as the leading radiative corrections of α(Zα)² ln[(Zα)⁻²]. It is shown that the corrections is gauge-invariant under a "hybrid" gauge transformation between Coulomb and Yennie gauge.Furthermore, QED corrections for Rydberg states in one-electron ions are investigated. The smallness of the corrections and the absence of nuclear size corrections enable very accurate theoretical predictions. Measuring transition frequencies and comparing them to the theoretical predictions, QED theory can be tested more precisely. In turn, this could yield a more accurate value for the Rydberg constant. Using a transition in a nucleus with a well determined mass, acting as a reference, a comparison to transition in other nuclei can even allow to determined nuclear masses.Finally, in order to avoid an additional uncertainty in nuclei with non zero nuclear spin, QED self-energy corrections to the hyperfine structure up to order α(Zα)²ΔEHFS are determined for highly excited Rydberg states"--Abstract, page iii.