Relativistic (Zα)2 Corrections and Leading Quantum Electrodynamic Corrections to the Two-Photon Decay Rate of Ionic States

We calculate the relativistic corrections of relative order (Zα) 2 to the two-photon decay rate of higher excited S and D states in ionic atomic systems, and we also evaluate the leading radiative corrections of relative order α (Zα) 2 ln [(Zα) -2]. We thus complete the theory of the two-photon decay rates up to relative order α3 ln (α). An approach inspired by nonrelativistic quantum electrodynamics is used. We find that the corrections of relative order (Zα) 2 to the two-photon decay are given by the Zitterbewegung, by the spin-orbit coupling and by relativistic corrections to the electron mass, and by quadrupole interactions. We show that all corrections are separately gauge invariant with respect to a hybrid transformation from velocity to length gauge, where the gauge transformation of the wave function is neglected. The corrections are evaluated for the two-photon decay from 2S, 3S, 3D, and 4S states in one-electron (hydrogenlike) systems, with 1S and 2S final states

Reparameterization Invariance of NRQED Self-Energy Corrections and Improved Theory for Excited D States in Hydrogenlike Systems

Canonically, the quantum electrodynamic radiative corrections in bound systems have been evaluated in photon energy regularization, i.e., using a noncovariant overlapping parameter that separates the high-energy relativistic scales of the virtual quanta from the nonrelativistic domain. Here, we calculate the higher-order corrections to the one-photon self-energy calculation with three different overlapping parameters (photon energy, photon mass and dimensional regularization) and demonstrate the reparameterization invariance of nonrelativistic quantum electrodynamics (NRQED) using this particular example. We also present new techniques for the calculation of the low-energy part of this correction, which lead to results for the Lamb shift of highly excited states that are important for high-precision spectroscopy

Quantum Dynamics in Atomic-Fountain Experiments for Measuring the Electric Dipole Moment of the Electron with Improved Sensitivity

An improved measurement of the electron electric dipole moment (EDM) appears feasible using groundstate alkali atoms in an atomic fountain in which a strong electric field, which couples to a conceivable EDM, is applied perpendicular to the fountain axis. In a practical fountain, the ratio of the atomic tensor Stark shift to the Zeeman shift is a factor μ ~ 100.We expand the complete time-evolution operator in inverse powers of this ratio; complete results are presented for atoms of total spin F = 3, 4, and 5. For a specific set of entangled hyperfine sublevels (coherent states), potential systematic errors enter only as even powers of 1/μ, making the expansion rapidly convergent. The remaining EDM-mimicking effects are further suppressed in a proposed double-differential setup, where the final state is interrogated in a differential laser configuration, and the direction of the strong electric field also is inverted. Estimates of the signal available at existing accelerator facilities indicate that the proposed apparatus offers the potential for a drastic improvement in EDM limits over existing measurements, and for constraining the parameter space of supersymmetric (SUSY) extensions of the Standard Model

Fundamental constants and tests of theory in Rydberg states of hydrogen-like ions

Comparison of precision frequency measurements to quantum electrodynamics (QED) predictions for Rydberg states of hydrogen-like ions can yield information on values of fundamental constants and test theory. With the results of a calculation of a key QED contribution reported here, the uncertainty in the theory of the energy levels is reduced to a level where such a comparison can yield an improved value of the Rydberg constant.Comment: 4 pages, RevTe

Quantum electrodynamics and fundamental constants

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