We performed a laser spectroscopic determination of the 2s hyperfine splitting (HFS) of Li-like 209 Bi 80+ and repeated the measurement of the 1s HFS of H-like 209 Bi 82+ . Both ion species were subsequently stored in the Experimental Storage Ring at the GSI Helmholtzzentrum für Schwerionenforschung Darmstadt and cooled with an electron cooler at a velocity of ≈ 0.71 c. Pulsed laser excitation of the M 1 hyperfine-transition was performed in anticollinear and collinear geometry for Bi 82+ and Bi 80+ , respectively, and observed by fluorescence detection. We obtain ∆E (1s) = 5086.3(11) meV for Bi 82+ , different from the literature value, and ∆E (2s) = 797.50(18) meV for Bi 80+ . These values provide experimental evidence that a specific difference between the two splitting energies can be used to test QED calculations in the strongest static magnetic fields available in the laboratory independent of nuclear structure effects. The experimental result is in excellent agreement with the theoretical prediction and confirms the sum of the Dirac term and the relativistic interelectronic-interaction correction at a level of 0.5% confirming the importance of accounting for the Breit interaction.Quantum electrodynamics (QED) is generally considered to be the best-tested theory in physics. In recent years a number of extremely precise experimental tests have been achieved on free particles as well as on bound states in light atomic systems. For free particles, the g-factor of the electron measured with ppb-accuracy [1] constitutes the most precise test, sensitive to the highest order in α [2]. In atomic systems the QED deals with the particles bound by the Coulomb field, what makes high-precision QED calculations more complicated. The bound-state QED (BS-QED) effects in light atomic systems are expanded in parameters Zα and m e /M in addition to α, where Z is the atomic number and m e and M are the electron and nuclear masses, respectively. The parameter Zα characterizes the binding strength in the Coulomb field of the nucleus, while the mass ratio m e /M is introduced for the nuclear recoil effects. Hence, tests of BS-QED are complementary to QED tests of the properties of free particles. The investigation of H-like systems with increasing charge provides the opportunity to systematically increase the influence of the binding effect.One of the most accurate test of BS-QED on low-Z ions is the measurement of the g-factor of a single electron bound to a Si nucleus [3]. Entering the regime of highly charged heavy ions like Pb 81+ , Bi 82+ or U 91+ the electron binding energy becomes comparable to the rest-mass energy and the parameter Zα can not be employed as an expansion parameter anymore. In other words, the extremely strong electric and magnetic fields in the close surrounding of the heavy nucleus require the inclusion of the binding corrections in all orders of Zα. Hence, BS-QED in this regime requires a very different approach and new tools to calculate the corresponding corrections, usually referred to as strong-fi...

We present the concluding result from an Ives-Stilwell-type time dilation experiment using 7Li+ ions confined at a velocity of β=v/c=0.338 in the storage ring ESR at Darmstadt. A Λ-type three-level system within the hyperfine structure of the 7Li+3S1 →3P2 line is driven by two laser beams aligned parallel and antiparallel relative to the ion beam. The lasers' Doppler shifted frequencies required for resonance are measured with an accuracy of <4×10(-9) using optical-optical double resonance spectroscopy. This allows us to verify the special relativity relation between the time dilation factor γ and the velocity β, γ√1-β2=1 to within ±2.3×10(-9) at this velocity. The result, which is singled out by a high boost velocity β, is also interpreted within Lorentz invariance violating test theories.

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We have recently reported on the first direct measurement of the 2s hyperfine transition in lithium-like bismuth 209 Bi 80+. Combined with a new measurement of the 1s hyperfine splitting in the hydrogen-like 209 Bi 82+ the so-called specific difference ∆ E = −61.37(36) meV was determined and is in good agreement with the strong-field bound-state QED prediction. Here we report on additional investigations performed to estimate systematic uncertainties of these results and on details of the experimental setup. We show that the dominating uncertainty arises from the insufficient knowledge of the ion beam velocity determined from the electroncooler voltage. Two routes to obtain a cooler-voltage calibration are discussed and it is shown that agreement in ∆ E with the QED calculations and of the hyperfine splitting in hydrogen-like bismuth as reported in the first measurement in 1994 are mutually exclusive.