S. Sturm

Inner-shell electrons naturally sense the electric field close to the nucleus, which can reach extreme values beyond $10^{15}\,\text{V}/\text{cm}$ for the innermost electrons. Especially in few-electron highly charged ions, the interaction with the electromagnetic fields can be accurately calculated within quantum electrodynamics (QED), rendering these ions good candidates to test the validity of QED in strong fields. Consequently, their Lamb shifts were intensively studied in the last decades. Another approach is the measurement of $g$ factors in highly charged ions. However, so far, either experimental accuracy or small field strength in low-$Z$ ions limited the stringency of these QED tests. Here, we report on our high-precision, high-field test of QED in hydrogenlike $^{118}$Sn$^{49+}$. The highly charged ions were produced with the Heidelberg-EBIT (electron beam ion trap) and injected into the ALPHATRAP Penning-trap setup, where the bound-electron $g$ factor was measured with a precision of 0.5 parts-per-billion. For comparison, we present state-of-the-art theory calculations, which together test the underlying QED to about $0.012\,\%$, yielding a stringent test in the strong-field regime. With this measurement, we challenge the best tests via the Lamb shift and, with anticipated advances in the $g$-factor theory, surpass them by more than an order of magnitude.

The cyclotron frequency ratio of $^{187}\mathrm{Os}^{29+}$ to $^{187}\mathrm{Re}^{29+}$ ions was measured with the Penning-trap mass spectrometer PENTATRAP. The achieved result of $R=1.000\:000\:013\:882(5)$ is to date the most precise such measurement performed on ions. Furthermore, the total binding-energy difference of the 29 missing electrons in Re and Os was calculated by relativistic multiconfiguration methods, yielding the value of $ΔE = 53.5(10)$ eV. Finally, using the achieved results, the mass difference between neutral $^{187}$Re and $^{187}$Os, i.e., the $Q$ value of the $β^-$ decay of $^{187}$Re, is determined to be 2470.9(13) eV.

Electron beam ion traps (EBIT) are ideal tools for both production and study of highly charged ions (HCI). In order to reduce their construction, maintenance, and operation costs we have developed a novel, compact, room-temperature design, the Heidelberg Compact EBIT (HC-EBIT). Four already commissioned devices operate at the strongest fields (up to 0.86 T) reported for such EBITs using permanent magnets, run electron beam currents up to 80 mA and energies up to 10 keV. They demonstrate HCI production, trapping, and extraction of pulsed Ar$^{16+}$ bunches and continuous 100 pA ion beams of highly charged Xe up to charge state 29+, already with a 4 mA, 2 keV electron beam. Moreover, HC-EBITs offer large solid-angle ports and thus high photon count rates, e. g., in x-ray spectroscopy of dielectronic recombination in HCIs up to Fe$^{24+}$, achieving an electron-energy resolving power of $E/ΔE > 1500$ at 5 keV. Besides traditional on-axis electron guns, we have also implemented a novel off-axis gun for laser, synchrotron, and free-electron laser applications, offering clear optical access along the trap axis. We report on its first operation at a synchrotron radiation facility demonstrating resonant photoexcitation of highly charged oxygen.

We have measured the ground-state $g$-factor of boronlike argon $^{40}\textrm{Ar}^{13+}$ with a fractional uncertainty of \SI{1.4e-9}{} with a single ion in the newly developed ALPHATRAP double Penning-trap setup. The here obtained value of $g=0.663\,648\,455\,32(93)$ is in agreement with our theoretical prediction of $0.663\,648\,12(58)$. The latter is obtained accounting for quantum electrodynamics, electron correlation, and nuclear effects within the state-of-the-art theoretical methods. Our experimental result distinguishes between existing predictions that are in disagreement, and lays the foundations for an independent determination of the fine-structure constant.

The determination of the electron mass from Penning-trap measurements with $^{12}$C$^{5+}$ ions and from theoretical results for the bound-electron $g$ factor is described in detail. Some recently calculated contributions slightly shift the extracted mass value. Prospects of a further improvement of the electron mass are discussed both from the experimental and from the theoretical point of view. Measurements with $^4$He$^+$ ions will enable a consistency check of the electron mass value, and in future an improvement of the $^4$He nuclear mass and a determination of the fine-structure constant.

The muonic vacuum polarization contribution to the $g$-factor of the electron bound in a nuclear potential is investigated theoretically. The electric as well as the magnetic loop contributions are evaluated. We found these muonic effects to be observable in planned trapped-ion experiments with light and medium-heavy highly charged ions. The enhancement due to the strong Coulomb field boosts these contributions much above the corresponding terms in the free-electron $g$-factor. Due to their magnitude, muonic vacuum polarization terms are also significant in planned determinations of the fine-structure constant from the bound-electron $g$-factor.

The novel five-Penning trap mass spectrometer PENTATRAP is developed at the Max-Planck-Institut für Kernphysik (MPIK), Heidelberg. Ions of interest are long-lived highly charged nuclides up to bare uranium. PENTATRAP aims for an accuracy of a few parts in 10^12 for mass ratios of mass doublets. A physics program for PENTATRAP includes Q-values measurements of β-transitions relevant for neutrino physics, stringent tests of quantum electrodynamics in the regime of extreme electric fields, and a test of special relativity. Main features of PENTATRAP are an access to a source of highly charged ions, a multi-trap configuration, simultaneous measurements of frequencies, a continuous precise monitoring of magnetic field fluctuations, a fast exchange between different ions, and a highly sensitive cryogenic non-destructive detection system. This paper gives a motivation for the new mass spectrometer PENTATRAP, presents its experimental setup, and describes the present status.

A novel Penning trap tower consisting of five compensated cylindrical Penning traps is developed for the PENTATRAP mass spectrometer at the Max-Planck-Institut für Kernphysik in Heidelberg, Germany. An analytical expression for the electrostatic potential inside the trap tower is derived to calculate standard Penning trap properties like the compensation of anharmonicities and an orthogonal geometry of the trap electrodes. Since the PENTATRAP project described in the preceding article aims for ultra high-precision mass-ratio measurements of highly charged ions up to uranium, systematic effects for highly charged ions inside the trap tower are considered for the design process as well. Finally, a limit due to remaining anharmonic shifts at large amplitudes is estimated for the resulting geometry, which is important for phase-sensitive measurements of the reduced cyclotron frequency of the ions.