Zoltán Harman

The investigation of the absolute scale of the effective neutrino mass remains challenging due to the exclusively weak interaction of neutrinos with all known particles in the standard model of particle physics. Currently, the most precise and least model-dependent upper limit on the electron antineutrino mass is set by the KATRIN experiment from the analysis of the tritium \b{eta}-decay. Another promising approach is the electron capture in $^{163}\mathrm{Ho}$, which is under investigation using microcalorimetry within the ECHo and HOLMES collab orations. An independently measured Q-value of this process is vital for the assessment of systematic uncertainties in the neutrino mass determination. Here, we report a direct, independent determination of this $Q$-value by measuring the free-space cyclotron frequency ratio of highly charged ions of $^{163}\mathrm{Ho}$ and $^{163}\mathrm{Dy}$ in the Penning trap experiment \textsc{Pentatrap}. Combining this ratio with atomic physics calculations of the electronic binding energies yields a $Q$-value of $2863.2(0.6)\,\mathrm{eV}/c^{2}$ - a more than 50-fold improvement over the state-of-the-art. This will enable the determination of the electron neutrino mass on a sub-eV level from the analysis of the electron capture in $^{163}\mathrm{Ho}$.

The atomic mass of uranium-238 has been determined to be $238.050\,787\,618(15)\,\text{u}$, improving the literature uncertainty by two orders of magnitude. It is obtained from a measurement of the mass ratio of $^{238}$U$^{47+}$ and $^{132}$Xe$^{26+}$ ions with an uncertainty of $3.5\times 10^{-12}$. The measurement was carried out with the Penning-trap mass spectrometer \textsc{Pentatrap} and was accompanied by a calculation of the binding energies $E_{\text{U}}$ and $E_{\text{Xe}}$ of the 47 and 26 missing electrons of the two highly charged ions, respectively. These binding energies were determined using an \textit{ab initio} multiconfiguration Dirac-Hartree-Fock (MCDHF) method to be $E_{\text{U}} = 39\,927(10)\,\text{eV}$ and $E_{\text{Xe}} = 8\,971.2(21)\,\text{eV}$. The new mass value will serve as a reference for high-precision mass measurements in the heavy mass region of the nuclear chart up to transuranium nuclides.

Highly charged ions (HCIs) offer many opportunities for next-generation clock research due to the vast landscape of available electronic transitions in different charge states. The development of XUV frequency combs has enabled the search for clock transitions based on shorter wavelengths in HCIs. However, without initial knowledge of the energy of the clock states, these narrow transitions are difficult to be probed by lasers. In this Letter, we provide experimental observation and theoretical calculation of a long-lived electronic state in Nb-like Pb$^{41+}$ which could be used as a clock state. With the mass spectrometer Pentatrap, the excitation energy of this metastable state is directly determined as a mass difference at an energy of 31.2(8) eV, corresponding to one of the most precise relative mass determinations to date with a fractional uncertainty of $4\times10^{-12}$. This experimental result agrees within 1 $σ$ with two partially different \textit{ab initio} multi-configuration Dirac-Hartree-Fock calculations of 31.68(13) eV and 31.76(35) eV, respectively. With a calculated lifetime of 26.5(5.3) days, the transition from this metastable state to the ground state bears a quality factor of $1.1\times10^{23}$ and allows for the construction of a HCI clock with a fractional frequency instability of $<10^{-19}/\sqrtτ$.

The quantum electrodynamic (QED) description of light-and-matter interaction is one of the most fundamental theories of physics and has been shown to be in excellent agreement with experimental results. Specifically, measurements of the electronic magnetic moment (or $g$ factor) of highly charged ions (HCI) in Penning traps can provide a stringent probe for QED, testing the Standard model in the strongest electromagnetic fields. When studying the difference of isotopes, even the intricate effects stemming from the nucleus can be resolved and tested as, due to the identical electron configuration, many common QED contributions do not have to be considered. Experimentally however, this becomes quickly limited, particularly by the precision of the ion masses or the achievable magnetic field stability. Here we report on a novel measurement technique that overcomes both of these limitations by co-trapping two HCIs in a Penning trap and measuring the difference of their $g$ factors directly. The resulting correlation of magnetic field fluctuations leads to drastically higher precision. We use a dual Ramsey-type measurement scheme with the ions locked on a common magnetron orbit, separated by only a few hundred micrometres, to extract the coherent spin precession frequency difference. We have measured the isotopic shift of the bound electron $g$ factor of the neon isotopes of $^{20}$Ne$^{9+}$ and $^{22}$Ne$^{9+}$ to 0.56 parts-per-trillion ($5.6 \cdot 10^{-13}$) precision relative to their $g$ factors, which is an improvement of more than two orders of magnitude compared to state-of-the-art techniques. This resolves the QED contribution to the nuclear recoil for the very first time and accurately validates the corresponding theory. Furthermore, the agreement with theory allows setting constraints for a fifth-force, resulting from Higgs-portal-type dark-matter interactions.

Theoretical and experimental resonance strengths for KLL dielectronic recombination (DR) into He-, Li-, Be-, and B-like mercury ions are presented, based on state-resolved DR x-ray spectra recorded at the Heidelberg electron beam ion trap. The DR resonance strengths were experimentally extracted by normalizing them to simultaneously recorded radiative recombination signals. The results are compared to state-of-the-art atomic calculations that include relativistic electron-electron correlation and configuration mixing effects. Combining the present data with other existing ones, we derive an improved semi-empirical $Z$-scaling law for DR resonance strength as a function of the atomic number, taking into account higher-order relativistic corrections, which are especially relevant for heavy highly charged ions.