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Electronic $K$ x rays emitted by muonic Ar atoms in the gas phase were observed using a superconducting transition-edge-sensor microcalorimeter. The high-precision energy spectra provided a clear signature of the presence of muonic atoms accompanied by a few electrons, which have never been observed before. One-, two-, and three-electron bound, i.e., H-like, He-like, and Li-like, muonic Ar atoms were identified from electronic $K$ x rays and hyper-satellite $K$ x rays. These $K$ x rays are emitted after the charge transfer process by the collisions with surrounding Ar atoms. With the aid of theoretical calculations, we confirmed that the peak positions are consistent with the x-ray energies from highly charged Cl ions, and the intensities reflecting deexcitation dynamics were successfully understood by taking into account the interaction between the muon and bound electrons.

We have measured several 2p $\rightarrow$ 1s transition energies in core-excited boron-like ions of sulfur and argon. The measurements are reference-free, with an accuracy of a few parts per million. The x-rays were produced by the plasma of a an electron-cyclotron resonance ion source and were measured by a double-crystal x-ray spectrometer. The precision obtained for the measured 1s2s22p2 J -- 1s2 2s2 2p J ' lines is $\approx$4 ppm for sulfur and $\approx$2 ppm for argon. The line energies are compared to relativistic atomic structure calculations performed with the mdfgme multi-configuration Dirac-Fock code. This comparison is used for line identification and test the theoretical methods, which reach an agreement with experimental data up to 15 meV. The theoretical calculations have been extended to C+, Si9+, Cr19+ and Fe21+, which were the only B-like ions where such transitions were measured up to now.

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 QUARTET collaboration aims to significantly improve the precision of the absolute nuclear charge radii of light nuclei from Li to Ne by using an array of metallic magnetic calorimeters to perform high-precision X-ray spectroscopy of low-lying states in muonic atoms. A proof-of-principle measurement with lithium, beryllium and boron is planned for fall 2023 at the Paul Scherrer Institute. We discuss the performance achieved with the maXs-30 detector module to be used. To place the detector close to the target chamber where the muon beam will impact the material under study, we have developed a new dilution refrigerator sidearm. We further discuss the expected efficiency given the transparency of the X-ray windows and the quantum efficiency of the detector. The expected muonic X-ray rate combined with the high resolving power and detection efficiency of the detector suggest that QUARTET will be able to study the de-excitation of light muonic atoms at an unprecedented level, increasing the relative energy resolution by up to a factor of 20 compared to conventional detector techniques.

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 $\sigma$ 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 $<10^{-19}/\sqrt{\tau}$.

A star completely destroyed in a tidal disruption event (TDE) ignites a luminous flare that is powered by the fallback of tidally stripped debris to a supermassive black hole (SMBH) of mass $M_{\bullet}$. We analyze two estimates for the peak fallback rate in a TDE, one being the "frozen-in" model, which predicts a strong dependence of the time to peak fallback rate, $t_{\rm peak}$, on both stellar mass and age, with $15\textrm{ days} \lesssim t_{\rm peak} \lesssim 10$ yr for main sequence stars with masses $0.2\le M_{\star}/M_{\odot} \le 5$ and $M_{\bullet} = 10^6M_{\odot}$. The second estimate, which postulates that the star is completely destroyed when tides dominate the maximum stellar self-gravity, predicts that $t_{\rm peak}$ is very weakly dependent on stellar type, with $t_{\rm peak} = \left(23.2\pm4.0\textrm{ days}\right)\left(M_{\bullet}/10^6M_{\odot}\right)^{1/2}$ for $0.2\le M_{\star}/M_{\odot} \le 5$, while $t_{\rm peak} = \left(29.8\pm3.6\textrm{ days}\right)\left(M_{\bullet}/10^6M_{\odot}\right)^{1/2}$ for a Kroupa initial mass function truncated at $1.5 M_{\odot}$. This second estimate also agrees closely with hydrodynamical simulations, while the frozen-in model is discrepant by orders of magnitude. We conclude that (1) the time to peak luminosity in complete TDEs is almost exclusively determined by SMBH mass, and (2) massive-star TDEs power the largest accretion luminosities. Consequently, (a) decades-long extra-galactic outbursts cannot be powered by complete TDEs, including massive-star disruptions, and (b) the most highly super-Eddington TDEs are powered by the complete disruption of massive stars, which -- if responsible for producing jetted TDEs -- would explain the rarity of jetted TDEs and their preference for young and star-forming host galaxies., Comment: 10 pages, 4 figures, ApJL accepted

We propose an experiment to measure the nuclear charge radii of light elements with up to 20~times higher accuracy. These are essential both for understanding nuclear physics at low energies, and for experimental and theoretical applications in simple atomic systems. Such comparisons advance the understanding of bound-state quantum electrodynamics and are useful for searching for new physics beyond the Standard Model. The energy levels of muonic atoms are highly susceptible to nuclear structure, especially to the mean square charge radius. The radii of the lightest nuclei (with the atomic number, $Z=1,2$) have been determined with high accuracy using laser spectroscopy in muonic atoms, while those of medium mass and above were determined using X-ray spectroscopy with semiconductor detectors. In this communication, we present a new experiment, aiming to obtain precision measurements of the radii of light nuclei $3 \leq Z \leq 10$ using single-photon energy measurements with cryogenic microcalorimeters; a quantum-sensing technology capable of high efficiency with outstanding resolution for low-energy X-rays.

We report on the first production of an antihydrogen beam by charge exchange of 6.1 keV antiprotons with a cloud of positronium in the GBAR experiment at CERN. The antiproton beam was delivered by the AD/ELENA facility. The positronium target was produced from a positron beam itself obtained from an electron linear accelerator. We observe an excess over background indicating antihydrogen production with a significance of 3-4 standard deviations.

Hydrogen-like light muonic ions, in which one negative muon replaces all the electrons, are extremely sensitive probes of nuclear structure, because the large muon mass increases tremendously the wave function overlap with the nucleus. Using pulsed laser spectroscopy we have measured three 2S-2P transitions in the muonic helium-3 ion ($\mu^3$He$^+$), an ion formed by a negative muon and bare helium-3 nucleus. This allowed us to extract the Lamb shift $E(2P_{1/2}-2S_{1/2})= 1258.598(48)^{\rm exp}(3)^{\rm theo}$ meV, the 2P fine structure splitting $E_{\rm FS}^{\rm exp} = 144.958(114)$ meV, and the 2S-hyperfine splitting (HFS) $E_{\rm HFS}^{\rm exp} = -166.495(104)^{\rm exp}(3)^{\rm theo}$ meV in $\mu^3$He$^+$. Comparing these measurements to theory we determine the rms charge radius of the helion ($^3$He nucleus) to be $r_h$ = 1.97007(94) fm. This radius represents a benchmark for few nucleon theories and opens the way for precision tests in $^3$He atoms and $^3$He-ions. This radius is in good agreement with the value from elastic electron scattering, but a factor 15 more accurate. Combining our Lamb shift measurement with our earlier one in $\mu^4$He$^+$ we obtain $r_h^2-r_\alpha^2 = 1.0636(6)^{\rm exp}(30)^{\rm theo}$ fm$^2$ to be compared to results from the isotope shift measurements in regular He atoms, which are however affected by long-standing tensions. By comparing $E_{\rm HFS}^{\rm exp}$ with theory we also obtain the two-photon-exchange contribution (including higher orders) which is another important benchmark for ab-initio few-nucleon theories aiming at understanding the magnetic and current structure of light nuclei., Comment: 8 pages, 5 figures

We review the progress in atomic structure theory with a focus on superheavy elements and the aim to predict their ground state configuration and element's placement in the periodic table. To understand the electronic structure and correlations in the regime of large atomic numbers, it is important to correctly solve the Dirac equation in strong Coulomb fields, and also to take into account quantum electrodynamic effects. We specifically focus on the fundamental difficulties encountered when dealing with the many-particle Dirac equation. We further discuss the possibility for future many-electron atomic structure calculations going beyond the critical nuclear charge \(Z_{\rm crit}\approx 170\), where levels such as the \(1s\) shell dive into the negative energy continuum (\(E_{n\kappa}<-m_ec^2\)). The nature of the resulting Gamow states within a rigged Hilbert space formalism is highlighted.

We have made the first absolute, reference-free measurement of the 1s2s 3 S1 $\rightarrow$ 1s 2 1 S0 relativistic magnetic dipole transition in He-like sulfur. The highly-charged S ions were provided by an electron-cyclotron resonance ion source, and the x rays were analysed with a high-precision double crystal spectrometer. A transition energy of 2430.3685(97) eV was obtained, and is compared to most advanced bound state quantum electrodynamics calculations, providing an important test of two-electron QED effects and precision atomic structure methods in medium-Z species. Thanks to the extremely narrow natural linewidth of this transition, and to the large dispersion of the spectrometer at this energy, a complementary study was also performed evaluating the impact of different silicon crystal atomic form factor models in the transition energy analysis. We find no significant dependence on the model used to determine the transition energy.

The CREMA collaboration is pursuing a measurement of the ground-state hyperfine splitting (HFS) in muonic hydrogen ($\mu$p) with 1 ppm accuracy by means of pulsed laser spectroscopy. In the proposed experiment, the $\mu$p atom is excited by a laser pulse from the singlet to the triplet hyperfine sub-levels, and is quenched back to the singlet state by an inelastic collision with a H$_2$ molecule. The resulting increase of kinetic energy after this cycle modifies the $\mu$p atom diffusion in the hydrogen gas and the arrival time of the $\mu$p atoms at the target walls. This laser-induced modification of the arrival times is used to expose the atomic transition. In this paper we present the simulation of the $\mu$p diffusion in the H$_2$ gas which is at the core of the experimental scheme. These simulations have been implemented with the Geant4 framework by introducing various low-energy processes including the motion of the H$_2$ molecules, i.e. the effects related with the hydrogen target temperature. The simulations have been used to optimize the hydrogen target parameters (pressure, temperatures and thickness) and to estimate signal and background rates. These rates allow to estimate the maximum time needed to find the resonance and the statistical accuracy of the spectroscopy experiment., Comment: Submission to SciPost

Recent progress in laser and x-ray spectroscopy of muonic atoms offers promising long-term possibilities at the intersection of atomic, nuclear and particle physics. In muonic hydrogen, laser spectroscopy measurements will determine the ground-state hyperfine splitting (HFS) and additionally improve the Lamb shift by a factor of 5. Precision spectroscopy with cryogenic microcalorimeters has the potential to significantly improve the charge radii of the light nuclei in the $Z=3-8$ range. Complementary progress in precision should be achieved on the theory of nucleon- and nuclear-structure effects. The impact of this muonic-atom spectroscopy program will be amplified by the upcoming results from H and He$^+$ spectroscopy, simple molecules such as HD$^+$ and Penning trap measurements. In this broader context, one can test ab-initio nuclear theories, bound-state QED for two- or three-body systems, and determine fundamental constants, such as the Rydberg ($R_\infty$) and the fine-structure ($\alpha$) constants., Comment: 8 pages, 2 figures, submitted as community input for the NuPECC Long Range Plan 2024 (https://indico.ph.tum.de/event/7050/)

Muonic atom spectroscopy -- the measurement of the x rays emitted during the formation process of a muonic atom -- has a long standing history in probing the shape and size of nuclei. In fact, almost all stable elements have been subject to muonic atom spectroscopy measurements and the absolute charge radii extracted from these measurements typically offer the highest accuracy available. However, so far only targets of at least a few hundred milligram could be used as it required to stop a muon beam directly in the target to form the muonic atom. We have developed a new method relying on repeated transfer reactions taking place inside a 100-bar hydrogen gas cell with an admixture of 0.25% deuterium that allows us to drastically reduce the amount of target material needed while still offering an adequate efficiency. Detailed simulations of the transfer reactions match the measured data, suggesting good understanding of the processes taking place inside the gas mixture. As a proof of principle we demonstrate the method with a measurement of the 2p-1s muonic x rays from a 5-{\mu}g gold target., Comment: 16 pages, 14 figures

Superconducting transition-edge sensor (TES) microcalorimeters have great utility in x-ray applications owing to their high energy resolution, good collecting efficiency and the feasibility of being multiplexed into large arrays. In this work, we develop hard x-ray TESs to measure the absolute energies of muonic-argon ($\mu$-Ar) transition lines around 44 keV and 20 keV. TESs with sidecar absorbers of different heat capacities were fabricated and characterized for their energy resolution and calibration uncertainty. We achieved ~ 1 eV absolute energy measurement accuracy at 44 keV, and < 12 eV energy resolution at 17.5 keV.

We present a description of the GBAR positron (e+) trapping apparatus, which consists of a three stage Buffer Gas Trap (BGT) followed by a High Field Penning Trap (HFT), and discuss its performance. The overall goal of the GBAR experiment is to measure the acceleration of the neutral antihydrogen (H) atom in the terrestrial gravitational field by neutralising a positive antihydrogen ion (H+), which has been cooled to a low temperature, and observing the subsequent H annihilation following free fall. To produce one H+ ion, about 10^10 positrons, efficiently converted into positronium (Ps), together with about 10^7 antiprotons (p), are required. The positrons, produced from an electron linac-based system, are accumulated first in the BGT whereafter they are stacked in the ultra-high vacuum HFT, where we have been able to trap 1.4(2) x 10^9 positrons in 1100 seconds.

First ever measurements of the ratios of free cyclotron frequencies of heavy highly charged ions with Z>50 with relative uncertainties close to 1e-11 are presented. Such accurate measurements have become realistic due to the construction of the novel cryogenic multi-Penning-trap mass spectrometer PENTATRAP. Based on the measured frequency ratios, the mass differences of five pairs of stable xenon isotopes, ranging from 126Xe to 134Xe, have been determined. Moreover, the first direct measurement of an electron binding energy in a heavy highly charged ion, namely of the 37th atomic electron in xenon, with an uncertainty of a few eV is demonstrated. The obtained value agrees with the calculated one using two independent different implementations of the multiconfiguration Dirac-Hartree-Fock method. PENTATRAP opens the door to future measurements of electron binding energies in highly charged heavy ions for more stringent tests of bound-state quantum electrodynamics in strong electromagnetic fields and for an investigation of the manifestation of Light Dark Matter in isotopic chains of certain chemical elements., Comment: 2 figures, 1 table, 28 references

The toolbox for material characterization has never been richer than today. Great progress with all kinds of particles and interaction methods provide access to nearly all properties of an object under study. However, a tomographic analysis of the subsurface region remains still a challenge today. In this regard, the Muon-Induced X-ray Emission (MIXE) technique has seen rebirth fueled by the availability of high intensity muon beams. We report here a study conducted at the Paul Scherrer Institute (PSI). It demonstrates that the absence of any beam time-structure leads to low pile-up events and a high signal-to-noise ratio (SNR) with less than one hour acquisition time per sample or data point. This performance creates the perspective to open this technique to a wider audience for the routine investigation of non-destructive and depth-sensitive elemental compositions, for example in rare and precious samples. Using a hetero-structured sample of known elements and thicknesses, we successfully detected the characteristic muonic X-rays, emitted during the capture of a negative muon by an atom, and the gamma-rays resulting from the nuclear capture of the muon, characterizing the capabilities of MIXE at PSI. This sample emphasizes the quality of a continuous beam, and the exceptional SNR at high rates. Such sensitivity will enable totally new statistically intense aspects in the field of MIXE, e.g. elemental 3D-tomography and chemical analysis. Therefore, we are currently advancing our proof-of-concept experiments with the goal of creating a full fledged permanently operated user station to make MIXE available to the wider scientific community as well as industry.

The CREMA collaboration is pursuing a measurement of the ground-state hyperfine splitting (HFS) in muonic hydrogen ($\mu$p) with 1 ppm accuracy by means of pulsed laser spectroscopy to determine the two-photon-exchange contribution with $2\times10^{-4}$ relative accuracy. In the proposed experiment, the $\mu$p atom undergoes a laser excitation from the singlet hyperfine state to the triplet hyperfine state, {then} is quenched back to the singlet state by an inelastic collision with a H$_2$ molecule. The resulting increase of kinetic energy after the collisional deexcitation is used as a signature of a successful laser transition between hyperfine states. In this paper, we calculate the combined probability that a $\mu$p atom initially in the singlet hyperfine state undergoes a laser excitation to the triplet state followed by a collisional-induced deexcitation back to the singlet state. This combined probability has been computed using the optical Bloch equations including the inelastic and elastic collisions. Omitting the decoherence effects caused by {the laser bandwidth and }collisions would overestimate the transition probability by more than a factor of two in the experimental conditions. Moreover, we also account for Doppler effects and provide the matrix element, the saturation fluence, the elastic and inelastic collision rates for the singlet and triplet states, and the resonance linewidth. This calculation thus quantifies one of the key unknowns of the HFS experiment, leading to a precise definition of the requirements for the laser system and to an optimization of the hydrogen gas target where $\mu$p is formed and the laser spectroscopy will occur., Comment: 21 pages, 4 figures

The knowledge of atomic fundamental parameters, such as the fluorescence yields with low uncertainties, is of decisive importance in elemental quantification involving X-ray fluorescence analysis techniques. However, especially for the low-Z elements, the available literature data are either of poor quality, of unknown or very large uncertainty, or both. For this reason, the K-shell fluorescence yield of carbon was determined in the PTB laboratory at the synchrotron radiation facility BESSY II. In addition, theoretical calculations of the same parameter were performed using the multiconfiguration Dirac-Fock method, including relativistic and quantum electrodynamics (QED) corrections. Both values obtained in this work are compared to the corresponding available literature data., Comment: 10 pages, 5 figures