The energy levels of hydrogen-like atomic systems can be calculated with great precision. Starting from their quantum mechanical solution, they have been refined over the years to include the electron spin, the relativistic and quantum field effects, and tiny energy shifts related to the complex structure of the nucleus. These energy shifts caused by the nuclear structure are vastly magnified in hydrogen-like systems formed by a negative muon and a nucleus, so spectroscopy of these muonic ions can be used to investigate the nuclear structure with high precision. Here we present the measurement of two 2S–2P transitions in the muonic helium-4 ion that yields a precise determination of the root-mean-square charge radius of the α particle of 1.67824(83) femtometres. This determination from atomic spectroscopy is in excellent agreement with the value from electron scattering¹, but a factor of 4.8 more precise, providing a benchmark for few-nucleon theories, lattice quantum chromodynamics and electron scattering. This agreement also constrains several beyond-standard-model theories proposed to explain the proton-radius puzzle^2–5, in line with recent determinations of the proton charge radius^6–9, and establishes spectroscopy of light muonic atoms and ions as a precise tool for studies of nuclear properties.

We report linear polarization measurements of x rays emitted due to dielectronic recombination into highly charged krypton ions. The ions in the He-like through O-like charge states were populated in an electron-beam ion trap with the electron-beam energy adjusted to recombination resonances in order to produce $K\alpha$ x rays. The x rays were detected with a newly developed Compton polarimeter using a beryllium scattering target and 12 silicon x-ray detector diodes sampling the azimuthal distribution of the scattered x rays. The extracted degrees of linear polarization of several dielectronic recombination transitions agree with results of relativistic distorted-wave calculations. We also demonstrate a high sensitivity of the polarization to the Breit interaction, which is remarkable for a medium-$Z$ element like krypton. The experimental results can be used for polarization diagnostics of hot astrophysical and laboratory fusion plasmas.

The 1s2s\,\,S13$\rightarrow${}1s2\,\,S01 relativistic magnetic dipole transition in heliumlike argon, emitted by the plasma of an electron-cyclotron resonance ion source, has been measured using a double-flat crystal x-ray spectrometer. Such a spectrometer, used for the first time on a highly charged ion transition, provides absolute (reference-free) measurements in the x-ray domain. We find a transition energy of 3104.1605(77)~eV (2.5~ppm accuracy). This value is the most accurate, reference-free measurement done for such a transition and is in good agreement with recent QED predictions.

Hydrogen-like light muonic ions, in which one negative muon replaces all of the electrons, are extremely sensitive probes of nuclear structure. Using pulsed laser spectroscopy, we have measured three 2 S -2 P transitions in the muonic helium-3 (μ ³ He ⁺ ) ion, an ion formed by a negative muon and bare helium-3 nucleus. This allowed us to extract the Lamb shift, the 2 P fine structure splitting, and the 2 S -hyperfine splitting in μ ³ He ⁺ . Comparing these measurements with theory, we determined the root-mean-square charge radius of the helion ( ³ He nucleus) to be r _h = 1.97007(94) fm, in good agreement with the value from elastic electron scattering but a factor 15 more accurate. Our results represent benchmarks for few-nucleon theories and open the way for precision quantum electrodynamics tests in He atoms and ions.

We performed a reference-free measurement of the transition energies of the $1s2p{}^1{P}_1\to 1s^2{}^1{S}_0$ line in He-like argon, and of the $1s2s^{2}2p{}^1{P}_1\to 1s^{2}2s^2{}^1{S}_0$ line in Be-like argon ions. The highly charged ions were produced in the plasma of an electron-cyclotron resonance ion source. Both energy measurements were performed with an accuracy better than 3 parts in ${10}^6$, using a double flat-crystal spectrometer, without reference to any theoretical or experimental energy. The $1s2s^{2}2p{}^1{P}_1\to 1s^{2}2s^2{}^1{S}_0$ transition measurement is the first reference-free measurement for this core-excited transition. The $1s2p{}^1{P}_1\to 1s^2{}^1{S}_0$ transition measurement confirms recent measurement performed at the Heidelberg electron-beam ion trap. The width measurement in the He-like transition provides test of a purely radiative decay calculation. In the case of the Be-like argon transition, the width results from the sum of a radiative channel and three main Auger channels. We also performed multiconfiguration Dirac-Fock calculations of transition energies and rates and have done an extensive comparison with theory and other experimental data. For both measurements reported here, we find agreement with the most recent theoretical calculations within the combined theoretical and experimental uncertainties.

The CREMA collaboration is pursuing a measurement of the ground-state hyperfine splitting (HFS) in muonic hydrogen ( \mu μ p) with 1 ppm accuracy by means of pulsed laser spectroscopy to determine the two-photon-exchange contribution with 2\times10^{-4} 2 × 10 − 4 relative accuracy. In the proposed experiment, the \mu μ 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 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 μ 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 μ p is formed and the laser spectroscopy will occur.