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.

Quasifree one-proton knockout reactions have been employed in inverse kinematics for a systematic study of the structure of stable and exotic oxygen isotopes at the ${\mathrm{R}}^3\mathrm{B}/\mathrm{LAND}$ setup with incident beam energies in the range of $300–450\mathrm{MeV}/\mathrm{u}$. The oxygen isotopic chain offers a large variation of separation energies that allows for a quantitative understanding of single-particle strength with changing isospin asymmetry. Quasifree knockout reactions provide a complementary approach to intermediate-energy one-nucleon removal reactions. Inclusive cross sections for quasifree knockout reactions of the type ${}^A\mathrm{O}(p,2p){}^{A-1}\mathrm{N}$ have been determined and compared to calculations based on the eikonal reaction theory. The reduction factors for the single-particle strength with respect to the independent-particle model were obtained and compared to state-of-the-art ab initio predictions. The results do not show any significant dependence on proton-neutron asymmetry.

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.

Quantum electrodynamics (QED), the quantum field theory that describes the interaction between light and matter, is commonly regarded as the best-tested quantum theory in modern physics. However, this claim is mostly based on extremely precise studies performed in the domain of relatively low field strengths and light atoms and ions^1–6. In the realm of very strong electromagnetic fields such as in the heaviest highly charged ions (with nuclear charge Z ≫ 1), QED calculations enter a qualitatively different, non-perturbative regime. Yet, the corresponding experimental studies are very challenging, and theoretical predictions are only partially tested. Here we present an experiment sensitive to higher-order QED effects and electron–electron interactions in the high-Z regime. This is achieved by using a multi-reference method based on Doppler-tuned X-ray emission from stored relativistic uranium ions with different charge states. The energy of the 1s_1/22p_3/2 J = 2 → 1s_1/22s_1/2 J = 1 intrashell transition in the heaviest two-electron ion (U⁹⁰⁺) is obtained with an accuracy of 37 ppm. Furthermore, a comparison of uranium ions with different numbers of bound electrons enables us to disentangle and to test separately the one-electron higher-order QED effects and the bound electron–electron interaction terms without the uncertainty related to the nuclear radius. Moreover, our experimental result can discriminate between several state-of-the-art theoretical approaches and provides an important benchmark for calculations in the strong-field domain.