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.

Muons are a fascinating probe to study nuclear properties. Muonic atoms can easily be formed by stopping negative muons inside a material. The muon is subsequently captured by the nucleus and, due to its much higher mass compared to the electron, orbits the nucleus at very small distances. During this atomic capture process, the muon emits characteristic X-rays during its cascade down to the ground state. The energies of these X-rays reveal the muonic energy level scheme, from which properties like the nuclear charge radius or its quadrupole moment can be extracted. While almost all stable elements have been examined using muons, probing highly radioactive atoms has so far not been possible. The muX experiment has developed a technique based on transfer reaction inside a high-pressure hydrogen/deuterium gas cell to examine targets available only in microgram quantities.

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.

Meson factories are powerful drivers of diverse physics programs. With beam powers already in the MW-regime attention has to be turned to target and beam line design to further significantly increase surface muon rates available for experiments. For this reason we have explored the possibility of using a neutron spallation target as a source of surface muons by performing detailed Geant4 simulations with pion production cross sections based on a parametrization of existing data. While the spallation target outperforms standard targets in the backward direction by more than a factor 7 it is not more efficient than standard targets viewed under 90°. Not surprisingly, the geometry of the target plays a large role in the generation of surface muons. Through careful optimization, a gain in surface muon rate of between 30% and 60% over the standard “box-like” target used at the Paul Scherrer Institute could be achieved by employing a rotated slab target. An additional 10% gain could also be possible by utilizing novel target materials such as, e.g., boron carbide.

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.

The gravitational acceleration of antimatter, $\overline{g}$ , has yet to be directly measured; an unexpected outcome of its measurement could change our understanding of gravity, the universe, and the possibility of a fifth force. Three avenues are apparent for such a measurement: antihydrogen, positronium, and muonium, the last requiring a precision atom interferometer and novel muonium beam under development. The interferometer and its few-picometer alignment and calibration systems appear feasible. With 100 nm grating pitch, measurements of $\overline{g}$ to 10%, 1%, or better can be envisioned. These could constitute the first gravitational measurements of leptonic matter, of 2nd-generation matter, and possibly, of antimatter.