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 2S-2P transitions in the muonic helium-3 (μ3He+) ion, an ion formed by a negative muon and bare helium-3 nucleus. This allowed us to extract the Lamb shift, the 2P fine structure splitting, and the 2S-hyperfine splitting in μ3He+. Comparing these measurements with theory, we determined the root-mean-square charge radius of the helion (3He nucleus) to be rh = 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.

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. In the proposed experiment, the \mu μ 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 2 molecule. The resulting increase of kinetic energy after this cycle modifies the \mu μ p atom diffusion in the hydrogen gas and the arrival time of the \mu μ 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 μ p diffusion in the H _2 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 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.

The CREMA collaboration is pursuing a measurement of the ground-state hyperfine splitting (HFS) in muonic hydrogen (µp) with 1 ppm accuracy by means of pulsed laser spectroscopy to determine the two-photon-exchange contribution with 2 × 10 -4 relative accuracy.In the proposed experiment, the µp atom that undergoes a laser excitation from the singlet hyperfine state to the triplet hyperfine state, 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 µp 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

The CREMA collaboration is pursuing a measurement of the ground-state hyperfine splitting (HFS) in muonic hydrogen (\muμp) 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 \muμp 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_22 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 \muμp 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 \muμp is formed and the laser spectroscopy will occur.

A Correction to this paper has been published: https://doi.org/10.1038/s41586-021-03360-2.

The energy levels of hydrogen-like atomic systems are shifted slightly by the complex structure of the nucleus, in particular by the finite size of the nucleus. These energy shifts are vastly magnified in muonic atoms and ions, i.e. the hydrogen-like systems formed by a negative muon and a nucleus. By measuring the 2S-2P energy splitting in muonic hydrogen, muonic deuterium and muonic helium, we have been able to deduce the p, d, ^33He and ^44He nuclear charge radii to an unprecedented accuracy. These radii provide benchmarks for hadron and nuclear theories, lead to precision tests of bound-state QED in regular atoms and to a better determination of the Rydberg constant.

In experiments at the Paul Scherrer Institute PSI, an international research collaboration has measured the radius of the atomic nucleus of helium five times more precisely than ever before. With the aid of the new value, fundamental physical theories can be tested and natural constants can be determined even more precisely. For their measurements, the researchers needed muons—these particles are similar to electrons but are around 200 times heavier. PSI is the only research site in the world where enough so-called low-energy muons are produced for such experiments. The researchers are publishing their results today in the journal Nature.

Precision spectroscopy of light muonic atoms provides unique information about the atomic and nuclear structure of these systems and thus represents a way to access fundamental interactions, properties and constants. One application comprises the determination of absolute nuclear charge radii with unprecedented accuracy from measurements of the 2S-2P Lamb shift. Here, we review recent results of nuclear charge radii extracted from muonic hydrogen and helium spectroscopy and present experiment proposals to access light muonic atoms with Z ≥ 3. In addition, our approaches towards a precise measurement of the Zemach radii in muonic hydrogen (μp) and helium (μ^3He^+) are discussed. These results will provide new tests of bound-state quantum-electrodynamics in hydrogen-like systems and can be used as benchmarks for nuclear structure theories.

The double response of a large area avalanche photodiode, a planar RMD model S1315, to 6-keV x-rays was investigated as a function of APD biasing voltage and for different operating temperatures. Our data are consistent with the interpretation that the dissimilar APD response is due to x-ray interactions in the different APD-layer structures; interactions in the APD entrance layer just below the front electrode, where the electric field intensity is very low lead to pulses with higher risetime and lower amplitudes, when compared with interactions in the deeper layers where the electric field is more intense. Average pulse risetime values of 14 and 7 ns have been measured in our setup, the slower pulses presenting average amplitudes which are around 20% lower than those of the faster pulses. While the fast risetime does not depend significantly on APD biasing voltage and on temperature, the slow risetime presents a slight decrease with increasing bias voltage and decreasing temperature, a behaviour that is consistent with the increase of the electric field as a result of the increase in the APD biasing voltage. The fraction of the slow pulses reduces from 60% to 40% as the APD biasing increases from about 1.58 to 1.64 kV, indicating a reduction in the thickness, from 25 to 15 mu m, in the weak-electric-field entrance layer.

We provide an up to date summary of the theory contributions to the 2S -> 2P Lamb shift and the fine structure of the 2P state in the muonic helium ion (mu He-4)(+). This summary serves as the basis for the extraction of the alpha particle charge radius from the muonic helium Lamb shift measurements at the Paul Scherrer Institute, Switzerland. Individual theory contributions needed for a charge radius extraction are compared and compiled into a consistent summary. The influence of the alpha particle charge distribution on the elastic two-photon exchange is studied to take into account possible model-dependencies of the energy levels on the electric form factor of the nucleus. We also discuss the theory uncertainty which enters the extraction of the(3)He-He-4 isotope shift from the muonic measurements. The theory uncertainty of the extraction is much smaller than a present discrepancy between previous isotope shift measurements. This work completes our series of n = 2 theory compilations in light muonic atoms which we have performed already for muonic hydrogen, deuterium, and helium-3 ions. (C) 2018 Elsevier Inc. All rights reserved.

The present knowledge of Lamb shift, fine-, and hyperfine structure of the 2S and 2P states in muonic helium-3 ions is reviewed in anticipation of the results of a first measurement of several 2S → 2P transition frequencies in the muonic helium-3 ion, μ3He+. This ion is the bound state of a single negative muon μ- and a bare helium-3 nucleus (helion), 3He++. A term-by-term comparison of all available sources, including new, updated, and so far unpublished calculations, reveals reliable values and uncertainties of the QED and nuclear structure-dependent contributions to the Lamb shift and the hyperfine splitting. These values are essential for the determination of the helion rms charge radius and the nuclear structure effects to the hyperfine splitting in μ3He+. With this review we continue our series of theory summaries in light muonic atoms [see A. Antognini et al., Ann. Phys. 331, 127 (2013); J.J. Krauth et al., Ann. Phys. 366, 168 (2016); and M. Diepold et al. arXiv:1606.05231 (2016)].

We give a pedagogical description of the method to extract the charge radii and Rydberg constant from laser spectroscopy in regular hydrogen (H) and deuterium (D) atoms, that is part of the CODATA least-squares adjustment (LSA) of the fundamental physical constants. We give a deuteron charge radius r(d) from D spectroscopy alone of 2.1415(45) fm. This value is independent of the measurements that lead to the proton charge radius, and five times more accurate than the value found in the CODATA Adjustment 10. The improvement is due to the use of a value for the 1S -> 2S transition in atomic deuterium which can be inferred from published data or found in a PhD thesis.

The deuteron is too small, too The radius of the proton has remained a point of debate ever since the spectroscopy of muonic hydrogen indicated a large discrepancy from the previously accepted value. Pohl et al. add an important clue for solving this so-called proton radius puzzle. They determined the charge radius of the deuteron, a nucleus consisting of a proton and a neutron, from the transition frequencies in muonic deuterium. Mirroring the proton radius puzzle, the radius of the deuteron was several standard deviations smaller than the value inferred from previous spectroscopic measurements of electronic deuterium. This independent discrepancy points to experimental or theoretical error or even to physics beyond the standard model. Science , this issue p. 669

We report the first laser spectroscopy of muonic deuterium. At the Paul Scherrer Institute, we have measured the frequency of the 2S-2P Lamb shift in muonic deuterium. As in the case of the muonic hydrogen, the observed lines are shifted from the theoretical predictions. Thanks to improved new QED and nuclear structure calculations, an accurate determination of the deuteron radius can be extracted from our study. This determination will give a new and important input to the proton size puzzle.

We review the status of the proton charge radius puzzle. Emphasis is given to the various experiments initiated to resolve the conflict between the muonic hydrogen results and the results from scattering and regular hydrogen spectroscopy.

The present knowledge of Lamb shift, fine- and hyperfine structure of the 2S and 2P states in muonic deuterium is reviewed in anticipation of the results of a first measurement of several 2S - 2P transition frequencies in muonic deuterium (mu d). A term-by-term comparison of all available sources reveals reliable values and uncertainties of the QED and nuclear structure-dependent contributions to the Lamb shift, which are essential for a determination of the deuteron rms charge radius from mu d. Apparent discrepancies between different sources are resolved, in particular for the difficult two-photon exchange contributions. Problematic single sourced terms are identified which require independent recalculation. (C) 2016 Elsevier Inc. All rights reserved.

Quantum interference between energetically close states is theoretically investigated, with the state structure being observed via laser spectroscopy. In this work, we focus on hyperfine states of selected hydrogenic muonic isotopes, and on how quantum interference affects the measured Lamb shift. The process of photon excitation and subsequent photon decay is implemented within the framework of nonrelativistic second-order perturbation theory. Due to its experimental interest, calculations are performed for muonic hydrogen, deuterium, and helium-3. We restrict our analysis to the case of photon scattering by incident linear polarized photons and the polarization of the scattered photons not being observed. We conclude that while quantum interference effects can be safely neglected in muonic hydrogen and helium-3, in the case of muonic deuterium there are resonances with close proximity, where quantum interference effects can induce shifts up to a few percent of the linewidth, assuming a pointlike detector. However, by taking into account the geometry of the setup used by the CREMA collaboration, this effect is reduced to less than 0.2% of the linewidth in all possible cases, which makes it irrelevant at the present level of accuracy.

Laser spectroscopy of the Lamb shift (2S-2P energy difference) in light muonic atoms or ions, in which one negative muon $\mu^-$ is bound to a nucleus, has been performed. The measurements yield significantly improved values of the root-mean-square charge radii of the nuclei, owing to the large muon mass, which results in a vastly increased muon wave function overlap with the nucleus. The values of the proton and deuteron radii are 10 and 3 times more accurate than the respective CODATA values, but 7 standard deviations smaller. Data on muonic helium-3 and -4 ions is being analyzed and will give new insights. In future, the (magnetic) Zemach radii of the proton and the helium-3 nuclei will be determined from laser spectroscopy of the 1S hyperfine splittings, and the Lamb shifts of muonic Li, Be and B can be used to improve the respective charge radii.

Thin-disk laser pump layouts yielding an increased number of passes for a given pump module size and pump source quality are proposed. These layouts result from a general scheme based on merging two simpler pump optics arrangements. Some peculiar examples can be realized by adapting standard, commercially available pump optics with an additional mirror pair. More pump passes yield better efficiency, opening the way for the usage of active materials with low absorption. In a standard multipass pump design, scaling of the number of beam passes brings about an increase in the overall size of the optical arrangement or an increase in the pump source quality requirements. Such increases are minimized in our scheme, making them eligible for industrial applications.