Measuring the α-particle charge radius with muonic helium-4 ions.

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 puzzle2-5, in line with recent determinations of the proton charge radius6-9, and establishes spectroscopy of light muonic atoms and ions as a precise tool for studies of nuclear properties.

Observation of a Low-Lying Metastable Electronic State in Highly Charged Lead by Penning-Trap Mass Spectrometry.

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 extreme ultraviolet 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+} that 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 4×10^{-12}. This experimental result agrees within 1σ with two partially different ab initio multiconfiguration 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 1.1×10^{23} and allows for the construction of a HCI clock with a fractional frequency instability of <10^{-19}/sqrt[τ].

Intensity Ratio of Kß/Kα in Selected Elements from Mg to Cu, and the Chemical Effects of Cr Kα1,2 Diagram Lines and Cr Kß/Kα Intensity Ratio in Cr Compounds.

Kα,ß X-ray lines from photon excitation were measured in selected elements from Mg to Cu using a high-resolution double-crystal X-ray spectrometer with a proportional counter, and the Kß/Kα intensity ratio for each element was obtained, after correcting for self-absorption, detection efficiency, and crystal reflectance. This intensity ratio increases rapidly from Mg to Ca but, in the 3d elements region, the increase becomes slower. This is related to the intensity of the Kß line involving valence electrons. The slow increase of this ratio in the 3d elements region is thought to be due to the correlation between 3d and 4s electrons. Moreover, the chemical shifts, FWHM, asymmetry indices, and Kß/Kα intensity ratios of the Cr compounds, due to different valences, were also investigated using the same double-crystal X-ray spectrometer. The chemical effects were clearly observed, and the Kß/Kα intensity ratio was found to be compound-dependent for Cr.

Testing Quantum Electrodynamics with Exotic Atoms.

Precision study of few-electron, high-Z ions is a privileged field for probing high-field, bound-state quantum electrodynamics (BSQED). However, the accuracy of such tests is plagued by nuclear uncertainties, which are often larger than the BSQED effects under investigation. We propose an alternative method with exotic atoms and show that transitions may be found between circular Rydberg states where nuclear contributions are vanishing while BSQED effects remain large. When probed with newly available quantum sensing detectors, these systems offer gains in sensitivity of 1 to 2 orders of magnitude, while the mean electric field largely exceeds the Schwinger limit.

The size of the proton.

The proton is the primary building block of the visible Universe, but many of its properties-such as its charge radius and its anomalous magnetic moment-are not well understood. The root-mean-square charge radius, r(p), has been determined with an accuracy of 2 per cent (at best) by electron-proton scattering experiments. The present most accurate value of r(p) (with an uncertainty of 1 per cent) is given by the CODATA compilation of physical constants. This value is based mainly on precision spectroscopy of atomic hydrogen and calculations of bound-state quantum electrodynamics (QED; refs 8, 9). The accuracy of r(p) as deduced from electron-proton scattering limits the testing of bound-state QED in atomic hydrogen as well as the determination of the Rydberg constant (currently the most accurately measured fundamental physical constant). An attractive means to improve the accuracy in the measurement of r(p) is provided by muonic hydrogen (a proton orbited by a negative muon); its much smaller Bohr radius compared to ordinary atomic hydrogen causes enhancement of effects related to the finite size of the proton. In particular, the Lamb shift (the energy difference between the 2S(1/2) and 2P(1/2) states) is affected by as much as 2 per cent. Here we use pulsed laser spectroscopy to measure a muonic Lamb shift of 49,881.88(76) GHz. On the basis of present calculations of fine and hyperfine splittings and QED terms, we find r(p) = 0.84184(67) fm, which differs by 5.0 standard deviations from the CODATA value of 0.8768(69) fm. Our result implies that either the Rydberg constant has to be shifted by -110 kHz/c (4.9 standard deviations), or the calculations of the QED effects in atomic hydrogen or muonic hydrogen atoms are insufficient.

Absolute measurement of the relativistic magnetic dipole transition energy in heliumlike argon.

The 1s2s (3)S(1)→1s(2) (1)S(0) 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.

Laser spectroscopy of muonic deuterium.

The deuteron is the simplest compound nucleus, composed of one proton and one neutron. Deuteron properties such as the root-mean-square charge radius rd and the polarizability serve as important benchmarks for understanding the nuclear forces and structure. Muonic deuterium µd is the exotic atom formed by a deuteron and a negative muon µ(-). We measured three 2S-2P transitions in µd and obtain r(d) = 2.12562(78) fm, which is 2.7 times more accurate but 7.5σ smaller than the CODATA-2010 value r(d) = 2.1424(21) fm. The µd value is also 3.5σ smaller than the r(d) value from electronic deuterium spectroscopy. The smaller r(d), when combined with the electronic isotope shift, yields a "small" proton radius r(p), similar to the one from muonic hydrogen, amplifying the proton radius puzzle.

Improved x-ray detection and particle identification with avalanche photodiodes.

Avalanche photodiodes are commonly used as detectors for low energy x-rays. In this work, we report on a fitting technique used to account for different detector responses resulting from photoabsorption in the various avalanche photodiode layers. The use of this technique results in an improvement of the energy resolution at 8.2 keV by up to a factor of 2 and corrects the timing information by up to 25 ns to account for space dependent electron drift time. In addition, this waveform analysis is used for particle identification, e.g., to distinguish between x-rays and MeV electrons in our experiment.

Proton structure from the measurement of 2S-2P transition frequencies of muonic hydrogen.

Accurate knowledge of the charge and Zemach radii of the proton is essential, not only for understanding its structure but also as input for tests of bound-state quantum electrodynamics and its predictions for the energy levels of hydrogen. These radii may be extracted from the laser spectroscopy of muonic hydrogen (µp, that is, a proton orbited by a muon). We measured the 2S(1/2)(F=0)-2P(3/2)(F=1) transition frequency in µp to be 54611.16(1.05) gigahertz (numbers in parentheses indicate one standard deviation of uncertainty) and reevaluated the 2S(1/2)(F=1)-2P(3/2)(F=2) transition frequency, yielding 49881.35(65) gigahertz. From the measurements, we determined the Zemach radius, r(Z) = 1.082(37) femtometers, and the magnetic radius, r(M) = 0.87(6) femtometer, of the proton. We also extracted the charge radius, r(E) = 0.84087(39) femtometer, with an order of magnitude more precision than the 2010-CODATA value and at 7σ variance with respect to it, thus reinforcing the proton radius puzzle.

Asymptotic properties of self-energy coefficients.

We investigate the asymptotic properties of higher-order binding corrections to the one-loop self-energy of excited states in atomic hydrogen. We evaluate the historically problematic A60 coefficient for all P states with principal quantum numbers n