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A very precise measurement of the magnetic moment of a single electron bound to a carbon nucleus, combined with a state-of-the-art calculation in the framework of bound-state quantum electrodynamics, gives a new value of the atomic mass of the electron that is more precise than the currently accepted one by a factor of 13. Electron mass to unprecedented precision The atomic mass of the electron is a key parameter for fundamental physics. A precise determination is a challenge because the mass is so low. Sven Sturm and colleagues report on a new determination of the electron's mass in atomic units. The authors measured the magnetic moment of a single electron bound to a reference ion (a bare nucleus of carbon-12). The results were analysed using state-of-the-art quantum electrodynamics theory to yield a mass value with a precision that exceeds the current literature value by more than an order of magnitude. The quest for the value of the electron’s atomic mass has been the subject of continuing efforts over the past few decades 1 , 2 , 3 , 4 . Among the seemingly fundamental constants that parameterize the Standard Model of physics 5 and which are thus responsible for its predictive power, the electron mass m e is prominent, being responsible for the structure and properties of atoms and molecules. It is closely linked to other fundamental constants, such as the Rydberg constant R ∞ and the fine-structure constant α (ref. 6 ). However, the low mass of the electron considerably complicates its precise determination. Here we combine a very precise measurement of the magnetic moment of a single electron bound to a carbon nucleus with a state-of-the-art calculation in the framework of bound-state quantum electrodynamics. The precision of the resulting value for the atomic mass of the electron surpasses the current literature value of the Committee on Data for Science and Technology (CODATA 6 ) by a factor of 13. This result lays the foundation for future fundamental physics experiments 7 , 8 and precision tests of the Standard Model 9 , 10 , 11 .

Despite being a complex many-body system, the atomic nucleus exhibits simple structures for certain ‘magic’ numbers of protons and neutrons. The calcium chain in particular is both unique and puzzling: evidence of doubly magic features are known in 40,48 Ca, and recently suggested in two radioactive isotopes, 52,54 Ca. Although many properties of experimentally known calcium isotopes have been successfully described by nuclear theory, it is still a challenge to predict the evolution of their charge radii. Here we present the first measurements of the charge radii of 49,51,52 Ca, obtained from laser spectroscopy experiments at ISOLDE, CERN. The experimental results are complemented by state-of-the-art theoretical calculations. The large and unexpected increase of the size of the neutron-rich calcium isotopes beyond N = 28 challenges the doubly magic nature of 52 Ca and opens new intriguing questions on the evolution of nuclear sizes away from stability, which are of importance for our understanding of neutron-rich atomic nuclei. Doubly magic atomic nuclei — having a magic number of both protons and neutrons — are very stable. Now, experiments revealing unexpectedly large charge radii for a series of Ca isotopes put the doubly magic nature of the 52 Ca nucleus into question.

The masses of the exotic calcium isotopes 53 Ca and 54 Ca measured by a multi-reflection time-of-flight method confirm predictions of calculations including nuclear three-body interactions. Exotic calcium isotopes weighed The calcium atom provides an ideal system for the study of nuclear shell evolution, from the valley of stability to the limits of existence. Although predictions for the masses of the neutron-rich isotopes 51 Ca and 52 Ca have been tested by direct measurements, it is an open question as to how nuclear masses evolve for heavier calcium isotopes. Frank Wienholtz and colleagues report the mass determination of the exotic calcium isotopes 53 Ca and 54 Ca, using a multi-reflection time-of-flight mass spectrometer. The results provide key information for theoretical models and show that a description of extreme neutron-rich nuclei can be closely connected to a deeper understanding of nuclear forces. The properties of exotic nuclei on the verge of existence play a fundamental part in our understanding of nuclear interactions 1 . Exceedingly neutron-rich nuclei become sensitive to new aspects of nuclear forces 2 . Calcium, with its doubly magic isotopes 40 Ca and 48 Ca, is an ideal test for nuclear shell evolution, from the valley of stability to the limits of existence. With a closed proton shell, the calcium isotopes mark the frontier for calculations with three-nucleon forces from chiral effective field theory 3 , 4 , 5 , 6 . Whereas predictions for the masses of 51 Ca and 52 Ca have been validated by direct measurements 4 , it is an open question as to how nuclear masses evolve for heavier calcium isotopes. Here we report the mass determination of the exotic calcium isotopes 53 Ca and 54 Ca, using the multi-reflection time-of-flight mass spectrometer 7 of ISOLTRAP at CERN. The measured masses unambiguously establish a prominent shell closure at neutron number N = 32, in excellent agreement with our theoretical calculations. These results increase our understanding of neutron-rich matter and pin down the subtle components of nuclear forces that are at the forefront of theoretical developments constrained by quantum chromodynamics 8 .

The magnetic moment of the proton is directly measured with unprecedented precision using a double Penning trap. An important moment for matter–antimatter symmetry Although less prominent than large synchrotron experiments, measurements of fundamental constants or atomic properties can still make valuable contributions to the search of physical laws beyond the Standard Model — if the measurement precision is high enough. In a direct measurement, Andreas Mooser et al . determine the magnetic moment of the proton with unprecedented precision. The measurement is performed using a double Penning trap, a system in which a single ion is confined and manipulated in a powerful homogeneous magnetic field. In combination with a direct measurement of the antiproton magnetic moment, this work will pave the way for a rigorous test of matter–antimatter symmetry. One of the fundamental properties of the proton is its magnetic moment, µ p . So far µ p has been measured only indirectly, by analysing the spectrum of an atomic hydrogen maser in a magnetic field 1 . Here we report the direct high-precision measurement of the magnetic moment of a single proton using the double Penning-trap technique 2 . We drive proton-spin quantum jumps by a magnetic radio-frequency field in a Penning trap with a homogeneous magnetic field. The induced spin transitions are detected in a second trap with a strong superimposed magnetic inhomogeneity 3 . This enables the measurement of the spin-flip probability as a function of the drive frequency. In each measurement the proton’s cyclotron frequency is used to determine the magnetic field of the trap. From the normalized resonance curve, we extract the particle’s magnetic moment in terms of the nuclear magneton: μ p = 2.792847350(9) μ N . This measurement outperforms previous Penning-trap measurements 4 , 5 in terms of precision by a factor of about 760. It improves the precision of the forty-year-old indirect measurement, in which significant theoretical bound state corrections 6 were required to obtain µ p , by a factor of 3. By application of this method to the antiproton magnetic moment, the fractional precision of the recently reported value 7 can be improved by a factor of at least 1,000. Combined with the present result, this will provide a stringent test of matter/antimatter symmetry with baryons 8 .

The advances in technology mainly concerning ion traps, storage rings, lasers, high-precision frequency measurements, detectors, and particle beams as well as advances in atom and ion manipulation have allowed for a considerable progress in the determination of fundamental parameters and quantities of radionuclides such as masses, electromagnetic moments, lifetimes and beta decay correlations. The main subjects covered by this topical collection are: high-precision mass measurements both with Penning traps and storage rings for neutrino physics, nuclear structure, astrophysics, and decay studies. Laser spectroscopy is applied for the determination of other ground state properties like spins, moments, and nuclear charge radii. Furthermore, results from decay studies of highly charged ions and reactions in storage rings are presented.

State-of-the-art optical clocks 1 achieve precisions of 10 −18 or better using ensembles of atoms in optical lattices 2 , 3 or individual ions in radio-frequency traps 4 , 5 . Promising candidates for use in atomic clocks are highly charged ions 6 (HCIs) and nuclear transitions 7 , which are largely insensitive to external perturbations and reach wavelengths beyond the optical range 8 that are accessible to frequency combs 9 . However, insufficiently accurate atomic structure calculations hinder the identification of suitable transitions in HCIs. Here we report the observation of a long-lived metastable electronic state in an HCI by measuring the mass difference between the ground and excited states in rhenium, providing a non-destructive, direct determination of an electronic excitation energy. The result is in agreement with advanced calculations. We use the high-precision Penning trap mass spectrometer PENTATRAP to measure the cyclotron frequency ratio of the ground state to the metastable state of the ion with a precision of 10 −11 —an improvement by a factor of ten compared with previous measurements 10 , 11 . With a lifetime of about 130 days, the potential soft-X-ray frequency reference at 4.96 × 10 16 hertz (corresponding to a transition energy of 202 electronvolts) has a linewidth of only 5 × 10 −8 hertz and one of the highest electronic quality factors (10 24 ) measured experimentally so far. The low uncertainty of our method will enable searches for further soft-X-ray clock transitions 8 , 12 in HCIs, which are required for precision studies of fundamental physics 6 . Penning trap mass spectrometry is used to measure the electronic transition energy from a long-lived metastable state to the ground state in highly charged rhenium ions with a precision of 10 −11 .

The magnetic moment of the antiproton is measured at the parts-per-billion level, improving on previous measurements by a factor of about 350. Magnetic moment of the antiproton Comparing the fundamental properties of normal-matter particles with their antimatter counterparts tests charge–parity–time (CPT) invariance, which is an important part of the standard model of particle physics. Many properties have been measured to the parts-per-billion level of uncertainty, but the magnetic moment of the antiproton has not. Christian Smorra and colleagues have now done so, and report that it is −2.7928473441 ± 0.0000000042 in units of the nuclear magneton. This is consistent with the magnetic moment of the proton, 2.792847350 ± 0.000000009 in the same units. Assuming CPT invariance, these two values should be the same, except for the difference in sign, so this result provides a more stringent constraint on certain CPT-violating effects. Precise comparisons of the fundamental properties of matter–antimatter conjugates provide sensitive tests of charge–parity–time (CPT) invariance 1 , which is an important symmetry that rests on basic assumptions of the standard model of particle physics. Experiments on mesons 2 , leptons 3 , 4 and baryons 5 , 6 have compared different properties of matter–antimatter conjugates with fractional uncertainties at the parts-per-billion level or better. One specific quantity, however, has so far only been known to a fractional uncertainty at the parts-per-million level 7 , 8 : the magnetic moment of the antiproton, . The extraordinary difficulty in measuring with high precision is caused by its intrinsic smallness; for example, it is 660 times smaller than the magnetic moment of the positron 3 . Here we report a high-precision measurement of in units of the nuclear magneton μ N with a fractional precision of 1.5 parts per billion (68% confidence level). We use a two-particle spectroscopy method in an advanced cryogenic multi-Penning trap system. Our result  = −2.7928473441(42) μ N (where the number in parentheses represents the 68% confidence interval on the last digits of the value) improves the precision of the previous best measurement 8 by a factor of approximately 350. The measured value is consistent with the proton magnetic moment 9 , μ p  = 2.792847350(9) μ N , and is in agreement with CPT invariance. Consequently, this measurement constrains the magnitude of certain CPT-violating effects 10 to below 1.8 × 10 −24 gigaelectronvolts, and a possible splitting of the proton–antiproton magnetic moments by CPT-odd dimension-five interactions to below 6 × 10 −12 Bohr magnetons 11 .

The tin isotope 100Sn is of singular interest for nuclear structure due to its closed-shell proton and neutron configurations. It is also the heaviest nucleus comprising protons and neutrons in equal numbers—a feature that enhances the contribution of the short-range proton–neutron pairing interaction and strongly influences its decay via the weak interaction. Decay studies in the region of 100Sn have attempted to prove its doubly magic character1 but few have studied it from an ab initio theoretical perspective2,3, and none of these has addressed the odd-proton neighbours, which are inherently more difficult to describe but crucial for a complete test of nuclear forces. Here we present direct mass measurements of the exotic odd-proton nuclide 100In, the beta-decay daughter of 100Sn, and of 99In, with one proton less than 100Sn. We use advanced mass spectrometry techniques to measure 99In, which is produced at a rate of only a few ions per second, and to resolve the ground and isomeric states in 101In. The experimental results are compared with ab initio many-body calculations. The 100-fold improvement in precision of the 100In mass value highlights a discrepancy in the atomic-mass values of 100Sn deduced from recent beta-decay results4,5.Accurate mass measurements of the indium isotopes adjacent to the doubly magic 100Sn provide critical benchmarks for ab initio theory, which withstands the challenge.

Inner-shell electrons naturally sense the electric field close to the nucleus, which can reach extreme values beyond 10 15  V cm −1 for the innermost electrons 1 . Especially in few-electron, highly charged ions, the interaction with the electromagnetic fields can be accurately calculated within quantum electrodynamics (QED), rendering these ions good candidates to test the validity of QED in strong fields. Consequently, their Lamb shifts were intensively studied in the past several decades 2 , 3 . Another approach is the measurement of gyromagnetic factors ( g factors) in highly charged ions 4 – 7 . However, so far, either experimental accuracy or small field strength in low- Z ions 5 , 6 limited the stringency of these QED tests. Here we report on our high-precision, high-field test of QED in hydrogen-like 118 Sn 49+ . The highly charged ions were produced with the Heidelberg electron beam ion trap (EBIT) 8 and injected into the ALPHATRAP Penning-trap setup 9 , in which the bound-electron g factor was measured with a precision of 0.5 parts per billion (ppb). For comparison, we present state-of-the-art theory calculations, which together test the underlying QED to about 0.012%, yielding a stringent test in the strong-field regime. With this measurement, we challenge the best tests by means of the Lamb shift and, with anticipated advances in the g -factor theory, surpass them by more than an order of magnitude. A high-precision, high-field test of quantum electrodynamics measuring the bound-electron g factor in hydrogen-like tin is described, which—together with state-of-the-art theory calculations—yields a stringent test in the strong-field regime.

The CPT theorem (the assumption that physical laws are invariant under simultaneous charge conjugation, parity transformation and time reversal) is central to the standard model of particle physics; here the charge-to-mass ratio of the antiproton is compared to that of the proton, with a precision of 69 parts per trillion, and the result supports the CPT theorem at the atto-electronvolt scale. CPT theorem put to the test The CPT theorem, the assumption that physical laws are invariant under simultaneous charge conjugation, parity transformation and time reversal, is central to the standard model of particle physics. Consequently, precision tests of the CPT theorem are a window onto the physics beyond the standard model. Here, Stefan Ulmer et al . test the CPT theorem by measuring whether particles and antiparticles, apart from a sign change, are identical. In a Penning-trap measurement, they compare the antiproton charge-to-mass ratio to its proton counterpart, showing that the CPT theorem holds at the atto-electronvolt scale. Their experiment improves the precision of previous proton–antiproton mass comparisons by a factor of four. Invariance under the charge, parity, time-reversal (CPT) transformation 1 is one of the fundamental symmetries of the standard model of particle physics. This CPT invariance implies that the fundamental properties of antiparticles and their matter-conjugates are identical, apart from signs. There is a deep link between CPT invariance and Lorentz symmetry—that is, the laws of nature seem to be invariant under the symmetry transformation of spacetime—although it is model dependent 2 . A number of high-precision CPT and Lorentz invariance tests—using a co-magnetometer, a torsion pendulum and a maser, among others—have been performed 3 , but only a few direct high-precision CPT tests that compare the fundamental properties of matter and antimatter are available 4 , 5 , 6 , 7 , 8 . Here we report high-precision cyclotron frequency comparisons of a single antiproton and a negatively charged hydrogen ion (H − ) carried out in a Penning trap system. From 13,000 frequency measurements we compare the charge-to-mass ratio for the antiproton to that for the proton and obtain . The measurements were performed at cyclotron frequencies of 29.6 megahertz, so our result shows that the CPT theorem holds at the atto-electronvolt scale. Our precision of 69 parts per trillion exceeds the energy resolution of previous antiproton-to-proton mass comparisons 7 , 9 as well as the respective figure of merit of the standard model extension 10 by a factor of four. In addition, we give a limit on sidereal variations in the measured ratio of <720 parts per trillion. By following the arguments of ref. 11 , our result can be interpreted as a stringent test of the weak equivalence principle of general relativity using baryonic antimatter, and it sets a new limit on the gravitational anomaly parameter of < 8.7 × 10 −7 .