There is renewed interest in studies of muonic atoms, which may provide detailed information on nuclear structure. A major limiting factor in the interpretation of measurements is the nuclear polarization contribution. We propose a method to determine this contribution to the hyperfine structure in muonic atoms from a combination of theory and experiment for hydrogenlike ions and muonic atoms. Applying the method to ^{203,205}Tl and ^{209}Bi, for which there are H-like ion and muonic atom hyperfine experimental data, we find that the nuclear polarization contribution for these systems is small and place a limit on its size of less than 10% the total hyperfine splitting. We have also performed direct calculations of the nuclear polarization contribution using a semianalytical model, which indicate that it may be as much as two orders of magnitude smaller. Therefore, the nuclear polarization correction to the hyperfine structure of muonic atoms does not represent a limiting factor for next-generation experiments.

Nonlinearities in King plots (KP) of isotope shifts (IS) can reveal the existence of beyond-standard-model (BSM) interactions that couple electrons and neutrons. However, it is crucial to distinguish higher-order standard model (SM) effects from BSM physics. We measure the IS of the transitions ^{3}P_{0}→^{3}P_{1} in Ca^{14+} and ^{2}S_{1/2}→^{2}D_{5/2} in Ca^{+} with sub-Hz precision as well as the nuclear mass ratios with relative uncertainties below 4×10^{-11} for the five stable, even isotopes of calcium (^{40,42,44,46,48}Ca). Combined, these measurements yield a calcium KP nonlinearity with a significance of ∼10^{3}σ. Precision calculations show that the nonlinearity cannot be fully accounted for by the expected largest higher-order SM effect, the second-order mass shift, and identify the little-studied nuclear polarization as the only remaining SM contribution that may be large enough to explain it. Despite the observed nonlinearity, we improve existing KP-based constraints on a hypothetical Yukawa interaction for most of the new boson masses between 10  eV/c^{2} and 10^{7}  eV/c^{2}.

With the increasing precision of spectroscopic measurements, there is a growing demand for more accurate theoretical predictions, which requires the estimation of various higher -order effects, such as the nuclear deformation effect. Here, we present the results for nuclear deformation correction for the widest range of nuclei. The effects are investigated in terms of electronic transition energies, g factors, and hyperfine splitting constants, by implementing the deformed Fermi nuclear model to the Dirac equation. Based on the improved methodology and appropriate data classification, we present the results for over 1100 nuclei on figures, showing the general trends and anomalies. Moreover, it can serve as a simple tool providing estimations for specific planned research. In addition, we examine the connections and significance of deformation effects in the search of new physics with singly charged ions.

The leading-order contribution of a new boson to the muonic fine-structure anomaly, which refers to a discrepancy between the predicted transition energies and spectroscopic measurements of μ−90Zr, μ−120Sn, and μ−208Pb, is investigated. We consider bosons of scalar, vector, pseudoscalar, and pseudovector type. Spin-dependent couplings sourced by pseudoscalars or pseudovectors are disfavoured as solutions to the anomaly due to the nuclei in question having vanishing angular momentum. Spin-independent interactions resulting from scalar or vector exchange are also disfavoured because no parameter space exists to simultaneously fit different atomic states of the same nucleus. Therefore, we conclude that a ‘Beyond-the-Standard-Model’ resolution of the muonic fine-structure anomaly is generally disfavoured, and the first-order solution by a single new boson is excluded.

The nuclear-polarization corrections to the energy levels of highly charged ions are systematically investigated to leading order in the fine-structure constant. To this end, the notion of effective photon propagators with nuclear-polarization insertions is employed, where the nuclear excitation spectrum is calculated by means of the Hartree-Fock-based random-phase approximation. The effective Skyrme force is used to describe the interaction between nucleons, and the model dependence is analyzed. To leading order, the formalism predicts two contributions given by the effective vacuum-polarization and self-energy diagrams. The existing ambiguity around the vacuum-polarization term is resolved by demonstrating that it is effectively absorbed in the standard finite-nuclear-size correction. The self-energy part is evaluated with the full electromagnetic electron-nucleus interaction taken into account, where the importance of the effects of the nuclear three-currents is emphasized.

Nuclear deformation effects are theoretically investigated in terms of deformation corrections of the electronic binding and transition energies, $g$ factor, and hyperfine splitting constant. By solving the Dirac equation twice, with the nuclear potential calculated from Fermi and deformed Fermi nuclear density distributions, we separate the deformation effect in binding energies and wavefunctions. The parameters for both models are determined from experimental data. The considered corrections are of interest for spectral analysis and are numerically calculated for the widest possible range of nuclei, consisting over 1100 different samples. The subtleties between different sources of measured data and the corresponding results are discussed. In addition, the importance of deformation effects for the search of new physics with singly-charged ions is examined.

When collecting spectroscopic data on at least four isotopes, nonlinearities in the King plot are a possible sign of Physics beyond the Standard Model. In this work, an improved approach to the search for hypothetical new interactions with isotope shift spectroscopy of few-electron ions is presented. Very careful account is taken of the small nuclear corrections to the energy levels and the gyromagnetic factors, which cause deviations from King linearity within the Standard Model and are hence a possible source of confounds. In this new approach, the experimental King nonlinearity is not compared to the vanishing prediction of the Standard Model at the leading order, but to the calculated full Standard Model contribution to King nonlinearity. This makes searching for beyond-the-Standard-Model physics with King linearity analysis possible in a very-high-precision experimental regime, avoiding confounds. The bounds which can be set on beyond-the-Standard-Model parameters remain limited by the uncertainties on the small Standard Model nuclear corrections which cause King nonlinearity. Direct comparison between theory and experiment on a single pair of isotopes is advocated as a more suitable approach for few-electron ions.

Helium-3 has nowadays become one of the most important candidates for studies in fundamental physics1-3, nuclear and atomic structure4,5, magnetometry and metrology6, as well as chemistry and medicine7,8. In particular, 3He nuclear magnetic resonance (NMR) probes have been proposed as a new standard for absolute magnetometry6,9. This requires a high-accuracy value for the 3He nuclear magnetic moment, which, however, has so far been determined only indirectly and with a relative precision of 12 parts per billon10,11. Here we investigate the 3He+ ground-state hyperfine structure in a Penning trap to directly measure the nuclear g-factor of 3He+ [Formula: see text], the zero-field hyperfine splitting [Formula: see text] Hz and the bound electron g-factor [Formula: see text]. The latter is consistent with our theoretical value [Formula: see text] based on parameters and fundamental constants from ref. 12. Our measured value for the 3He+ nuclear g-factor enables determination of the g-factor of the bare nucleus [Formula: see text] via our accurate calculation of the diamagnetic shielding constant13 [Formula: see text]. This constitutes a direct calibration for 3He NMR probes and an improvement of the precision by one order of magnitude compared to previous indirect results. The measured zero-field hyperfine splitting improves the precision by two orders of magnitude compared to the previous most precise value14 and enables us to determine the Zemach radius15 to [Formula: see text] fm.

When collecting spectroscopic data on at least four isotopes, nonlinearities in the King plot are a possible sign of Physics beyond the Standard Model. In this work, an improved approach to the search for hypothetical new interactions with isotope shift spectroscopy of few-electron ions is presented. Very careful account is taken of the small nuclear corrections to the energy levels and the gyromagnetic factors, which cause deviations from King linearity within the Standard Model and are hence a possible source of confounds. In this new approach, the experimental King nonlinearity is not compared to the vanishing prediction of the Standard Model at the leading order, but to the calculated full Standard Model contribution to King nonlinearity. This makes searching for beyond-the-Standard-Model physics with King linearity analysis possible in a very-high-precision experimental regime, avoiding confounds. The bounds which can be set on beyond-the-Standard-Model parameters remain limited by the uncertainties on the small Standard Model nuclear corrections which cause King nonlinearity. Direct comparison between theory and experiment on a single pair of isotopes is advocated as a more suitable approach for few-electron ions.

Single-ion magnet properties are improved by embedding in a non-isostructural diamagnetic host lattice.

A means to extract the fine-structure constant $α$ from precision spectroscopic data on one-electron ions is presented. We show that in an appropriately weighted difference of the bound-electron $g$ factor and the ground state energy, nuclear structural effects can be effectively suppressed. This method is anticipated to deliver an independent value of $α$ via existing or near-future combined Penning trap and x-ray spectroscopic technology, and enables decreasing the uncertainty of $α$ by orders of magnitude.

Structural control over the magnetic properties of molecular nanomagnets (MNM) is key to bottom up design strategies for novel molecule-based magnetic materials, for e.g. data storage, magnetic cooling or spintronics. Herein, we switch the magnetism of materials made of the single-molecule magnet [CoxZn(1 x)(piv)2(2 NH2 Py)2], by structural changes induced by gradual replacement of complexes containing paramagnetic Co(II) with analogues containing diamagnetic Zn(II). Combining advanced structural and magnetic characterization techniques, we show that a change of the ratio of the two ions induces a change of the Co(II) coordination structure, changed magnetic relaxation times and a switch from easy-plane to easy-axis type magnetic anisotropy. Complementary quantum chemical calculations reveal magneto structural correlations, rationalizing the structural origin of the changed magnetic properties upon magnetic dilution. This approach provides an important new lever to understand, predict and tune the magnetic properties of a large range of MNM based magnetic materials.

A state-of-the-art approach for calculating the finite nuclear size correction to atomic energy levels and the bound-electron $g$ factor is introduced and demonstrated for a series of highly charged hydrogen-like ions. Firstly, self-consistent mean-field calculations based on the Skyrme-type nuclear interaction are employed in order to produce a realistic nuclear proton distribution. In the second step, the obtained nuclear charge density is used to construct the potential of an extended nucleus, and the Dirac equation is solved numerically. The ambiguity in the choice of a Skyrme parametrization is supressed by fine-tuning of only one parameter of the Skyrme force in order to accurately reproduce the experimental values of nuclear radii in each particular case. The homogeneously charged sphere approximation, the two-parameter Fermi distribution and experimental nuclear charge distributions are used for comparison with our approach, and the uncertainties of the presented calculations are estimated. In addition, suppression of the finite nuclear size effect for the specific differences of $g$ factors is demonstrated.

The ruthenium complex with bridging H3O2− ligand was obtained and the crystal structure was determined. The compound cis-[{RuNO(NH3)2Cl2}2(μ2-H3O2)]Cl crystallizes in the monoclinic space group P21/n with cell parameters a=15.0651(5), b=6.3624(2), c=15.3813(6)Å, β=94.9690(10)°, Z=4 and R=0.0185. The hydroxide hydrate anion is coordinated to the ruthenium atoms of the identical cis-{RuNO(NH3)2Cl2} fragments. The protonation of the starting cis-[RuNO(NH3)2(NO2)2OH] complex leads to the required coordinated aqua/hydroxide ratio if the specific amount of hydrochloric acid is used. The DFT calculations confirm the formation of the dimer structure in the gas phase. However, the presence of water molecules dramatically reduces the dimerization efficiency.