CODATA recommended values of the fundamental physical constants: 2018

Precision spectroscopy on 9Be overcomes limitations from nuclear structure

Many powerful tests of the standard model of particle physics and searches for new physics with precision atomic spectroscopy are hindered by our lack of knowledge of nuclear properties. Ideally, these properties may be derived from precise measurements of the most sensitive and theoretically best-understood observables, often found in hydrogen-like systems. Although these measurements are abundant for the electric properties of nuclei, they are scarce for the magnetic properties, and precise experimental results are limited to the lightest of nuclei1-4. Here we focus on 9Be, which offers the unique possibility to use comparisons between different charge states available for high-precision spectroscopy in Penning traps to test theoretical calculations typically obscured by nuclear structure. In particular, we perform high-precision spectroscopy of the 1s hyperfine and Zeeman structure in hydrogen-like 9Be3+. We determine the effective Zemach radius with an uncertainty of 500 ppm, and the bare nuclear magnetic moment with an uncertainty of 0.6 parts per billion- uncertainties unmatched beyond hydrogen. Moreover, we compare our measurements with the measurements conducted on the three-electron charge state 9Be+ (ref. 5), which enables testing the calculation of multi-electron diamagnetic shielding effects of the nuclear magnetic moment at the parts per billion level. Furthermore, we test the quantum electrodynamics methods used for the calculation of the hyperfine splitting. Our results serve as a crucial benchmark for transferring high-precision results of nuclear magnetic properties across different electronic configurations.

Impact of Two-Body Currents on Magnetic Dipole Moments of Nuclei

We investigate the effects of two-body currents on magnetic dipole moments of medium-mass and heavy nuclei using the valence-space in-medium similarity renormalization group with chiral effective field theory interactions and currents. Focusing on near doubly magic nuclei from oxygen to bismuth, we have found that the leading two-body currents globally improve the agreement with experimental magnetic moments. Moreover, our results show the importance of multishell effects for ^{41}Ca, which suggest that the Z=N=20 gap in ^{40}Ca is not as robust as in ^{48}Ca. The increasing contribution of two-body currents in heavier systems is explained by the operator structure of the center-of-mass dependent Sachs term.

Efficient computational model of the in-flow capturing of magnetic nanoparticles by a cylindrical magnet for cancer nanomedicine

Magnetic nanoparticles have emerged as a promising approach to improving cancer treatment. However, many nanoparticle designs fail in clinical trials due to a lack of understanding of how to overcome the in vivo transport barriers. To address this shortcoming, we develop a computational model aimed at the study of magnetic nanoparticles in vitro and in vivo. In this paper, we present an important building block for this overall goal, namely an efficient computational model of the in-flow capture of magnetic nanoparticles by a cylindrical permanent magnet in an idealized test setup. We use a continuum approach based on the Smoluchowski advection-diffusion equation, combined with a simple approach to consider the capture at an impenetrable boundary, and derive an analytical expression for the magnetic force of a cylindrical magnet of finite length on the nanoparticles. This provides a simple and numerically efficient way to study different magnet configurations and their influence on the nanoparticle distribution in three dimensions. Such an in silico model can increase insight into the underlying physics, help to design prototypes, and serve as a precursor to more complex systems in vivo and in silico.

Rydberg atom electric field sensing for metrology, communication and hybrid quantum systems

Rydberg atoms-based electric field sensing has developed rapidly over the past decade. A variety of theoretical proposals and experiment configurations are suggested and realized to improve the measurement metrics, such as intensity sensitivity, bandwidth, phase, and accuracy. The Stark effect and electromagnetically induced transparency (EIT) or electromagnetically induced absorption (EIA) are fundamental physics principles behind the stage. Furthermore, various techniques such as amplitude- or frequency-modulation, optical homodyne read-out, microwave superheterodyne and frequency conversion based on multi-wave mixing in atoms are utilized to push the metrics into higher levels. In this review, different technologies and the corresponding metrics they had achieved were presented, hoping to inspire more possibilities in the improvement of metrics of Rydberg atom-based electric field sensing and broadness of application scenarios.

Toward Accurate Quantum Mechanical Thermochemistry: (1) Extensible Implementation and Comparison of Bond Additivity Corrections and Isodesmic Reactions

Obtaining accurate enthalpies of formation of chemical species, ΔHf, often requires empirical corrections that connect the results of quantum mechanical (QM) calculations with the experimental enthalpies of elements in their standard state. One approach is to use atomization energy corrections followed by bond additivity corrections (BACs), such as those defined by Petersson et al. or Anantharaman and Melius. Another approach is to utilize isodesmic reactions (IDRs) as shown by Buerger et al. We implement both approaches in Arkane, an open-source software that can calculate species thermochemistry using results from various QM software packages. In this work, we collect 421 reference species from the literature to derive ΔHf corrections and fit atomization energy corrections and BACs for 15 commonly used model chemistries. We find that both types of BACs yield similar accuracy, although Anantharaman- and Melius-type BACs appear to generalize better. Furthermore, BACs tend to achieve better accuracy than IDRs for commonly used model chemistries, and IDRs can be less robust because of the sensitivity to the chosen reference species and reactions. Overall, Anantharaman- and Melius-type BACs are our recommended approach for achieving accurate QM corrections for enthalpies.

Precision Calculation of the Electromagnetic Radii of the Proton and Neutron from Lattice QCD

We present lattice-QCD results for the electromagnetic form factors of the proton and neutron including both quark-connected and -disconnected contributions. The parametrization of the Q^{2} dependence of the form factors is combined with the extrapolation to the physical point. In this way, we determine the electric and magnetic radii and the magnetic moments of the proton and neutron. For the proton, we obtain at the physical pion mass and in the continuum and infinite-volume limit sqrt[⟨r_{E}^{2}⟩^{p}]=0.820(14)  fm, sqrt[⟨r_{M}^{2}⟩^{p}]=0.8111(89)  fm, and μ_{M}^{p}=2.739(66), where the errors include all systematics.

Restricted internal diffusion weakens transpiration-photosynthesis coupling during heatwaves: Evidence from leaf carbonyl sulphide exchange

Increasingly frequent and intense heatwaves threaten ecosystem health in a warming climate. However, plant responses to heatwaves are poorly understood. A key uncertainty concerns the intensification of transpiration when heatwaves suppress photosynthesis, known as transpiration-photosynthesis decoupling. Field observations of such decoupling are scarce, and the underlying physiological mechanisms remain elusive. Here, we use carbonyl sulphide (COS) as a leaf gas exchange tracer to examine potential mechanisms leading to transpiration-photosynthesis decoupling on a coast live oak in a southern California woodland in spring 2013. We found that heatwaves suppressed both photosynthesis and leaf COS uptake but increased transpiration or sustained it at non-heatwave levels throughout the day. Despite statistically significant decoupling between transpiration and photosynthesis, stomatal sensitivity to environmental factors did not change during heatwaves. Instead, midday photosynthesis during heatwaves was restricted by internal diffusion, as indicated by the lower internal conductance to COS. Thus, increased evaporative demand and nonstomatal limitation to photosynthesis act jointly to decouple transpiration from photosynthesis without altering stomatal sensitivity. Decoupling offered limited potential cooling benefits, questioning its effectiveness for leaf thermoregulation in xeric ecosystems. We suggest that adding COS to leaf and ecosystem flux measurements helps elucidate diverse physiological mechanisms underlying transpiration-photosynthesis decoupling.

Klein-Gordon equation on a Lagrange mesh

The Lagrange-mesh method is an approximate variational method which provides accurate solutions of the Schrödinger equation for bound-state and scattering few-body problems. The stationary Klein-Gordon equation depends quadratically on the energy. For a central potential, it is solved on a Lagrange-Laguerre mesh by iteration. Results are tested with the Coulomb potential for which exact solutions are available. A high accuracy is obtained with a rather small number of mesh points. For various potentials and levels, few iterations provide accurate energies and mean values in short computer times. Analytical expressions of the wave functions are available.

Precision-Spectroscopic Determination of the Binding Energy of a Two-Body Quantum System: The Hydrogen Atom and the Proton-Size Puzzle

Precision measurements in Rydberg states of H with principal quantum number n in the range between 20 and 30 are reported. In the presence of homogeneous electric fields with strengths below 2  V cm^{-1}, these Rydberg states are subject to a linear Stark effect with accurately calculable Stark shifts. From the spectral positions of field-independent and field-dependent Rydberg-Stark states, we derive the n=20 and 24 Bohr energies, and the ionization energy with respect to the 2 ^{2}S_{1/2}(f=0,1) [short 2S(0,1)] metastable states. Combining these results with the 2S(1)-1S(1) transition frequency [C. G. Parthey et al., Phys. Rev. Lett. 107, 203001 (2011)PRLTAO0031-900710.1103/PhysRevLett.107.203001; A. Matveev et al., Phys. Rev. Lett. 110, 230801 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.230801] and the 1S hyperfine splitting [L. Essen et al., Nature (London) 229, 110 (1971)NATUAS0028-083610.1038/229110a0], we determine the ionization frequency of the 1S(0) ground state to be 3 288 087 922 407.2(3.7)_{stat}(1.8)_{syst}  kHz, which is the most precise value ever determined for the binding energy of a two-body quantum system. Using the 2S(0)-2P_{1/2}(1) interval [N. Bezginov et al., Science 365, 1007 (2019)SCIEAS0036-807510.1126/science.aau7807], we determine the Rydberg frequency to be cR_{∞}=3 289 841 960 204(15)_{stat}(7)_{syst}(13)_{2S-2P}  kHz in a procedure that is insensitive to the value of the proton charge radius. These new results are discussed in the context of the proton-size puzzle.

Accurate Determination of Blackbody Radiation Shifts in a Strontium Molecular Lattice Clock

Molecular lattice clocks enable the search for new physics, such as fifth forces or temporal variations of fundamental constants, in a manner complementary to atomic clocks. Blackbody radiation (BBR) is a major contributor to the systematic error budget of conventional atomic clocks and is notoriously difficult to characterize and control. Here, we combine infrared Stark-shift spectroscopy in a molecular lattice clock and modern quantum chemistry methods to characterize the polarizabilities of the Sr_{2} molecule from dc to infrared. Using this description, we determine the static and dynamic blackbody radiation shifts for all possible vibrational clock transitions to the 10^{-16} level. This constitutes an important step toward millihertz-level molecular spectroscopy in Sr_{2} and provides a framework for evaluating BBR shifts in other homonuclear molecules.

High-Precision Determination of g Factors and Masses of ^{20}Ne^{9+} and ^{22}Ne^{9+}

We present the measurements of individual bound electron g factors of ^{20}Ne^{9+} and ^{22}Ne^{9+} on the relative level of 0.1 parts per billion. The comparison with theory represents the most stringent test of bound-state QED in strong electric fields. A dedicated mass measurement results in m(^{20}Ne)=19.992 440 168 77(9)  u, which improves the current literature value by a factor of 18, disagrees by 4 standard deviations, and represents the most precisely measured mass value in atomic mass units. Together, these measurements yield an electron mass on the relative level of 0.1 ppb with m_{e}=5.485 799 090 99(59)×10^{-4}  u as well as a factor of seven improved m(^{22}Ne)=21.991 385 098 2(26)  u.

Kerr-induced synchronization of a cavity soliton to an optical reference

The phase-coherent frequency division of a stabilized optical reference laser to the microwave domain is made possible by optical-frequency combs (OFCs)1,2. OFC-based clockworks3-6 lock one comb tooth to a reference laser, which probes a stable atomic transition, usually through an active servo that increases the complexity of the OFC photonic and electronic integration for fieldable clock applications. Here, we demonstrate that the Kerr nonlinearity enables passive, electronics-free synchronization of a microresonator-based dissipative Kerr soliton (DKS) OFC7 to an externally injected reference laser. We present a theoretical model explaining this Kerr-induced synchronization (KIS), which closely matches experimental results based on a chip-integrated, silicon nitride, micro-ring resonator. Once synchronized, the reference laser captures an OFC tooth, so that tuning its frequency provides direct external control of the OFC repetition rate. We also show that the stability of the repetition rate is linked to that of the reference laser through the expected frequency division factor. Finally, KIS of an octave-spanning DKS exhibits enhancement of the opposite dispersive wave, consistent with the theoretical model, and enables improved self-referencing and access to the OFC carrier-envelope offset frequency. The KIS-mediated enhancements we demonstrate can be directly implemented in integrated optical clocks and chip-scale low-noise microwave generators.

Impact of NNLO QED corrections on lepton-proton scattering at MUSE

We present the complete next-to-next-to-leading order (NNLO) pure pointlike QED corrections to lepton-proton scattering, including three-photon-exchange contributions, and investigate their impact in the case of the MUSE experiment. These corrections are computed with no approximation regarding the energy of the emitted photons and taking into account lepton-mass effects. We contrast the NNLO QED corrections to known next-to-leading order corrections, where we include the elastic two-photon exchange (TPE) through a simple hadronic model calculation with a dipole ansatz for the proton electromagnetic form factors. We show that, in the low-momentum-transfer region accessed by the MUSE experiment, the improvement due to more sophisticated treatments of the TPE, including inelastic TPE, is of similar if not smaller size than some of the NNLO QED corrections. Hence, the latter have to be included in a precision determination of the low-energy proton structure from scattering data, in particular for electron-proton scattering. For muon-proton scattering, the NNLO QED corrections are considerably smaller.

Fundamental Equation of State for Fluid Tetrahydrofuran

An empirical fundamental equation of state in terms of the Helmholtz energy for tetrahydrofuran is presented. In the validity range from the triple-point temperature up to 550 K and pressures up to 600 MPa, the equation of state enables the calculation of all thermodynamic properties in the liquid, vapor, and super-critical regions including saturation states. Based on an extensive literature review, experimental data are represented within their experimental uncertainty. In the homogeneous liquid phase at atmospheric pressure, the uncertainty in density is 0.015 %, speed of sound is represented with an uncertainty of 0.03 %, and isobaric heat capacity has an uncertainty of 0.4 %. Isobaric heat capacities in the homogeneous vapor phase are described with an uncertainty of 0.2 %. Higher uncertainties occur above atmospheric pressure for all homogeneous properties. Depending on the temperature range, vapor pressure can be calculated with an uncertainty from 0.02 % to 3 %. The extrapolation behavior is evaluated, showing reasonable extrapolation behavior towards extreme conditions.

Supplementary Information

The online version contains supplementary material available at 10.1007/s10765-023-03258-3.

Viscosity and diffusion in life processes and tuning of fundamental constants

Viewed as one of the grandest questions in modern science, understanding fundamental physical constants has been discussed in high-energy particle physics, astronomy and cosmology. Here, I review how condensed matter and liquid physics gives new insights into fundamental constants and their tuning. This is based on two observations: first, cellular life and the existence of observers depend on viscosity and diffusion. Second, the lower bound on viscosity and upper bound on diffusion are set by fundamental constants, and I briefly review this result and related recent developments in liquid physics. I will subsequently show that bounds on viscosity, diffusion and the newly introduced fundamental velocity gradient in a biochemical machine can all be varied while keeping the fine-structure constant and the proton-to-electron mass ratio intact. This implies that it is possible to produce heavy elements in stars but have a viscous planet where all liquids have very high viscosity (for example that of tar or higher) and where life may not exist. Knowing the range of bio-friendly viscosity and diffusion, we will be able to calculate the range of fundamental constants which favour cellular life and observers and compare this tuning with that discussed in high-energy physics previously. This invites an inter-disciplinary research between condensed matter physics and life sciences, and I formulate several questions that life science can address. I finish with a conjecture of multiple tuning and an evolutionary mechanism.

Stringent test of QED with hydrogen-like tin

Inner-shell electrons naturally sense the electric field close to the nucleus, which can reach extreme values beyond 1015 V cm-1 for the innermost electrons1. 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 decades2,3. Another approach is the measurement of gyromagnetic factors (g factors) in highly charged ions4-7. However, so far, either experimental accuracy or small field strength in low-Z ions5,6 limited the stringency of these QED tests. Here we report on our high-precision, high-field test of QED in hydrogen-like 118Sn49+. The highly charged ions were produced with the Heidelberg electron beam ion trap (EBIT)8 and injected into the ALPHATRAP Penning-trap setup9, 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.

Three-body potential and third virial coefficients for helium including relativistic and nuclear-motion effects

The non-additive three-body interaction potential for helium was computed using the coupled-cluster theory and the full configuration interaction method. The obtained potential comprises an improved nonrelativistic Born-Oppenheimer energy and the leading relativistic and nuclear-motion corrections. The mean absolute uncertainty of our calculations due to the incompleteness of the orbital basis set was determined employing complete-basis-set extrapolation techniques and was found to be 1.2%. For three helium atoms forming an equilateral triangle with the side length of 5.6 bohr - a geometry close to the minimum of the total potential energy surface - our three-body potential amounts to -90.6 mK, with an estimated uncertainty of 0.5 mK. An analytic function, developed to accurately fit the computed three-body interaction energies, was chosen to correctly describe the asymptotic behavior of the three-body potential for trimer configurations corresponding to both the three-atomic and the atom-diatom fragmentation channels. For large triangles with sides r12, r23, and r31, the potential takes correctly into account all angular terms decaying as r-l12 r-m23 r-n21 with l + m + n ≤ 14 for the nonrelativistic Born-Oppenheimer energy and l + m + n ≤ 9 for the post-Born-Oppenheimer corrections. We also developed a short-range analytic function describing the local behavior of the total uncertainty of the computed three-body interaction energies. Using both fits we calculated the third pressure and acoustic virial coefficients for helium and their uncertainties for a wide range of temperatures. The results of these calculations were compared with available experimental data and with previous theoretical determinations. The estimated uncertainties of present calculations are 3-5 times smaller than those reported in the best previous works.

Imaging-Assisted Single-Photon Doppler-Free Laser Spectroscopy and the Ionization Energy of Metastable Triplet Helium

Skimmed supersonic beams provide intense, cold, collision-free samples of atoms and molecules and are one of the most widely used tools in atomic and molecular laser spectroscopy. High-resolution optical spectra are typically recorded in a perpendicular arrangement of laser and supersonic beams to minimize Doppler broadening. Typical Doppler widths are nevertheless limited to tens of MHz by the residual transverse-velocity distribution in the gas-expansion cones. We present an imaging method to overcome this limitation that exploits the correlation between the positions of the atoms and molecules in the supersonic expansion and their transverse velocities, and thus their Doppler shifts. With the example of spectra of (1s)(np) ^{3}P_{0-2}←(1s)(2s) ^{3}S_{1} transitions to high Rydberg states of metastable triplet He, we demonstrate the suppression of the residual Doppler broadening and a reduction of the full linewidths at half maximum to only about 1 MHz in the UV. Using a retroreflection arrangement for the laser beam and a cross-correlation method, we determine Doppler-free spectra without any signal loss from the selection, by imaging, of atoms within ultranarrow transverse-velocity classes. As an illustration, we determine the ionization energy of triplet metastable He and confirm the significant discrepancy between recent experimental [G. Clausen et al., Phys. Rev. Lett. 127, 093001 (2021)PRLTAO0031-900710.1103/PhysRevLett.127.093001] and high-level theoretical [V. Patkós et al., Phys. Rev. A 103, 042809 (2021)PLRAAN2469-992610.1103/PhysRevA.103.042809] values of this quantity.

Penning-Trap Mass Measurement of Helium-4

Light-ion trap (LIONTRAP), a high-precision Penning-trap mass spectrometer, was used to determine the atomic mass of ^{4}He. Here, we report a 12 parts-per-trillion measurement of the mass of a ^{4}He^{2+} ion, m(^{4}He^{2+})=4.001 506 179 651(48)  u. From this, the atomic mass of the neutral atom can be determined without loss of precision: m(^{4}He)=4.002 603 254 653(48)  u. This result is slightly more precise than the current CODATA18 literature value but deviates by 6.6 standard deviations.

A Ramsey apparatus for proton spins in flowing water

We present an apparatus that applies Ramsey's method of separated oscillatory fields to proton spins in water molecules. The setup consists of a water circuit, a spin polarizer, a magnetically shielded interaction region with various radio frequency elements, and a nuclear magnetic resonance system to measure the spin polarization. We show that this apparatus can be used for Rabi resonance measurements and to investigate magnetic and pseudomagnetic field effects in Ramsey-type precision measurements with a sensitivity below 100 pT.

Mono-valent salt corrections for RNA secondary structures in the ViennaRNA package

BACKGROUND

RNA features a highly negatively charged phosphate backbone that attracts a cloud of counter-ions that reduce the electrostatic repulsion in a concentration dependent manner. Ion concentrations thus have a large influence on folding and stability of RNA structures. Despite their well-documented effects, salt effects are not handled consistently by currently available secondary structure prediction algorithms. Combining Debye-Hückel potentials for line charges and Manning's counter-ion condensation theory, Einert et al. (Biophys J 100: 2745-2753, 2011) modeled the energetic contributions of monovalent cations on loops and helices.

RESULTS

The model of Einert et al. is adapted to match the structure of the dynamic programming recursion of RNA secondary structure prediction algorithms. An empirical term describing the salt dependence of the duplex initiation energy is added to improve co-folding predictions for two or more RNA strands. The slightly modified model is implemented in the ViennaRNA package in such way that only the energy parameters but not the algorithmic structure is affected. A comparison with data from the literature show that predicted free energies and melting temperatures are in reasonable agreement with experiments.

CONCLUSION

The new feature in the ViennaRNA package makes it possible to study effects of salt concentrations on RNA folding in a systematic manner. Strictly speaking, the model pertains only to mono-valent cations, and thus covers the most important parameter, i.e., the NaCl concentration. It remains a question for future research to what extent unspecific effects of bi- and tri-valent cations can be approximated in a similar manner.

AVAILABILITY

Corrections for the concentration of monovalent cations are available in the ViennaRNA package starting from version 2.6.0.

Ramsey Spectroscopy of the 2S_{1/2} Hyperfine Interval in Atomic Hydrogen

The 2S_{1/2} hyperfine interval in atomic hydrogen was measured using Ramsey spectroscopy with a thermal beam cooled to cryogenic temperatures. The measured value is 177 556 838.87(85) Hz, which represents the most precise determination of this interval to date. The 1S_{1/2} hyperfine interval f(1S_{1/2}) and the 2S_{1/2} hyperfine interval f(2S_{1/2}) can be combined to give the quantity D_{21}=8f(2S_{1/2})-f(1S_{1/2}), which mostly eliminates uncertainty due to nuclear structure effects and is well described by bound-state quantum electrodynamics. Using the value of f(2S_{1/2}) from this work gives a value of D_{21}^{expt}=48 959.2(6.8)  Hz, which is in agreement with the theoretical value of D_{21}^{Theory}=48 954.1(2.3)  Hz.

Self-Consistent Extraction of Spectroscopic Bounds on Light New Physics

Fundamental physical constants are determined from a collection of precision measurements of elementary particles, atoms, and molecules. This is usually done under the assumption of the standard model (SM) of particle physics. Allowing for light new physics (NP) beyond the SM modifies the extraction of fundamental physical constants. Consequently, setting NP bounds using these data, and at the same time assuming the Committee on Data of the International Science Council recommended values for the fundamental physical constants, is not reliable. As we show in this Letter, both SM and NP parameters can be simultaneously determined in a consistent way from a global fit. For light vectors with QED-like couplings, such as the dark photon, we provide a prescription that recovers the degeneracy with the photon in the massless limit and requires calculations only at leading order in the small new physics couplings. At present, the data show tensions partially related to the proton charge radius determination. We show that these can be alleviated by including contributions from a light scalar with flavor nonuniversal couplings.

Equation of state for the Mie (λr,6) fluid with a repulsive exponent from 11 to 13

An empirical multi-parameter equation of state in terms of the reduced Helmholtz energy is presented for the Mie (λ_r-6) fluid with a repulsive exponent λ_r from 11 to 13. The equation is fitted to an extensive dataset from molecular dynamics simulation as well as the second and third thermal virial coefficients. It is comprehensively compared with the SAFT-VR model and is a more accurate description of the considered fluid class. The equation is valid for reduced temperatures T/T_c from 0.55 to 4.5 and for reduced pressures of up to p/p_c = 265. A good extrapolation behavior and the occurrence of a single Maxwell loop down to the vicinity of the triple point temperature are realized.

Electron affinity of atomic scandium and yttrium and excited states of their negative ions

The latest experimental electron affinity (EA) values of atomic scandium and yttrium were 0.189(20) and 0.308(12) eV as reported by Feigerle et al. in 1981. The measurement accuracy of these was far lower than that of other transition elements, and no conclusive result had been made on the excited states of their negative ions. In the current work, we report more accurate EA values of Sc and Y and the electronic structure of their negative ions using the slow-electron velocity-map imaging method. The EA values of Sc and Y are determined to be 0.179 378(22) and 0.311 29(22) eV, respectively. The ground state of Sc^- is identified as 3d4s²4p ¹D₂, and the ground state is 4d5s²5p ¹D₂ for Y^-. Furthermore, several excited states of Sc^- and Y^- are observed: Sc^- (³D₁) and Y^- (³D₁, ³D₂, ³D₃, ³F₂, and ³F₃), and their energy levels are determined to be 1131.8(28), 1210.0(13), 1362.3(30), 1467.7(26), 1747(16), and 1987(33) cm^-1, respectively.

QED Theory of the Nuclear Recoil with Finite Size

We investigate the modification of the transverse electromagnetic interaction between two pointlike particles when one particle acquires a finite size. It is shown that the correct treatment of such interaction cannot be accomplished within the Breit approximation but should be addressed within the QED. The complete QED formula is derived for the finite-size nuclear recoil, exact in the coupling strength parameter Zα. Numerical calculations are carried out for a wide range of Z and verified against the (Zα)^{5} contribution. The comparison with the Zα expansion identifies the contribution of order (Zα)^{6}, which is linear in the nuclear radius and numerically dominates over the lower-order (Zα)^{5} term.

Recoil Corrections to the Energy Levels of Hydrogenic Atoms

We have completed the calculation of pure-recoil corrections of order (Zα)^{6} to Coulombic bound states of two spin-1/2 fermions without approximation in the particle masses. Our result applies to systems of arbitrary mass ratio such as muonium and positronium, as well as hydrogen and muonic hydrogen (with the neglect of proton structure effects). We have shown how the two-loop master integrals that occur in the relativistic region can be computed in analytic form and suggest that the same method can be applied to the three-loop integrals that would be present in a calculation of order (Zα)^{7} corrections.

Update of Muonium 1S-2S transition frequency

Abstract

We present an updated value of the Muonium 1S-2S transition frequency, highlighting contributions from different QED corrections as well as the large uncertainty in the Dirac contribution, stemming from the uncertainty of the electron to muon mass ratio. Improving the measurement of this spectral line would allow to extract a more accurate determination of fundamental constants, such as the electron to muon mass ratio or, combined with the Muonium hyperfine splitting, an independent value of the Rydberg constant. Furthermore, we report on the current status of the Mu-MASS experiment, which aims at measuring the Muonium 1S-2S transition frequency at a 10 kHz uncertainty level.

Graphic abstract

An Introduction to Relativistic Theory as Implemented in GRASP

Computational atomic physics continues to play a crucial role in both increasing the understanding of fundamental physics (e.g., quantum electrodynamics and correlation) and producing atomic data for interpreting observations from large-scale research facilities ranging from fusion reactors to high-power laser systems, space-based telescopes and isotope separators. A number of different computational methods, each with their own strengths and weaknesses, is available to meet these tasks. Here, we review the relativistic multiconfiguration method as it applies to the General Relativistic Atomic Structure Package [grasp2018, C. Froese Fischer, G. Gaigalas, P. Jönsson, J. Bieroń, Comput. Phys. Commun. (2018). DOI: 10.1016/j.cpc.2018.10.032]. To illustrate the capacity of the package, examples of calculations of relevance for nuclear physics and astrophysics are presented.

Apparatuses for verifying the precision of gravimeters with lifting spherical source masses

Two apparatuses with lifting spherical source masses are built and used to verify the precision of gravimeters. The 333-kg source mass produces a maximum acceleration of 200 nm/s² with an uncertainty of 0.31 nm/s², which corresponds to a relative uncertainty of 0.16%. After evaluating the temperature effect, drift of the gravimeter, the atmospheric effect, and the tidal effect, a combined uncertainty of 1 nm/s² is obtained. One CG6 gravimeter is tested using two apparatuses, the measured accelerations agree with the theoretical values within the error range. Differential measurement with two CG6 gravimeters on one apparatus is performed, which provides a common-mode rejection of the effects due to ambient noise, such as the gravity tide, atmospheric effect, and drift. The difference in acceleration measured by the two gravimeters is determined to be 199 ± 6 nm/s², which agrees well with the value 200 ± 1 nm/s² obtained by using apparatus II. Our apparatuses provide a verification of the precision of gravimeters with an uncertainty of 1 nm/s², which is one of the lowest uncertainties reached so far. The determination of geometrical metrology and mass distribution and detailed error analysis are presented. The methods on error analysis as well as differential measurement used in our work are helpful for gravity measurement.

Two-photon exchange in (muonic) deuterium at N3LO in pionless effective field theory

We present a study of the two-photon-exchange (2 γ -exchange) corrections to the S-levels in muonic ( μ D) and ordinary (D) deuterium within the pionless effective field theory (EFT). Our calculation proceeds up to next-to-next-to-next-to-leading order (N3LO) in the EFT expansion. The only unknown low-energy constant entering the calculation at this order corresponds to the coupling of a longitudinal photon to the nucleon-nucleon system. To minimise its correlation with the deuteron charge radius, it is extracted using the information about the hydrogen-deuterium isotope shift. We find the elastic 2 γ -exchange contribution in μ D larger by several standard deviations than obtained in other recent calculations. This discrepancy ameliorates the mismatch between theory and experiment on the size of 2 γ -exchange effects, and is attributed to the properties of the deuteron elastic charge form factor parametrisation used to evaluate the elastic contribution. We identify a correlation between the deuteron charge and Friar radii, which can help one to judge how well a form factor parametrisation describes the low-virtuality properties of the deuteron. We also evaluate the higher-order 2 γ -exchange contributions in μ D, generated by the single-nucleon structure and expected to be the most important terms beyond N3LO. The uncertainty of the theoretical result is dominated by the truncation of the EFT series and is quantified using a Bayesian approach. The resulting extractions of the deuteron charge radius from the μ D Lamb shift, the 2 S - 1 S transition in D, and the 2 S - 1 S hydrogen-deuterium isotope shift, with the respective 2 γ -exchange effects evaluated in a unified EFT approach, are in perfect agreement.

Diamond surface engineering for molecular sensing with nitrogen-vacancy centers

Quantum sensing using optically addressable atomic-scale defects, such as the nitrogen-vacancy (NV) center in diamond, provides new opportunities for sensitive and highly localized characterization of chemical functionality. Notably, near-surface defects facilitate detection of the minute magnetic fields generated by nuclear or electron spins outside of the diamond crystal, such as those in chemisorbed and physisorbed molecules. However, the promise of NV centers is hindered by a severe degradation of critical sensor properties, namely charge stability and spin coherence, near surfaces (< ca. 10 nm deep). Moreover, applications in the chemical sciences require methods for covalent bonding of target molecules to diamond with robust control over density, orientation, and binding configuration. This forward-looking Review provides a survey of the rapidly converging fields of diamond surface science and NV-center physics, highlighting their combined potential for quantum sensing of molecules. We outline the diamond surface properties that are advantageous for NV-sensing applications, and discuss strategies to mitigate deleterious effects while simultaneously providing avenues for chemical attachment. Finally, we present an outlook on emerging applications in which the unprecedented sensitivity and spatial resolution of NV-based sensing could provide unique insight into chemically functionalized surfaces at the single-molecule level.

Variational versus perturbative relativistic energies for small and light atomic and molecular systems

Variational and perturbative relativistic energies are computed and compared for two-electron atoms and molecules with low nuclear charge numbers. In general, good agreement of the two approaches is observed. Remaining deviations can be attributed to higher-order relativistic, also called non-radiative quantum electrodynamics (QED), corrections of the perturbative approach that are automatically included in the variational solution of the no-pair Dirac--Coulomb--Breit (DCB) equation to all orders of the $\alpha$ fine-structure constant. The analysis of the polynomial $\alpha$ dependence of the DCB energy makes it possible to determine the leading-order relativistic correction to the non-relativistic energy to high precision without regularization. Contributions from the Breit--Pauli Hamiltonian, for which expectation values converge slowly due the singular terms, are implicitly included in the variational procedure. The $\alpha$ dependence of the no-pair DCB energy shows that the higher-order ($\alpha^4 E_\mathrm{h}$) non-radiative QED correction is 5~\% of the leading-order ($\alpha^3 E_\mathrm{h}$) non-radiative QED correction for $Z=2$ (He), but it is 40~\% already for $Z=4$ (Be$^{2+}$), which indicates that resummation provided by the variational procedure is important already for intermediate nuclear charge numbers.

Direct measurement of the 3He+ magnetic moments

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.

Precision Spectroscopy of the Pionic Helium-4

The transition frequency of (n,ℓ)=(17,16)→(16,15) in pionic helium-4 is calculated to an accuracy of 4 ppb (parts per billion), including relativistic and quantum electrodynamic corrections up to O(R_{∞}α^{5}). Our calculations significantly improve the recent theoretical values [Hori et al., Phys. Rev. A 89, 042515 (2014)PLRAAN1050-294710.1103/PhysRevA.89.042515]. In addition, collisional effects between pionic helium and target helium on transition frequencies are estimated. Once measurements reach the ppb level, our Letter will improve the value of the π^{-} mass by 2-3 orders of magnitude.

The NIST Vacuum Double-Crystal Spectrometer: A Tool for SI-Traceable Measurement of X-Ray Emission Spectra

The NIST Vacuum Double-Crystal Spectrometer (VDCS) has been modernized and is now capable of recording reference-free wavelength-dispersive spectra in the 2 keV to 12 keV x-ray energy range. The VDCS employs crystals in which the lattice spacings are traceable to the definition of the meter through x-ray optical interferometry with a relative uncertainty ﹤10-⁸. VDCS wavelength determination relies upon precision angle difference measurements for which the encoders of the rotation stages have been calibrated using the circle closure method for accurate, absolute angle measurement. The new vacuum-compatible area detector allows quantification of the aberration functions contributing to the observed line shape and in situ alignment of the crystal optics. This latter procedure is augmented with the use of a thin lamella as the first crystal. With these new techniques, x-ray spectra are registered with the VDCS on an absolute energy scale with a relative uncertainty of 10-⁶.

On the Breit interaction in an explicitly correlated variational Dirac–Coulomb framework

The Breit interaction is implemented in the no-pair variational Dirac–Coulomb (DC) framework using an explicitly correlated Gaussian basis reported in the previous paper [P. Jeszenszki, D. Ferenc, and E. Mátyus, J. Chem. Phys. 156, 084111 (2022)]. Both a perturbative and a fully variational inclusion of the Breit term are considered. The no-pair DC plus perturbative Breit and the no-pair DC–Breit energies are compared with perturbation theory results including the Breit–Pauli Hamiltonian and leading-order non-radiative quantum electrodynamics corrections for low Z values. Possible reasons for the observed deviations are discussed.

Variational Dirac–Coulomb explicitly correlated computations for atoms and molecules

The Dirac–Coulomb equation with positive-energy projection is solved using explicitly correlated Gaussian functions. The algorithm and computational procedure aims for a parts-per-billion convergence of the energy to provide a starting point for further comparison and further developments in relation with high-resolution atomic and molecular spectroscopy. Besides a detailed discussion of the implementation of the fundamental spinor structure, permutation, and point-group symmetries, various options for the positive-energy projection procedure are presented. The no-pair Dirac–Coulomb energy converged to a parts-per-billion precision is compared with perturbative results for atomic and molecular systems with small nuclear charge numbers. Paper II [D. Ferenc, P. Jeszenszki, and E. Mátyus, J. Chem. Phys. 156, 084110 (2022).] describes the implementation of the Breit interaction in this framework.

Reactions of H2, HD, and D2 with H2+, HD+, and D2+: Product-Channel Branching Ratios and Simple Models

We present measurements of the product-channel branching ratios of the reactions (i) HD+ + HD forming H2D+ + D (38.1(30)%) and HD2+ + H (61.9(30)%), (ii) HD+ + D2 forming HD2+ + D (61.4(35)%) and D3+ + H (38.6(35)%), and (iii) D2+ + HD forming HD2++ D (60.5(20)%) and D3+ + H (39.5(20)%) at collision energies Ecoll near zero, i.e., below kB × 1 K. These branching ratios are compared with branching ratios predicted using three simple models: a combinatorial model (M1), a model (M2) describing the reactions as H-, H+-, D-, and D+-transfer processes, and a statistical model (M3) that relates the reaction rate coefficients to the translational and rovibrational state densities of the HnD3-n+ + H/D (n = 0, 1, 2 or 3) product channels. The experimental data are incompatible with the predictions of models M1 and M2 and reveal that the branching ratios exhibit clear correlations with the product state densities.

Measurement of the 2S_{1/2}-8D_{5/2} Transition in Hydrogen

We present a measurement of the hydrogen 2S_{1/2}-8D_{5/2} transition performed with a cryogenic atomic beam. The measured resonance frequency is ν=770649561570.9(2.0)  kHz, which corresponds to a relative uncertainty of 2.6×10^{-12}. Combining our result with the most recent measurement of the 1S-2S transition, we find a proton radius of r_{p}=0.8584(51)  fm and a Rydberg constant of R_{∞}=10973731.568332(52)  m^{-1}. This result has a combined 3.1σ disagreement with the Committee on Data for Science and Technology (CODATA) 2018 recommended value.

Long-Range Interactions for Hydrogen Atoms in Excited D States

Pressure shifts inside an atomic beam are among the more theoretically challenging effects in high-precision measurements of atomic transitions. A crucial element in their theoretical analysis is the understanding of long-range interatomic interactions inside the beam. For excited reference states, the presence of quasi-degenerate states leads to additional challenges, due to the necessity to diagonalize large matrices in the quasi-degenerate hyperfine manifolds. Here, we focus on the interactions of hydrogen atoms in reference states composed of an excited nD state (atom A), and in the metastable 2S state (atom B). We devote special attention to the cases n=3 and n=8. For n=3, the main effect is generated by quasi-degenerate virtual P states from both atoms A and B and leads to experimentally relevant second-order long-range (van-der-Waals) interactions proportional to the sixth inverse power of the interatomic distance. For n=8, in addition to virtual states with two states of P symmetry, one needs to take into account combined virtual P and F states from atoms A and B. The numerical value of the so-called C6 coefficients multiplying the interaction energy was found to grow with the principal quantum number of the reference D state; it was found to be of the order of 1011 in atomic units. The result allows for the calculation of the pressure shift inside atomic beams while driving transitions to nD states.

QED Effect on the Nuclear Magnetic Shielding of ^{3}He

The leading quantum electrodynamic corrections to the nuclear magnetic shielding in one- and two-electron atomic systems are obtained in a complete form, and the shielding constants of ^{1}H, ^{3}He^{+}, and ^{3}He are calculated to be 17.735 436(3)×10^{-6}, 35.507 434(9)×10^{-6}, and 59.967 029(23)×10^{-6}, respectively. These results are orders of magnitude more accurate than previous ones, and, with the ongoing measurement of the nuclear magnetic moment of ^{3}He^{+} and planned ^{3}He^{2+}, they open the window for high-precision absolute magnetometry using ^{3}He NMR probes. The presented theoretical approach is applicable to all other light atomic and molecular systems, which facilitates the improved determination of magnetic moments of any light nuclei.

Towards an Independent Determination of Muon g-2 from Muonium Spectroscopy

We show that muonium spectroscopy in the coming years can reach a precision high enough to determine the anomalous magnetic moment of the muon below one part per million (ppm). Such an independent determination of muon g-2 would certainly shed light on the ∼2  ppm difference currently observed between spin-precession measurements and (R-ratio based) standard model predictions. The magnetic dipole interaction between electrons and (anti)muons bound in muonium gives rise to a hyperfine splitting (HFS) of the ground state which is sensitive to the muon anomalous magnetic moment. A direct comparison of the muonium frequency measurements of the HFS at J-PARC and the 1S-2S transition at PSI with theory predictions will allow us to extract muon g-2 with high precision. Improving the accuracy of QED calculations of these transitions by about 1 order of magnitude is also required. Moreover, the good agreement between theory and experiment for the electron g-2 indicates that new physics interactions are unlikely to affect muonium spectroscopy down to the envisaged precision.

Deuteron-to-Proton Mass Ratio from Simultaneous Measurement of the Cyclotron Frequencies of H_{2}^{+} and D^{+}

By simultaneously measuring the cyclotron frequencies of an H_{2}^{+} ion and a deuteron in a coupled magnetron orbit we have made an extended series of measurements of their cyclotron frequency ratio. From the observed changes in H_{2}^{+} mass energy we have followed the decay of three H_{2}^{+} ions to the vibrational ground state. We are able to assign some of our measured ratios to specific rovibrational levels, hence reducing uncertainty due to H_{2}^{+} rotational energy. Assuming the most probable assignment, we obtain a deuteron-to-proton mass ratio, m_{d}/m_{p}=1.999 007 501 272(9). Combined with the atomic mass of the deuteron [S. Rau et al., Nature (London) 585, 43 (2020).NATUAS0028-083610.1038/s41586-020-2628-7] we also obtain a new value for the atomic mass of the proton, m_{p}=1.007 276 466 574(10)  u.