CODATA Recommended Values of the Fundamental Physical Constants: 2018

Mass Difference of Tritium and Helium-3

From cyclotron frequency ratios of HD^{+}/^{3}He^{+}, HD^{+}/T^{+}, and T^{+}/^{3}He^{+} we measure the mass difference between atoms of T and ^{3}He to be 1.995 940 8 (23)×10^{-5} u, corresponding to a Q value for tritium β decay of 18 592.071(22) eV. This enables an improved check on systematics of β decay experiments that set limits on neutrino mass. Using the HD^{+} mass calculated from the atomic masses of the proton and deuteron as given by Rau et al. [Nature 585, 43 (2020)NATUAS0028-083610.1038/s41586-020-2628-7], we also obtain improved atomic masses for the triton and helion (considered to be fundamental constants), namely, 3.015 500 716 066 (39) and 3.014 932 246 957 (38) u.

Light antiproton one-electron quasi-molecular ions within the relativistic A-DKB method

In the present work, two quasi-molecular compounds each involving one antiproton and one electron (p̄), He+-p̄ and H-p̄, are investigated. Using completely relativistic calculations within the finite-basis method adapted to systems with axial symmetry, the adiabatic potential curves are constructed by numerically solving the two-center Dirac equation. The binding energies of electron are obtained as a function of the inter-nuclear distance and compared with the corresponding nonrelativistic values and relativistic leading-order corrections calculated in the framework of other approaches. A semantic analysis of antiproton quasi-molecular ions with compounds containing a proton (p) instead of an antiproton is given. The advantages of the A-DKB method are demonstrated.

Precision spectroscopy of molecular hydrogen

Precision measurements on the hydrogen molecule are of fundamental importance in understanding molecular theory. Comparison of accurate experimental data and theoretical results are used to test the quantum electrodynamics theory and determine physical constants used in the calculation. We review recent advances and perspectives in the precision spectroscopy of molecular hydrogen, representing state-of-the-art molecular spectroscopy methods and cutting-edge high-precision calculations.

Phase Structure of Electroweak Vacuum in a Strong Magnetic Field: The Lattice Results

Using first-principle lattice simulations, we demonstrate that in the background of a strong magnetic field (around 10^{20}  T), the electroweak sector of the vacuum experiences two consecutive crossover transitions associated with dramatic changes in the zero-temperature dynamics of the vector W bosons and the scalar Higgs particles, respectively. Above the first crossover, we observe the appearance of large, inhomogeneous structures consistent with a classical picture of the formation of W and Z condensates pierced by vortices. The presence of the W and Z condensates supports the emergence of the exotic superconducting and superfluid properties induced by a strong magnetic field in the vacuum. We find evidence that the vortices form a disordered solid or a liquid rather than a crystal. The second transition restores the electroweak symmetry. Such conditions can be realized in the near-horizon region of the magnetized black holes.

Thermodynamics of an Empty Box

A gas in a box is perhaps the most important model system studied in thermodynamics and statistical mechanics. Usually, studies focus on the gas, whereas the box merely serves as an idealized confinement. The present article focuses on the box as the central object and develops a thermodynamic theory by treating the geometric degrees of freedom of the box as the degrees of freedom of a thermodynamic system. Applying standard mathematical methods to the thermodynamics of an empty box allows equations with the same structure as those of cosmology and classical and quantum mechanics to be derived. The simple model system of an empty box is shown to have interesting connections to classical mechanics, special relativity, and quantum field theory.

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

Small Corrections to 1989 NIST Constant-Volume Gas Thermometry Data

Constant-volume gas thermometry data published in 1989 for the difference between the thermodynamic temperature and the International Practical Temperature Scale of 1968 are corrected in two ways. A refined estimate of the thermal expansivity of the material of the gas bulb, published in 1990, increases the thermodynamic temperature by amounts on the order of 1 mK to 3 mK. Better knowledge of the nonideality of helium gas reduces the uncertainty of the nonideality correction to near zero and decreases the thermodynamic temperature by amounts on the order of 0.1 mK to 0.5 mK. The net effect is a small increase in the thermodynamic temperature derived from the 1989 experiments. The magnitude of this increase is approximately 2 mK at 505 K, increasing to 3 mK at temperatures near 700 K, and then diminishing to near 0.5 mK at the highest temperature of the measurements (933 K). These corrections are smaller than the uncertainty of the experiments, but may be of significance for future recommendations for the relationship between the thermodynamic temperature and the consensus scale in this temperature range.

Electron affinity of tantalum and excited states of its anion

Tantalum anion has the most complicated photoelectron spectrum among all atomic anions of transition elements, which is the main obstacle to accurately measuring its electron affinity via the generic method. The latest experimental value of the electron affinity of Ta was 0.323(12) eV reported by Feigerle et al. in 1981. In the present work, we report the high-resolution photoelectron spectroscopy of Ta- via the slow electron velocity-map imaging (SEVI) method in combination with a cryogenic ion trap. The electron affinity of Ta was measured to be 2652.38(17) cm-1 or 0.328 859(23) eV. Three excited states 5 D1, 3 P0, and 5 D2 of Ta- were observed and their energy levels were determined to be 1169.64(17) cm-1 for 5 D1, 1735.9(10) cm-1 for 3 P0, and 2320.1(20) cm-1 for 5 D2 above the ground state 5 D0, respectively.

Muonium Lamb shift: theory update and experimental prospects

We review the theory of the Lamb shift for muonium, provide an updated numerical value and present the prospects of the Mu-MASS collaboration at PSI to improve upon their recent measurement. Due to its smaller nuclear mass, the contributions of the higher-order recoil corrections (160 kHz level) and nucleus self-energy (40 kHz level) are enhanced for muonium compared to hydrogen where those are below the level of the latest measurement performed by Hessels et al. and thus could not be tested yet. The ongoing upgrades to the Mu-MASS setup will open up the possibility to probe these contributions and improve the sensitivity of this measurement to searches for new physics in the muonic sector.

Characterizing atom clouds using a charge-coupled device for atom-interferometry-based G measurements

Precise information of positions and sizes of atom clouds is required for atom-interferometry-based G measurements. In this work, characterizing atom clouds using a charge-coupled device (CCD) is presented. The parameters of atom clouds are extracted from fluorescence images captured by the CCD. For characterization, in-situ calibration of the magnification of the imaging system is implemented using the free-fall distance of atom clouds as the dimension reference. Moreover, influence of the probe beam on measuring the positions of atom clouds is investigated, and a differential measurement by reversing the direction of the probe beam is proposed to suppress the influence. Finally, precision at sub-mm level for characterizing atom clouds is achieved.

Nonlinear Quantum Electrodynamics in Dirac Materials

Classical electromagnetism is linear. However, fields can polarize the vacuum Dirac sea, causing quantum nonlinear electromagnetic phenomena, e.g., scattering and splitting of photons, that occur only in very strong fields found in neutron stars or heavy ion colliders. We show that strong nonlinearity arises in Dirac materials at much lower fields ∼1  T, allowing us to explore the nonperturbative, extremely high field limit of quantum electrodynamics in solids. We explain recent experiments in a unified framework and predict a new class of nonlinear magnetoelectric effects, including a magnetic enhancement of dielectric constant of insulators and a strong electric modulation of magnetization. We propose experiments and discuss the applications in novel materials.

CODATA Recommended Values of the Fundamental Physical Constants: 2018

We report the 2018 self-consistent values of constants and conversion factors of physics and chemistry recommended by the Committee on Data of the International Science Council. The recommended values can also be found at physics.nist.gov/constants. The values are based on a least-squares adjustment that takes into account all theoretical and experimental data available through 31 December 2018. A discussion of the major improvements as well as inconsistencies within the data is given. The former include a decrease in the uncertainty of the dimensionless fine-structure constant and a nearly two orders of magnitude improvement of particle masses expressed in units of kg due to the transition to the revised International System of Units (SI) with an exact value for the Planck constant. Further, because the elementary charge, Boltzmann constant, and Avogadro constant also have exact values in the revised SI, many other constants are either exact or have significantly reduced uncertainties. Inconsistencies remain for the gravitational constant and the muon magnetic-moment anomaly. The proton charge radius puzzle has been partially resolved by improved measurements of hydrogen energy levels.

Development of Argon Isotope Reference Standards for the U.S. Geological Survey

The comparison of physical ages of geological materials measured by laboratories engaged in geochronological studies has been limited by the accuracy of mineral standards or monitors for which reported ages have differed by as much as 2 %. In order to address this problem, the U.S. Geological Survey is planning to calibrate the conventional (40)Ar/(40)K age of a new preparation of an international hornblende standard labeled MMhb-2. The (40)K concentration in MMhb-2 has already been determined by the Analytical Chemistry Division at NIST with an uncertainty of 0.2 %. The (40)Ar concentration will be measured by the USGS using the argon isotope reference standards that were recently developed by NIST and are described in this paper. The isotope standards were constructed in the form of pipette/reservoir systems and calibrated by gas expansion techniques to deliver small high-precision aliquots of high-purity argon. Two of the pipette systems will deliver aliquots of (38)Ar having initial molar quantities of 1.567 × 10(-10) moles and 2.313 × 10(-10) moles with expanded (k = 2) uncertainties of 0.058 % and 0.054 %, respectively. Three other pipette systems will deliver aliquots (nominally 4 × 10(-10) moles) of (40)Ar:(36)Ar artificial mixtures with similar accuracy and with molar ratios of 0.9974 ± 0.06 %, 29.69 ± 0.06 %, and 285.7 ± 0.08 % (k = 2). These isotope reference standards will enable the USGS to measure the (40)Ar concentration in MMhb-2 with an expanded uncertainty of ≈ 0.1 %. In the process of these measurements, the USGS will re-determine the isotopic composition of atmospheric Ar and calculate a new value for its atomic weight. Upon completion of the USGS calibrations, the MMhb-2 mineral standard will be certified by NIST for its K and Ar concentrations and distributed as a Standard Reference Material (SRM). The new SRM and the NIST-calibrated transportable pipette systems have the potential for dramatically improving the accuracy of interlaboratory calibrations and thereby the measured ages of geological materials, by as much as a factor of ten.

RM 8111: Development of a Prototype Linewidth Standard

Staffs of the Semiconductor Electronics Division, the Information Technology Laboratory, and the Precision Engineering Laboratory at NIST, have developed a new generation of prototype Single-Crystal CD (Critical Dimension) Reference (SCCDRM) Materials with the designation RM 8111. Their intended use is calibrating metrology instruments that are used in semiconductor manufacturing. Each reference material is configured as a 10 mm × 11 mm silicon test-structure chip that is mounted in a 200 mm silicon carrier wafer. The fabrication of both the chip and the carrier wafer uses the type of lattice-plane-selective etching that is commonly employed in the fabrication of micro electro-mechanical systems devices. The certified CDs of the reference features are determined from Atomic Force Microscope (AFM) measurements that are referenced to high-resolution transmission-electron microscopy images that reveal the cross-section counts of lattice planes having a pitch whose value is traceable to the SI meter.

Hysteresis and Related Error Mechanisms in the NIST Watt Balance Experiment

The NIST watt balance experiment is being completely rebuilt after its 1998 determination of the Planck constant. That measurement yielded a result with an approximately 1×10(-7) relative standard uncertainty. Because the goal of the new incarnation of the experiment is a ten-fold decrease in uncertainty, it has been necessary to reexamine many sources of systematic error. Hysteresis effects account for a substantial portion of the projected uncertainty budget. They arise from mechanical, magnetic, and thermal sources. The new experiment incorporates several improvements in the apparatus to address these issues, including stiffer components for transferring the mass standard on and off the balance, better servo control of the balance, better pivot materials, and the incorporation of erasing techniques into the mass transfer servo system. We have carried out a series of tests of hysteresis sources on a separate system, and apply their results to the watt apparatus. The studies presented here suggest that our improvements can be expected to reduce hysteresis signals by at least a factor of 10-perhaps as much as a factor of 50-over the 1998 experiment.

Vapor Pressure Formulation for Water in Range 0 to 100 °C. A Revision

In 1971 Wexler and Greenspan published a formulation for the vapor pressure of water encompassing the temperature range 0 to 100 °C. In this paper a revision is made of that earlier formulation to make it consistent with the definitive experimental value of the vapor pressure of water at its triple point recently obtained by Guildner, Johnson, and Jones. The two formulations are essentially identical at temperatures from 25 to 100 °C. For temperatures below 25 °C the new formulation predicts values that are higher than the 1971 formulation. At the triple point, the vapor pressure given by the new formulation is 611.657 Pa whereas the value given by the 1971 formulation is 611.196 Pa. A table is given of the vapor pressure as a function of temperature at 0.1-deg intervals over the range 0 to 100 °C on the International Practical Temperature Scale of 1968, together with values of the temperature derivative at 1-deg intervals.