Article

CODATA recommended values of the fundamental physical constants: 1998

Authors:
To read the full-text of this research, you can request a copy directly from the authors.

Abstract

This paper gives the 2006 self-consistent set of values of the basic constants and conversion factors of physics and chemistry recommended by the Committee on Data for Science and Technology (CODATA) for international use. Further, it describes in detail the adjustment of the values of the constants, including the selection of the final set of input data based on the results of least-squares analyses. The 2006 adjustment takes into account the data considered in the 2002 adjustment as well as the data that became available between 31 December 2002, the closing date of that adjustment, and 31 December 2006, the closing date of the new adjustment. The new data have led to a significant reduction in the uncertainties of many recommended values. The 2006 set replaces the previously recommended 2002 CODATA set and may also be found on the World Wide Web at physics.nist.gov/constants.

No full-text available

Request Full-text Paper PDF

To read the full-text of this research,
you can request a copy directly from the authors.

... The energy value of the M 2S 1/2 − 2P 3/2 transition is based on well-established calculations for the hydrogen (H) atom which are summarized in Ref. [30,31]. Higher-order QED corrections that are negligible in H but are relevant for the M n = 2 manifold are described in Ref. [32]. ...
... We use the total mass M = m e + m n , the reduced mass m r = m e m n /(m e + m n ), and the vacuum speed of light c. In contrast to Eq. 30 of CODATA 2022 [30], we define E M without the Barker-Glover recoil correction E BKG and thus write: ...
... Radiative recoils for the nP states are addressed in Ref. [37] and are of the order of magnitude of 100 Hz for M and 10 Hz for H. They are not directly utilized here because of the different derivation compared to Ref. [30,31] and we take the order of magnitude contribution as its uncertainty. ...
Preprint
Full-text available
We review the status of the QED calculations for the muonium 2S1/22P3/22S_{1/2}-2P_{3/2} energy interval and provide the updated theoretical value of 9874.357±0.001MHz9874.357\pm0.001\,\mathrm{MHz}. Additionally, we present a model for probing Lorentz-violating coefficients within the Standard Model Extension framework using the fine structure measurement in the presence and absence of a weak external magnetic field, enabling novel tests of CPT and Lorentz symmetry. Using Monte Carlo simulations, we estimate that a precision of 10kHz\sim 10\,\mathrm{kHz} on the isolated 2S1/2,F=12P3/2,F=12S_{1/2}, F=1 - 2P_{3/2}, F=1 transition could be achievable employing Ramsey's separate oscillatory fields (SOF) technique. Collecting the required statics will become feasible with the upcoming High-Intensity Muon Beam (HiMB) at the Paul Scherrer Institute (PSI) in Switzerland. These advancements will enable precise tests of radiative QED corrections and nuclear self-energy contributions, while also providing tests of new physics and sensitivity to unconstrained coefficients for Lorentz violation within the Standard Model Extension framework.
... The proton rms charge radius (r p ), the deuteron rms charge radius (r d ) and the Rydberg constant (R) are co-determined from a set of experimental and theoretical results including, in particular, high precision spectroscopic measurements in muonic hydrogen and deuterium (µH, µD) and in electronic hydrogen and deuterium (eH, eD) [23]. In principle, these data may be significantly affected by the hypothetical fifth force considered in the present work. ...
... Energy differences between states of electronic hydrogen or deuterium are usually expressed as transition frequencies, e.g., ν ba for the energy difference between a state b and a state a. Theoretically, these transition frequencies have the following general [23]; value derived from measurements of the 1s -2s and 2s -4p intervals in eH [33]; value derived from measurements of the 1s -2s interval and of the 2p -2s Lamb shift in eH [32]; value derived from measurements of the 1s -2s and 1s -3s intervals in eH [29]; value derived from measurements in muonic hydrogen [15]. From top to bottom in (b): Value recommended by CODATA (2014 adjustment) [38]; values recommended by CODATA (2018 adjustment) [23]; result derived from the isotope shift of the 1s -2s interval in the electronic species [12]; value derived from measurements in muonic hydrogen and muonic deuterium [15]. ...
... Energy differences between states of electronic hydrogen or deuterium are usually expressed as transition frequencies, e.g., ν ba for the energy difference between a state b and a state a. Theoretically, these transition frequencies have the following general [23]; value derived from measurements of the 1s -2s and 2s -4p intervals in eH [33]; value derived from measurements of the 1s -2s interval and of the 2p -2s Lamb shift in eH [32]; value derived from measurements of the 1s -2s and 1s -3s intervals in eH [29]; value derived from measurements in muonic hydrogen [15]. From top to bottom in (b): Value recommended by CODATA (2014 adjustment) [38]; values recommended by CODATA (2018 adjustment) [23]; result derived from the isotope shift of the 1s -2s interval in the electronic species [12]; value derived from measurements in muonic hydrogen and muonic deuterium [15]. From top to bottom in (c): Values derived from the isotope shift of the 2 3 S -2 3 P interval in the electronic species as measured by Shiner et al [40,42] (left) or as measured by Cancio Pastor et al [40,43,44] (right); value derived from the isotope shift of the 2 3 S -2 1 S interval in the electronic species [16,17]; value derived from measurements in muonic 3 He and muonic 4 He [13,18] as redetermined in [19]. ...
Preprint
Newly calculated bounds on the strength of the coupling of an electron to a proton or a neutron by a fifth force are presented. These results are derived from the high precision spectroscopic data currently available for hydrogen, deuterium, helium-3 and helium-4. They do not depend on specific assumptions on how the interaction would couple to a deuteron compared to a proton or would couple to an α\alpha particle compared to a helion. They depend on its coupling to a muon, but not in a significant way for carrier masses below 100~keV if one assumes that the strength of the interaction with a muon would be of a similar order of magnitude as the strength of the interaction with an electron in that mass region.
... using the standard model of particle physics, including quantum electrodynamics to fifth order (involving >10,000 Feynman diagrams) and muonic as well as hadronic physics (1,3). This path leads to 0.24 part-per-billion (ppb) accuracy (2,8,10), and was up to now the most accurate measurement of α. ...
... An independent measurement of α at comparable accuracy creates an opportunity to test the The Rydberg constant R ¥ is known to 0.006 ppb accuracy (10), and the atom-to-electron mass ratio is known to better than 0.1 ppb for many species. ...
... This proposed definition will assign a fixed numerical value to the Planck constant, to which mass measurements could then be linked through measurements of h/M, such as this one, via Avogadro spheres. Our result agrees within 1 sigma with previous recoil measurements (4) and has a 2.5 sigma tension with measurements (2,8,10) based on the gyromagnetic moment. ...
Preprint
Measurements of the fine-structure constant alpha require methods from across subfields and are thus powerful tests of the consistency of theory and experiment in physics. Using the recoil frequency of cesium-133 atoms in a matter-wave interferometer, we recorded the most accurate measurement of the fine-structure constant to date: alpha = 1/137.035999046(27) at 2.0 x 10^-10 accuracy. Using multiphoton interactions (Bragg diffraction and Bloch oscillations), we demonstrate the largest phase (12 million radians) of any Ramsey-Borde interferometer and control systematic effects at a level of 0.12 parts per billion. Comparison with Penning trap measurements of the electron gyromagnetic anomaly ge-2 via the Standard Model of particle physics is now limited by the uncertainty in ge-2; a 2.5 sigma tension rejects dark photons as the reason for the unexplained part of the muon's magnetic moment at a 99 percent confidence level. Implications for dark-sector candidates and electron substructure may be a sign of physics beyond the Standard Model that warrants further investigation.
... The fine structure constant α [1] describes the strength of the electromagnetic interaction and is thus important in all of physics, from elementary particle, nuclear and atomic physics to mesoscopic and macroscopic systems; an improved measurement will thus be a basis for many applications in both fundamental and applied science. This also implies that α can be measured by a wide variety of precision experiments, see Table I [2]. This also provides one of the best measures of the overall consistency of our basic theories and experimental methods. ...
... (The latter value also depends on the electron and neutron masses and crystal lattice spacings.) It is unclear whether the uncertainties of these TABLE I: Precision measurements of the fine-structure constant [2]. See Table XV in Ref. [2] for a more complete overview. ...
... It is unclear whether the uncertainties of these TABLE I: Precision measurements of the fine-structure constant [2]. See Table XV in Ref. [2] for a more complete overview. ...
Preprint
We report on progress towards a measurement of the fine structure constant to an accuracy of 5×10105\times 10^{-10} or better by measuring the ratio of the Planck constant to the mass of the cesium atom. Compared to similar experiments, ours is improved in three significant ways: (i) simultaneous conjugate interferometers, (ii) multi-photon Bragg diffraction between same internal states, and (iii) an about 1000 fold reduction of laser phase noise to -138 dBc/Hz. Combining that with a new method to simultaneously stabilize the phases of four frequencies, we achieve 0.2 mrad effective phase noise at the location of the atoms. In addition, we use active stabilization to suppress systematic effects due to beam misalignment.
... High-precision spectroscopy experiments on atomic hydrogen [1][2][3][4][5] are critically important sources of data for the least-square adjustment of fundamental constants [6]. The discrepancy in the interpretation of the results of related experiments, notably, in extracting the proton charge radius from ordinary hydrogen versus muonic hydrogen (known as the proton size puzzle, see Refs. ...
... (21a), (21b), (22a), and (22b). The coefficients ξ (6) ω,γ for perturber 1S atoms were averaged over the manifold of all available hyperfine substates, while the 2S perturber atoms were taken only in the F = 0 substates. The averaging is done according to Eq. (40). ...
... where the superscript in C 6 indicates that the interactions are of the nonretarded van der Waals type and the proportionality coefficients ξ (6) ω, γ are given by ...
Preprint
We investigate collisional shifts of spectral lines involving excited hydrogenic states, where van der Waals coefficients have recently been shown to have large numerical values when expressed in atomic units. Particular emphasis is laid on the recent hydrogen 2S-4P experiment (and an ongoing 2S-6P experiment) in Garching, but numerical input data are provided for other transitions (e.g., involving S states), as well. We show that the frequency shifts can be described, to sufficient accuracy, in the impact approximation. The pressure related effects were separated into two parts, (i) related to collisions of atoms inside of the beam, and (ii) related to collisions of the atoms in the atomic beam with the residual background gas. The latter contains both atomic as well as molecular hydrogen. The dominant effect of intra-beam collisions is evaluated by a Monte-Carlo simulation, taking the geometry of the experimental apparatus into account. While, in the Garching experiment, the collisional shift is on the order of 10 Hz, and thus negligible, it can decisively depend on the experimental conditions. We present input data which can be used in order to describe the effect for other transitions of current and planned experimental interest.
... This qualitative difference between premetric and metric quantities is also reflected in the universal constants of physics; for an overview of the fundamental constants, see Flowers & Petley [46] and Mohr et al. [109,110]. There are universal scalars, like the Planck constant , the elementary charge e, the magnetic flux quantum Φ 0 , which are invariant under all coordinate transformations (that is, under the diffeomorphism group). ...
... We discussed these results previously, see [62]. If we pick for q the elementary charge e and for h the Planck constant h, we immediately arrive at the the Josephson [81,2] and the von Klitzing [84,80] constants of modern metrology-for reviews, see [46,108,109,134,53]-which provide highly precise measurements 9 of e and h, ...
... In modern metrology [109,156] the value of the constant c 0 = 299 792.458 km s −1 is exact, and the role of c 0 is reduced to a conversion factor that is used to define an SI unit of length: the meter is introduced as the length which the light passes in vacuum during a time that equals 1/299 792 458 of a second. The possibility of a similar definition of a kilogram, by making use of the fundamental physical constants, is now widely discussed, see Haddad et al. [53]. ...
Preprint
In 1922, Kottler put forward the program to remove the gravitational potential, the metric of spacetime, from the fundamental equations in physics as far as possible. He successfully applied this idea to Newton's gravitostatics and to Maxwell's electrodynamics, where Kottler recast the field equations in premetric form and specified a metric-dependent constitutive law. We will discuss the basics of the premetric approach and some of its beautiful consequences, like the division of universal constants into two classes. We show that classical electrodynamics can be developed without a metric quite straightforwardly: the Maxwell equations, together with a local and linear response law for electromagnetic media, admit a consistent premetric formulation. Kottler's program succeeds here without provisos. In Kottler's approach to gravity, making the theory relativistic, two premetric quasi-Maxwellian field equations arise, but their field variables, if interpreted in terms of general relativity, do depend on the metric. However, one can hope to bring the Kottler idea to work by using the teleparallelism equivalent of general relativity, where the gravitational potential, the coframe, can be chosen in a premetric way.
... For example, in the case of the 4P (H)-1S(H) interaction, the fine structure and the hyperfine structure splitting parameters are of the order of 2×10 −7 E h and 9 × 10 −9 E h , respectively, where E h = 27.211396 eV is the Hartree energy [21]. However, in the case of the 4P (H)-1S(H 2 ) interaction, the atom-molecules degenerate states' separation is in the order of 2 × 10 −2 E h and the ro-vibrational level splitting is at-most ∼ 5.5 × 10 −5 E h . ...
... Also, S i = σ i /2 is the (dimensionless) spin operator for the electron i, where σ is the vector of Pauli spin matrices, and I i is the spin operator for the nucleus of atom i (proton i). According to Ref. [21], the protonic g factors is g p ≃ 5.585 695, µ B ≃ 9.274 010 × 10 −24 Am 2 is the Bohr magneton, while µ N ≃ 5.050 784 × 10 −27 Am 2 is the nuclear magneton. In order to simplify the expressions, we use the approximation g s = 2 in the following calculations. ...
... Throughout this paper, we perform final numerical evaluations in the non-recoil approximation, which corresponds to an infinite mass of the proton, i.e., we set the reduced mass of the electron in hydrogen atom equal to the electron mass, and ignore the different reduced-mass dependence for the fine-structure and the hyperfine-structure terms in the Hamiltonian. Values for physical constants are taken from Ref. [21]. ...
Preprint
We study the theoretical foundations for the pressure shifts in high-precision atomic beam spectrosopy of hydrogen, with a particular emphasis on transitions involving higher excited P states. In particular, the long-range interaction of an excited hydrogen atom in a 4P state with a ground-state and metastable hydrogen atom is studied, with a full resolution of the hyperfine structure. It is found that the full inclusion of the 4P_1/2 and 4P_3/2 manifolds becomes necessary in order to obtain reliable theoretical predictions, because the 1S ground state hyperfine frequency is commensurate with the 4P fine-structure splitting. An even more complex problem is encountered in the case of the 4P-2S interaction, where the inclusion of quasi-degenerate 4S-2P_1/2 state becomes necessary in view of the dipole couplings induced by the van der Waals Hamiltonian. Matrices of dimension up to 40 have to be treated despite all efforts to reduce the problem to irreducible submanifolds within the quasi-degenerate basis. We focus on the phenomenologically important second-order van der Waals shifts, proportional to 1/R^6 where R is the interatomic distance, and obtain results with full resolution of the hyperfine structure. The magnitude of van der Waals coefficients for hydrogen atom-atom collisions involving excited P states is drastically enhanced due to energetic quasi-degeneracy; we find no such enhancement for atom-molecule collisions involving atomic nP states, even if the complex molecular spectrum involving ro-vibrational levels requires a deeper analysis.
... In the past decades, high-precision spectroscopy measurements in atomic physics scale systems have pushed precision tests of quantum electrodynamics (QED), one of the cornerstones of the standard model of physics, ever further [1,2] and have led to accurate determinations of fundamental constants [3][4][5][6]. Recently however, measurements of transition frequencies in muonic hydrogen (µH) have revealed a discrepancy of six standard deviations [7,8] with respect to the accepted CODATA value for the proton charge radius. ...
... The lineshape due to the mean-field shift is given by equation 25 of ref. [3], and can be written as ...
... where a tt and a ts are the triplet-triplet and triplet-singlet scattering lengths respectively, n(0) is the peak density of the BEC, and µ is the chemical potential of the BEC. A number of factors of two are different between equation 4 and equation 25 of ref. [3] because we use a one-photon, rather than a two-photon transition. The average frequency shift of the lineshape can be calculated according to ...
Preprint
Improvements in both theory and frequency metrology of few-electron systems such as hydrogen and helium have enabled increasingly sensitive tests of quantum electrodynamics (QED), as well as ever more accurate determinations of fundamental constants and the size of the nucleus. At the same time advances in cooling and trapping of neutral atoms have revolutionized the development of increasingly accurate atomic clocks. Here, we combine these fields to reach the highest precision on an optical tranistion in the helium atom to date by employing a Bose-Einstein condensate confined in a magic wavelength optical dipole trap. The measured transition accurately connects the ortho- and parastates of helium and constitutes a stringent test of QED theory. In addition we test polarizability calculations and ultracold scattering properties of the helium atom. Finally, our measurement probes the size of the nucleus at a level exceeding the projected accuracy of muonic helium measurements currently being performed in the context of the proton radius puzzle.
... In line with pedagogical principle, one begins from the known to the unknown. The Rydberg constant (R) is given as (Mohr et al., 2016): ...
... where α, me c, and h are the fine structure constant, rest mass of an electron, velocity of light in a vacuum, and Planck constant respectively. The 'α' is given as (Mohr et al., 2016): ...
Article
Full-text available
The use of the reduced mass concept as opposed to the rest mass seems to give conflicting results. The objectives were to derive variants of the equation of the Rydberg constant (R∞), fine structure constant, and wave number that relate with the Rydberg constant. The derived R∞ equations are variants of each other and of those known in the literature; this is also applicable to the fine structure constant (a). The values of R∞ range between 10973731.6 and 10973733.89 /m for the rest mass case, while for the reduced mass case, the range is between 10966253.06 and 10967784.63 /m; regarding ‘a’, the derived equations gave results that are the same. The use of rest mass and reduced mass gave conflicting values for physical constants. Other variants of the equation for R∞ may be determined in the future. Classification numbers: 32.10.Bi; 32.10.Dk
... The spectrum of hydrogen-like atoms can be calculated very accurately and compared with experiments, making spectroscopy on such systems an invaluable tool for tests of fundamental physics 1,2 . It plays an important role in the determination of some of the fundamental constants, most notably the Rydberg constant 2,3 . ...
... The spectrum of hydrogen-like atoms can be calculated very accurately and compared with experiments, making spectroscopy on such systems an invaluable tool for tests of fundamental physics 1,2 . It plays an important role in the determination of some of the fundamental constants, most notably the Rydberg constant 2,3 . So far, a variety of hydrogen-like systems have been investigated with precision spectroscopy, e.g., atomic hydrogen 4-10 , antihydrogen 11 , muonic hydrogen (where a muon takes the place of the electron) 12,13 , positronium 14 , muonium 15 , and highly-charged ions 16,17 . ...
Article
Full-text available
Laser spectroscopy of atomic hydrogen and hydrogen-like atoms is a powerful tool for tests of fundamental physics. The 1S–2S transition of hydrogen in particular is a cornerstone for stringent Quantum Electrodynamics (QED) tests and for an accurate determination of the Rydberg constant. We report laser excitation of the 1S–2S transition in singly-ionized helium (³He⁺), a hydrogen-like ion with much higher sensitivity to QED than hydrogen itself. The transition requires two-photon excitation in the challenging extreme ultraviolet wavelength range, which we achieve with a tabletop coherent laser system suitable for precision spectroscopy. The transition is excited by combining an ultrafast amplified pulse at 790 nm (derived from a frequency comb laser) with its 25th harmonic at 32 nm (produced by high-harmonic generation). The results are well described by our simulations and we achieve a sizable 2S excitation fraction of 10⁻⁴ per pulse, paving the way for future precision studies.
... shown. The values and corresponding error bars are taken from CODATA recommended values [32] and the latest result for g e [22]. Note that the ultra-precise mass values for Cs and Rb from Penning trap measurements are part of the α determination from atom recoil experiments by means of optical spectroscopy. ...
... Since the gfactor calculations have been checked independently by different authors and are believed to be correct it has been agreed to select a value for α which establishes agreement between theory and experiment. In fact, the presently most precise value for α as listed in the CODATA table of fundamental constants [32] is taken from this comparison [22]: ...
Preprint
This review article describes the trapping of charged particles. The main principles of electromagnetic confinement of various species from elementary particles to heavy atoms are briefly described. The preparation and manipulation with trapped single particles, as well as methods of frequency measurements, providing unprecedented precision, are discussed. Unique applications of Penning traps in fundamental physics are presented. Ultra-precise trap-measurements of masses and magnetic moments of elementary particles (electrons, positrons, protons and antiprotons) confirm CPT-conservation, and allow accurate determination of the fine-structure constant alpha and other fundamental constants. This together with the information on the unitarity of the quark-mixing matrix, derived from the trap-measurements of atomic masses, serves for assessment of the Standard Model of the physics world. Direct mass measurements of nuclides targeted to some advanced problems of astrophysics and nuclear physics are also presented.
... with energy-dependent quantum defects of the respective series. Using the currently recommended values of fundamental constants [47] and the Cs mass [48] we calculate R Cs = 109 736.862 733 9(6) cm −1 . We performed a global fit of Eq. ...
... Such calculations can now reach an accuracy comparable to that of the experiments. The uncertainty in the electron-proton mass ratio (currently 5.446 170 213 52(52) · 10 −4 , i.e., a fractional uncertainty of 9.5 · 10 −11 [47]) imposes a fundamental limit of a few kHz to the accuracy of theoretical determinations of the ionization energy of H 2 [12]. Precision spectroscopy of Rydberg states of H 2 in combination with Rydberg-series extrapolation has the potential to be even more accurate. ...
Preprint
We present absolute-frequency measurements for the transitions from the 6s1/2_{1/2} ground state of 133^{133}Cs to np1/2_{1/2} and np3/2_{3/2} Rydberg states. The transition frequencies are determined by one-photon UV spectroscopy in ultracold samples of Cs atoms using a narrowband laser system referenced to a frequency comb. From a global fit of the ionization energy EIE_\mathrm{I} and the quantum defects of the two series we determine an improved value of EI=hc31406.4677325(14)E_\mathrm{I} = h c \cdot 31 406.467 732 5(14) cm1^{-1} for the ionization energy of Cs with a relative uncertainty of 5×10115\times10^{-11}. We also report improved values for the quantum defects of the np1/2_{1/2}, np3/2_{3/2}, ns1/2_{1/2}, and nd5/2_{5/2} series.
... It provided an improvement of the accuracy of the electron mass by a factor of 4, as compared to the previous value based on measurements involving protons and electrons in Penning traps [11]. As a result, the presently recommended value for the electron mass [12] is derived mainly from the bound-electron g factor. The current uncertainty of the theoretical values for the g factor in H-like carbon and oxygen (as well as for other lowand medium-Z ions) originates predominately from the twoloop binding QED correction. ...
... The result for the two-loop self-energy contribution is given by Eq. (12). We estimate the uncertainty due to uncalculated parts g (2) 1 and g (2) 2 as 30% of the constant term. ...
Preprint
Within a systematic approach based on nonrelativistic quantum electrodynamics (NRQED), we derive the one-loop self-energy correction of order alpha (Zalpha)^4 to the bound-electron g factor. In combination with numerical data, this analytic result improves theoretical predictions for the self-energy correction for carbon and oxygen by an order of magnitude. Basing on one-loop calculations, we obtain the logarithmic two-loop contribution of order alpha^2 (Zalpha)^4 ln[(Zalpha)^-2] and the dominant part of the corresponding constant term. The results obtained improve the accuracy of the theoretical predictions for the 1S bound-electron g factor and influence the value of the electron mass determined from g factor measurements.
... The position of the DI threshold, 145796.8413(4) cm −1 [45,59] is marked by a grey dashed vertical line and coincides with the onset of a continuum in the spectra. Because the spectra display the yield of electrons produced by delayed PFI, the electron signal measured in the continuum must stem from the field ionization of high-n Rydberg states of H, a conclusion that was confirmed by the MATI spectra, displayed in the upper part of Fig. 2(b). ...
... (17) and E h /hc = 2194746.313702(13) cm −1 [59]. The relativistic and radiative corrections as reported by Moss [12] were added to our nonadiabatic energies. ...
Preprint
Although the existence of quasi-bound rotational levels of the X+ 2Σg+X^+ \ ^2\Sigma_g^+ ground state of H2+_2^+ has been predicted a long time ago, these states have never been observed. Calculated positions and widths of quasi-bound rotational levels located close to the top of the centrifugal barriers have not been reported either. Given the role that such states play in the recombination of H(1s) and H+^+ to form H2+_2^+, this lack of data may be regarded as one of the largest unknown aspects of this otherwise accurately known fundamental molecular cation. We present measurements of the positions and widths of the lowest-lying quasi-bound rotational levels of H2+_2^+ and compare the experimental results with the positions and widths we calculate using a potential model for the X+X^+ state of H2+_2^+ which includes adiabatic, nonadiabatic, relativistic and radiative corrections to the Born-Oppenheimer approximation.
... Many impressive experimental results have been achieved. For example, the value of the fine structure constant, α, was determined to be α −1 =137.035999037(91) in the 87 Rb-atom recoil experiment [17], which is the second best value compared to the one deduced from the electron anomaly measurement [18]. Using a double atom-interferometer-gravitygradiometer, the Newtonian gravitational constant was measured to be G = 6.67191(99)× 10 −11 m 3 kg −1 s −2 [19], which was one of the 14 measured values adopted by the 2014 CODATA adjustment [18]. ...
... For example, the value of the fine structure constant, α, was determined to be α −1 =137.035999037(91) in the 87 Rb-atom recoil experiment [17], which is the second best value compared to the one deduced from the electron anomaly measurement [18]. Using a double atom-interferometer-gravitygradiometer, the Newtonian gravitational constant was measured to be G = 6.67191(99)× 10 −11 m 3 kg −1 s −2 [19], which was one of the 14 measured values adopted by the 2014 CODATA adjustment [18]. A 10 −8 -level test of the weak equivalence principle (WEP) using the dual-species atom interferometer was reported in a recent work [20], which is the best result in the quantum test of the WEP with microscopic objects. ...
Preprint
Various models of quantum gravity imply the Planck-scale modifications of Heisenberg's uncertainty principle into a so-called generalized uncertainty principle (GUP). The GUP effects on high-energy physics, cosmology, and astrophysics have been extensively studied. Here, we focus on the weak-equivalence-principle (WEP) violation induced by the GUP. Results from the WEP test with the 85^{85}Rb-87^{87}Rb dual-species atom interferometer are used to set upper bounds on parameters in two GUP proposals. A 104510^{45}-level bound on the Kempf-Mangano-Mann proposal, and a 102710^{27}-level bound on Maggiore's proposal, which are consistent with bounds from other experiments, are obtained. All these bounds have huge room for improvement in the future.
... Here, by the term "physical reality", we mean a set of empirical observer-independence data, which includes all fundamental physical constants [30]. The term "partial description of nature" expresses the fact that, in practice, an observer has access only to a part of the world called a "system". ...
Article
Full-text available
We consider the status of quantum information in the quantum theory and based on the correspondence principle, we propose an interpretation of the wave function as a mathematical representation of quantum information. We consider Clauser’s analysis of incompatibility formulations of quantum theory in laboratory space and configuration space in the context of local realism. Then, we introduce the hypothesis of quantum space of directly unobserved relations, which precede quantum correlations, and are compatible with the Reichenbach common cause principle. The possible implications of the hypothesis are discussed in the context of the latest experimental and theoretical results on the dynamics of entanglement formation in helium atoms. Finally, we present the Chyliński model as an example of quantum relational continuum space, which predicts potentially measurable effects for the bound states.
... Avogadro number and Unified atomic mass unit [1][2][3][4][5][6] play a vital role in every day various branches of physics and chemistry. Scientists are seriously working on estimating them with various methods with advanced engineering techniques. ...
... Кроме того, использование фундаментальных констант в СИ, таких как скорость света в вакууме, заряд электрона, масса электрона, постоянная Планка и постоянная тонкой структуры, обеспечивает фиксированный интервал, в пределах которого могут использоваться различные модели. Эти константы действуют как якоря, обеспечивая согласованность и минимизируя неоднозначность в интерпретации физических явлений [18,19]. Подводя итог вышеизложенным этапам процесса формулирования модели, следует отметить, что разум мыслителя, сформированный существующими знаниями, научными парадигмами, обусловленный его знаниями, опытом и интуицией, определяет первоначальный выбор структуры модели. ...
Preprint
Full-text available
The article examines the complex relationship between the choice of model structure, the influence of the thinker's intuition, knowledge and experience, and the inherent freedom of choice in physics. The presented concept of the "thinker's problem" emphasizes the role of the observer's mental picture in the perception of reality represented by the model. The Abelian structure of the International System of Units, widely used in the scientific community, is the basis for constructing a model, setting the limits of achievable accuracy in scientific research. The article examines the balance between the thinker's freedom of choice and the possibility of discovering physical laws and the limited accuracy of experimental measurements, acknowledging the lack of a generally accepted criterion for choosing a model at present. The article discusses the nature of scientific progress, which is determined by the continuous improvement of models, the relationship between the constructed model, the experimental data and the philosophical position of the observer/thinker, and the importance of the methodological approach in scientific research. В статье рассматривается сложная взаимосвязь между выбором структуры модели, влиянием интуиции, знаний и опыта мыслителя и неотъемлемой свободой выбора в физике. Излагаемая концепция «проблемы мыслителя» подчеркивает роль ментальной картины наблюдателя в восприятии реальности, представленной моделью. Абелева структура Международной системы единиц, широко используемая в научном сообществе, является основой для построения модели, устанавливая рамки достигаемой точности при проведении научных исследований. В статье рассматривается баланс между свободой выбора мыслителя и возможностью открытия физических законов и ограниченной точностью экспериментальных измерений, признавая отсутствие в настоящее время общепринятого критерия выбора модели. В статье обсуждается природа научного прогресса, обусловленная непрерывным совершенствованием моделей, связью между построенной моделью, данными эксперимента и философской позицией наблюдателя/мыслителя, а также важностью методологического подхода в научном исследовании.
... over multiple atoms [23][24][25][26] . The muon hfc and the hfcs of other nuclei in the radical with nuclear spin I > 0 can be used to map the distribution of the unpaired electron and determine the structure of the radical. ...
Article
Full-text available
This paper describes muon spin spectroscopy studies of 12-phosphatetraphene stabilized by a peri-trifluoromethyl group and a meso-aryl substituent. Even though the prepared solution in tetrahydrofuran (THF) was quite dilute (0.060 M) for transverse-field muon spin rotation (TF-µSR) measurements, the π-extended heavier congener of tetraphene presented a pair of signals due to a muoniated radical from which the muon hyperfine coupling constant (hfc) was determined. This muoniated radical was produced by the diffusion-controlled regioselective addition of muonium (Mu = [µ⁺e–]) to the sp²-hybridized phosphorus atom. The assignment of the muoniated radical structure was confirmed by observing a resonance due to the I = 1/2 (³¹P) nucleus in a muon (avoided) level-crossing resonance (µLCR) spectrum. The ³¹P hfc was determined from the resonance position, and a comparison with the value obtained from density functional theory (DFT) calculations indicated that the radical retained a flat π-delocalized tetracyclic skeleton. This higher energy structure is hypothesized to be preferable because of the increased zero-point energy of the light mass of the muon. The findings of this study could be fruitful in developing novel spin-functional materials featuring efficient radical capture and π-delocalized paramagnetic molecular systems.
... A discrepancy between theory and experiment could be interpreted as new physics. Thus, the theoretical value of Eides [18] is preferred to CODATA adjustment value [21] to take into account the proper magnitude of the error bars of the theoretical prediction for muonium HFS (see also the discussion in [22]). Underestimating the error bars could result in a new physics discovery being misreported. ...
Preprint
At the J-PARC Muon Science Facility (MUSE), the MuSEUM collaboration is now performing new precision measurements of the ground state hyperfine structure (HFS) of both muonium and muonic helium atoms. High-precision measurements of the muonium ground-state HFS are recognized as one of the most sensitive tools for testing bound-state quantum electrodynamics theory to precisely probe the standard model and determine fundamental constants of the positive muon magnetic moment and mass. The same technique can also be employed to measure muonic helium HFS, obtain the negative muon magnetic moment and mass, and test and improve the theory of the three-body atomic system. Measurements at zero magnetic field have already yielded more accurate results than previous experiments for both muonium and muonic helium atoms. High-field measurements are now ready to start collecting data using the world's most intense pulsed muon beam at the MUSE H-line. We aim to improve the precision of previous measurements ten times for muonium and a hundred times or more for muonic helium. We review all the key developments for these new measurements, focusing on the high-field experiment, and report the latest results and prospects.
... and then, the factor G F ZK/( √ 2 a 3 0 ) = ZK 0.103 403 426 h kHz was used to convert the values of Ws,K from a.u. to h kHz. All values of the fundamental constants were taken from Ref. 40. ...
Article
Full-text available
In this work, the molecular enhancement factors of the P,T-odd interactions involving the electron electric dipole moment (Wd) and the scalar–pseudoscalar nucleon–electron couplings (Ws) are computed for the ground state of the bimetallic molecules YbCu, YbAg, and YbAu. These systems offer a promising avenue for creating cold molecules by associating laser-cooled atoms. The relativistic coupled-cluster approach is used in the calculations, and a thorough uncertainty analysis is performed to give accurate and reliable uncertainties to the obtained values. Furthermore, an in-depth investigation of the different electronic structure effects that determine the magnitude of the calculated enhancement factors is carried out, and two different schemes for computing Wd are compared. The final values for the enhancement factors are (13.32±0.13)×1024hHzecm, (12.19±0.12)×1024hHzecm, and (2.36±0.48)×1024hHzecm for Wd and (−48.63 ± 0.53) h kHz, (−45.68 ± 0.60) h kHz, and (3.81 ± 2.58) h kHz for Ws, for YbCu, YbAg, and YbAu, respectively.
... Traditional techniques, such as time-of-flight measurement and displacement measuring interferometry, employ top-down approaches in dimensional nanometrology but are constrained by fringe subdivision and periodic nonlinearities in visible-wavelength interferometry [1][2][3][4][5]. In 2018, the 26th General Conference of Weights & Measures (CGPM) recommended the use of Si {220} lattice spacing at a temperature of 22.5°C in vacuum as a secondary realization of the definition of the meter to support nanometrology [6,7]. Si lattice provides a bottom-up approach to traceability at the nanometer and sub-nanometer level. ...
... The anomalous magnetic moment, ae, represents the deviation of the electron's actual magnetic moment from the value predicted by Dirac theory, which accounts only for basic relativistic effects and spin interactions. In Dirac's theory, the electron's magnetic moment is given by where g is the electron's gyromagnetic ratio, also known as the g-factor, which is theoretically set to 2 [16][17][18]. However, due to higher-order QED effects, the experimentally measured g-factor deviates slightly from 2. This deviation results from interactions between the electron and the quantized electromagnetic field, which can be understood as exchanges of virtual photons and electronpositron pairs. ...
Preprint
Full-text available
The fine-structure constant, α, is a fundamental constant central to electromagnetic interaction strength and the behavior of atomic systems. Despite extensive study, the origin of α remains an open question. This paper explores a new approach by examining the connection between α, the electron’s anomalous magnetic moment, and the ratio π/γ, where γ is a relativistic Lorentz factor. Specifically, we propose that α may arise from the electron’s rotational dynamics at near-light speeds, represented by γ ≈ 430. The electron’s anomalous magnetic moment reflects deviations from Dirac’s predictions, influenced by higher-order quantum electrodynamic (QED) corrections due to virtual photon exchanges and electron spin interactions. These interactions alter the electron’s magnetic moment, giving rise to a slight discrepancy from the g-factor value of 2. By expressing α as the ratio π/γ, we investigate whether this relationship captures both the fine-structure constant’s specific value and the QED corrections underlying the anomalous magnetic moment. Our findings suggest that α could be interpreted as a dimensionless outcome of electron spin and relativistic effects, with π/γ potentially explaining the approximate value of α as 1/137. This perspective proposes a unifying framework in which α emerges from intrinsic electron properties and relativistic corrections, linking quantum mechanics with special relativity. This approach may enhance our understanding of α and its role across fundamental physics, offering insight into the constants that govern particle interactions.
... We have adopted the values of Pelissetto and Vicari 73 and have set α = 0.1100 and β = 0.3265. The value for the molar mass of H 2 O (18.015 268 g/mol) was taken from Wagner and Pruß 12 and the ideal-gas constant R (8.314 4621 J mol −1 K −1 ) was taken from Mohr et al. 90 The molar mass of D 2 O (20.027 508 g/mol) was taken from an IAPWS guideline. 91 The number of terms in the background ∆μ r [Eq. ...
Preprint
We review the available experimental information on the thermodynamic properties of supercooled ordinary and heavy water and demonstrate the possibility of modeling these thermodynamic properties on a theoretical basis. We show that by assuming the existence of a liquid-liquid critical point in supercooled water, the theory of critical phenomena can give an accurate account of the experimental thermodynamic-property data up to a pressure of 150 MPa. In addition, we show that a phenomenological extension of the theoretical model can account for all currently available experimental data in the supercooled region, up to 400 MPa. The stability limit of the liquid state and possible coupling between crystallization and liquid-liquid separation are discussed. It is concluded that critical-point thermodynamics describes the available thermodynamic data for supercooled water within experimental accuracy, thus establishing a benchmark for further developments in this area.
... The essence of quantum mechanics is fluctuations in sources (currents) and fields. This underlies the great successes of quantum electrodynamics such as explaining the Lamb shift [1] and the anomalous magnetic moment of the electron [2]. Most directly, these fluctuations are manifested through the Casimir effect, the quantum vacuum forces between macroscopic neutral objects. ...
Preprint
For more than 35 years theorists have studied quantum or Casimir friction, which occurs when two smooth bodies move transversely to each other, experiencing a frictional dissipative force due to quantum electromagnetic fluctuations, which break time-reversal symmetry. These forces are typically very small, unless the bodies are nearly touching, and consequently such effects have never been observed, although lateral Casimir forces have been seen for corrugated surfaces. Partly because of the lack of contact with phenomena, theoretical predictions for the frictional force between parallel plates, or between a polarizable atom and a metallic plate, have varied widely. Here we review the history of these calculations, show that theoretical consensus is emerging, and offer some hope that it might be possible to experimentally confirm this phenomenon of dissipative quantum electrodynamics.
... The IAC's N A values are converted into Planck constant values via the molar Planck constant N A h = 3.9903127176(28) × 10 −10 Js mol −1 , which has a negligible uncertainty [18]. The correlation of the N A values reported in 2011 and 2015 by the IAC is investigated in [19], which gives also the mean of the correlated values. ...
Preprint
Statistical parametric models are proposed to explain the values of the Planck constant obtained by comparing electrical and mechanical powers and by counting atoms in Si 28 enriched crystals. They assume that uncertainty contributions -- having heterogeneous, datum-specific, variances -- might not be included in the error budgets of some of the measured values. Model selection and model averaging are used to investigate data consistency, to identify a reference value of the Planck constant, and to include the model uncertainty in the error budget.
... We use as a code input the value ofα ew (m Z ) =α ew (m Z ) given in Refs. [41,43] which includes an estimate of this numerical uncertainty. Whenα ew is used as an input parameter, the mapping of this expression to Lagrangian parameters is given in Eqn. ...
Preprint
We report codes for the Standard Model Effective Field Theory (SMEFT) in FeynRules -- the SMEFTsim package. The codes enable theoretical predictions for dimension six operator corrections to the Standard Model using numerical tools, where predictions can be made based on either the electroweak input parameter set {α^ew,m^Z,G^F}\{\hat{\alpha}_{ew}, \hat{m}_Z, \hat{G}_F \} or {m^W,m^Z,G^F}\{\hat{m}_{W}, \hat{m}_Z, \hat{G}_F\}. All of the baryon and lepton number conserving operators present in the SMEFT dimension six Lagrangian, defined in the Warsaw basis, are included. A flavour symmetric U(3)5{\rm U}(3)^5 version with possible non-SM CP\rm CP violating phases, a (linear) minimal flavour violating version neglecting such phases, and the fully general flavour case are each implemented. The SMEFTsim package allows global constraints to be determined on the full Wilson coefficient space of the SMEFT. As the number of parameters present is large, it is important to develop global analyses on reduced sets of parameters minimizing any UV assumptions and relying on IR kinematics of scattering events and symmetries. We simultaneously develop the theoretical framework of a "W-Higgs-Z pole parameter" physics program that can be pursued at the LHC using this approach and the SMEFTsim package. We illustrate this methodology with several numerical examples interfacing SMEFTsim with MadGraph5. The SMEFTsim package can be downloaded at https://feynrules.irmp.ucl.ac.be/wiki/SMEFT
... Appropriate units converted to SI-units. The values for the hydrogen atom are taken from[50]. Here we assume, that the mass of the proton is infinite as compared to the mass of the electron. ...
Preprint
Exceptional points are special parameter points in spectra of open quantum systems, at which resonance energies degenerate and the associated eigenvectors coalesce. Typical examples are Rydberg systems in parallel electric and magnetic fields, for which we solve the Schr\"odinger equation in a complete basis to calculate the resonances and eigenvectors. Starting from an avoided crossing within the parameter-dependent spectra and using a two-dimensional matrix model, we develop an iterative algorithm to calculate the field strengths and resonance energies of exceptional points and to verify their basic properties. Additionally, we are able to visualise the wave functions of the degenerate states. We report the existence of various exceptional points. For the hydrogen atom these points are in an experimentally inaccessible regime of field strengths. However, excitons in cuprous oxide in parallel electric and magnetic fields, i. e., the corresponding hydrogen analogue in a solid state body, provide a suitable system, where the high-field regime can be reached at much smaller external fields and for which we propose an experiment to detect exceptional points.
... The accurate determination of Newton's constant G has become a highly debated subject [45,46]. Although some experiments are now reaching precision levels up to ∆G/G ≈ 1 · 10 −5 [19], different implementations continue to disagree in the absolute value of G by multiple standard deviations [47,48,18]. A significant, if not dominant, contribution to the error budget of most of these measurements is due to uncertainties associated with the manufacture of the macroscopic source masses and their incorporation and use in the experimental arrangements. ...
Preprint
This paper addresses a simple question: how small can one make a gravitational source mass and still detect its gravitational coupling to a nearby test mass? We describe an experimental scheme based on micromechanical sensing to observe gravity between milligram-scale source masses, thereby improving the current smallest source mass values by three orders of magnitude and possibly even more. We also discuss the implications of such measurements both for improved precision measurements of Newton's constant and for a new generation of experiments at the interface between quantum physics and gravity.
... • (g − 2) µ : The muon anomalous magnetic moment (g − 2) µ has had a persistent ∼ 3σ discrepancy between the measured value [64,65] and SM prediction [66][67][68]. It has long been recognized that a dark photon with vector couplings can contribute to this (positive) discrepancy; axial-vector couplings contribute to (g − 2) µ with the opposite sign. ...
Preprint
We investigate the landscape of constraints on MeV-GeV scale, hidden U(1) forces with nonzero axial-vector couplings to Standard Model fermions. While the purely vector-coupled dark photon, which may arise from kinetic mixing, is a well-motivated scenario, several MeV-scale anomalies motivate a theory with axial couplings which can be UV-completed consistent with Standard Model gauge invariance. Moreover, existing constraints on dark photons depend on products of various combinations of axial and vector couplings, making it difficult to isolate the effects of axial couplings for particular flavors of SM fermions. We present a representative renormalizable, UV-complete model of a dark photon with adjustable axial and vector couplings, discuss its general features, and show how some UV constraints may be relaxed in a model with nonrenormalizable Yukawa couplings at the expense of fine-tuning. We survey the existing parameter space and the projected reach of planned experiments, briefly commenting on the relevance of the allowed parameter space to low-energy anomalies in pi^0 and 8-Be* decay.
... and E h /hc = 219474.6313702(13) cm −1[55]. ...
Preprint
The pulsed-field-ionization zero-kinetic-energy photoelectron spectrum of H2_2 has been recorded in the vicinity of the dissociative-ionization threshold following three-photon excitation via selected rotational levels of the B 1Σu+^1\Sigma_u^+ (v=19) and Hˉ\bar{\rm H} 1Σg+^1\Sigma_g^+ (v=11) intermediate states. The spectra consist of transitions to bound levels of the X+^+ 2Σg+^2\Sigma_g^+ state of H2+_2^+ with v+v^+ in the range 14-19 and N+N^+ in the range 0-9, of the A+^+ 2Σu+^2\Sigma_u^+ state with v+=0v^+=0 and N+=02N^+=0-2, and of shape resonances corresponding to the X+ (v+=17,N+=7)^+\ (v^+=17,N^+=7) and X+ (v+=18,N+=4)^+\ (v^+=18,N^+=4) quasibound levels. Calculations of the level structure of H2+_2^+ have been carried out and the influence of adiabatic, nonadiabatic, relativistic and radiative corrections on the positions of these levels, and in the case of the shape resonances also on their widths, has been investigated. Different methods of calculating the widths and profiles of the shape resonances have been tested for comparison with the experimental observations. Slow oscillations of the dissociative-ionization yield have been observed and reflect, in first approximation, the Franck-Condon factors of the Hˉ\bar{\text H} \rightarrow X+^+, A+^+ bound - free transitions.
... Many experimental groups have precisely measured the Planck constant, and the level of the relative uncertainty is in the range of 10 −6 to 10 −9 [39]. In this paper we use the CODATA recommended value, = 1.054571800(13) × 10 −34 J · s [40], and hence we require ...
Preprint
We study the noncommutative corrections on the time-dependent Aharonov-Bohm effect when both the coordinate-coordinate and momentum-momentum noncommutativities are considered. This study is motivated by the recent observation that there is no net phase shift in the time-dependent AB effect on the ordinary space, and therefore tiny derivation from zero can indicate new physics. The vanishing of the time-dependent AB phase shift on the ordinary space is preserved by the gauge and Lorentz symmetries. However, on the noncomutative phase space, while the ordinary gauge symmetry can be kept by the Seiberg-Witten map, but the Lorentz symmetry is broken. Therefore nontrivial noncommutative corrections are expected. We find there are three kinds of noncommutative corrections in general: 1) ξ\xi-dependent correction which comes from the noncommutativity among momentum operators; 2) momentum-dependent correction which is rooted in the nonlocal interactions in the noncommutative extended model; 3) momentum-independent correction which emerges become of the gauge invariant condition on the nonlocal interactions in the noncommutative model. We proposed two dimensionless quantities, which are based on the distributions of the measured phase shift with respect to the external magnetic field and to the cross section enclosed by the particle trajectory, to extract the noncommutative parameters. We find that stronger (weaker) magnetic field strength can give better bounds on the coordinate-coordinate (momentum-momentum) noncommutative parameter, and large parameter space region can be explored by the time-dependent AB effect.
... Due to their high sensitivity, atom interferometers have already been used in various precision measurements, and many important experimental results came out. For example, the value of the Newtonian gravitational constant was measured to be G = 6.67191(99) × 10 −11 m 3 kg −1 s −2 [15], which just differs by 1.5 combined standard deviations from the CO-DATA recommended value [16]. A 10 −8 -level test of the weak equivalence principle (WEP) was reported in a recent work [17]. ...
Preprint
Various theories of quantum gravity predict the existence of a minimum length scale, which implies the Planck-scale modifications of the Heisenberg uncertainty principle to a so-called generalized uncertainty principle (GUP). Previous studies of the GUP focused on its implications for high-energy physics, cosmology, and astrophysics. Here, the application of the GUP to low-energy quantum systems, and particularly cold atoms, is studied. Results from the 87^{87}Rb atom recoil experiment are used to set upper bounds on parameters in three different GUP proposals. A 101410^{14}-level bound on the Ali-Das-Vagenas proposal is found, which is the second best bound so far. A 102610^{26}-level bound on Maggiore's proposal is obtained, which turns out to be the best available bound on it.
... Here, R ∞ is the Rydberg constant, m e is the electron mass, and M is the mass of the test atom. Since R ∞ is known to 5 parts in 10 12 , and the mass ratio M/m e is typically known to a few parts in 10 10 [12], the quantity that limits the precision of a determination of α using Eq. (1) is the ratio h/M . ...
Preprint
We describe progress toward a precise measurement of the recoil energy of an atom measured using a perturbative grating-echo atom interferometer (AI) that involves three standing-wave (sw) pulses. With this technique, a perturbing sw pulse is used to shift the phase of excited momentum states---producing a modulation in the contrast of the interference pattern. The signal exhibits narrow fringes that revive periodically at twice the two-photon recoil frequency, 2ωq2\omega_q, as a function of the onset time of the pulse. Experiments are performed using samples of laser-cooled rubidium atoms with temperatures 5\lesssim 5 μ\muK in a non-magnetic apparatus. We demonstrate a measurement of ωq\omega_q with a statistical uncertainty of 37 parts per 10910^9 (ppb) on a time scale of 45\sim 45 ms in 14 hours. Further statistical improvements are anticipated by extending this time scale and narrowing the signal fringe width. However, the total systematic uncertainty is estimated to be 6\sim 6 parts per 10610^6 (ppm). We describe methods of reducing these systematic errors.
... The LEFT RGE is non-linear, and dimension-six operator coefficients have terms that depend on the square of dimension-five dipole coefficients. The non-linear dipole term in Eq. (6.20) depends on the e and µ dipole operators, which are strongly constrained by the electric and magnetic moments of the electron and muon [63][64][65][66][67] The Lagrangian coefficients at µ = m b are related to those at µ = M Z by  ...
Preprint
The gauge-invariant operators up to dimension six in the low-energy effective field theory below the electroweak scale are classified. There are 70 Hermitian dimension-five and 3631 Hermitian dimension-six operators that conserve baryon and lepton number, as well as ΔB=±ΔL=±1\Delta B= \pm \Delta L = \pm 1, ΔL=±2\Delta L=\pm 2, and ΔL=±4\Delta L=\pm 4 operators. The matching onto these operators from the Standard Model Effective Field Theory (SMEFT) up to order 1/Λ21/\Lambda^2 is computed at tree level. SMEFT imposes constraints on the coefficients of the low-energy effective theory, which can be checked experimentally to determine whether the electroweak gauge symmetry is broken by a single fundamental scalar doublet as in SMEFT. Our results, when combined with the one-loop anomalous dimensions of the low-energy theory and the one-loop anomalous dimensions of SMEFT, allow one to compute the low-energy implications of new physics to leading-log accuracy, and combine them consistently with high-energy LHC constraints.
... This work 204.5 ± 21.4 −92.9 ± 10.5 48.4 ± 8.2 GDH sum rule 204.784481(4) a BχPT [15] −90 ± 140 110 ± 50 HBχPT [17] −260 ± 190 a Right-hand side of Eq. (7) with CODATA [19] values of proton M and κ. ...
Preprint
The forward Compton scattering off the proton is determined by substituting the empirical total photoabsorption cross sections into dispersive sum rules. In addition to the spin-independent amplitude evaluated previously [Phys. Rev. D 92, 074031 (2015)], we obtain the spin-dependent amplitude over a broad energy range. The two amplitudes contain all the information about this process, and we, hence, can reconstruct the nonvanishing observables of the proton Compton scattering in the forward kinematics. The results are compared with predictions of chiral perturbation theory where available. The low-energy expansion of the spin-dependent Compton scattering amplitude yields the Gerasimov-Drell-Hearn (GDH) sum rule and relations for the forward spin polarizabilities (FSPs) of the proton. Our evaluation provides an empirical verification of the GDH sum rule for the proton, and yields empirical values of the proton FSPs. For the GDH integral, we obtain 204.5(21.4) μ\mub, in agreement with the sum rule prediction: 204.784481(4) μ\mub. For the FSPs, we obtain: γ0=92.9(10.5)×106\gamma_0=-92.9(10.5) \times 10^{-6} fm4^4, and γ0ˉ=48.4(8.2)×106\bar{\gamma_0}=48.4(8.2) \times 10^{-6} fm6^6, improving on the accuracy of previous evaluations.
... While measurements of the proton charge radius has been fluctuating some in recent years, we used the most recent measurements above. However using a proton radius of a = 0.8751 f m based on other experiments (see for example [7]), we obtain for the charged pion mass 143 MeV /c 2 , which only differs by 2.9% from measurements. The density fluctuations of the q d cloud in the neutron is oscillating back and forth between the slightly polarized positive cloud in the neutron and the positive field from the proton. ...
Article
Full-text available
Closed expressions for the masses of the charged and neutral pions are derived based on a simple approximate model for electrostatic screening when a proton is located adjacent to a neutron. The estimated mass values agree to a few percent of experimentally measured values. The electric dipole moment of the deuteron is also estimated based on the phenomenological toy model used here.
... This value is determined using Einstein's equation, E = ∆mc 2 , where ∆m is the change in mass for Eq. (1) [4]. The negative sign implies that this reaction (thermodynamic system) releases heat energy to the surroundings. ...
Article
Discussions with Professor Bockris prompted this thermodynamic and kinetic analysis of the D + D fusion reaction to form He-4. The results clearly show that this fusion reaction is thermodynamically possible at room temperatures. The kinetic analysis indicates that the reaction rate in the Pd/D system is controlled by the diffusion of deuterium within the palladium. Based on electrochemical double layer concepts, likely reaction zones exist near the surface of the palladium cathode.
... The value of the inverse of the fine-structure constant used during creation of Tables 1-14 was α −1 = 137.035 999 177, and was taken from the newest CODATA report on Recommended Values of the Fundamental Physical Constants [18]. However, in order to make the best comparison of the present results with the numerical results reported earlier by other authors for some atomic states [17], we have performed two additional tables (Tables 15-16) with the values of σ d and σ p obtained using α −1 = 137.035 ...
Preprint
We present tabulated data for numerical calculations of relative para- and diamagentic contributions to the magnetic shielding constant (σ\sigma) of the Dirac one-electron atoms with a pointlike, spinless and motionless nuclei of charge Ze. Exploiting the analytical formulas for the diamagnetic (σd\sigma_{d}) and paramagnetic (σp\sigma_{p}) terms of σ\sigma, valid for an arbitrary discrete energy state, recently derived by us with the aid of the Gordon decomposition technique, we have found the numerical values of σd/σ\sigma_{d}/\sigma and σp/σ\sigma_{p}/\sigma for the ground state and for the first two sets of excited states (i.e.: 2s1/22s_{1/2}, 2p1/22p_{1/2}, 2p3/22p_{3/2}, 3s1/23s_{1/2}, 3p1/23p_{1/2}, 3p3/23p_{3/2}, 3d3/23d_{3/2}, and 3d5/23d_{5/2}) of the relativistic hydrogenic ions with the nuclear charge number from the range 1Z1371 \leqslant Z \leqslant 137. The comparisons of our results with those reported by other authors for some atomic states are also presented. We also compile here the numerical values of the total magnetic shielding constants for the ground state 1s1/21s_{1/2} and for each state belonging to the first set of excited states of selected hydrogenlike ions, obtained with the use of three different values of the fine-structure constant, i.e.: α1=137.035999139\alpha^{-1}=137.035 \: 999 \: 139 (from CODATA 2014), α1=137.035999084\alpha^{-1}=137.035 \: 999 \: 084 (from CODATA 2018) and α1=137.035999177\alpha^{-1}=137.035 \: 999 \: 177 (from CODATA 2024).
... The nucleon mass radius is sizeably larger than the proton charge radius r 2 C , which is 0.840 +0.004 −0.003 fm 2 extracted using DRs [100] and (0.84075(64) fm) 2 recommended by the Committee on Data of the International Science Council (CODATA) [101]. The hierarchy in radii suggests, in the sense of Wigner phase-space distribution [102,103], that gluons, which are responsible for the [54], where "I" and "II" correspond to extractions therein using tripole and z-expansion fits, respectively. ...
Preprint
Being closely connected to the origin of the nucleon mass, the gravitational form factors of the nucleon have attracted significant attention in recent years. We present the first model-independent precise determinations of the gravitational form factors of the pion and nucleon at the physical pion mass, using a data-driven dispersive approach. The so-called ``last unknown global property'' of the nucleon, the D-term, is determined to be (3.380.32+0.26)-\left(3.38^{+0.26}_{-0.32}\right). The root mean square radius of the mass distribution inside the nucleon is determined to be 0.970.03+0.02 fm0.97^{+0.02}_{-0.03}~\text{fm}. Notably, this value is larger than the proton charge radius, suggesting a modern structural view of the nucleon where gluons, responsible for most of the nucleon mass, are distributed over a larger spatial region than quarks, which dominate the charge distribution. We also predict the nucleon angular momentum and mechanical radii, providing further insights into the intricate internal structure of the nucleon.
... The block of data provides the universal constants, whose values were also adopted by Gaussian 09 and recommended by Mohr et al. [39]. The users are then required to input the primary molecular constants (see Tables 7 and S3), and the secondary molecular constants (see Tables 7 and S4) are further calculated in this block. ...
Article
Full-text available
In this paper, I present Diatomic, an open-source Excel application that calculates molar thermodynamic properties for diatomic ideal gases. This application is very easy to use and requires only a limited number of molecular constants, which are freely available online. Despite its simplicity, Diatomic provides methodologies and results that are usually unavailable in general quantum chemistry packages. This application uses the general formalism of statistical mechanics, enabling two models to describe the rotational structure and two models to describe the vibrational structure. In this work, Diatomic was used to calculate standard molar thermodynamic properties for a set of fifteen diatomic ideal gases. A special emphasis was placed on the analysis of four properties (standard molar enthalpy of formation, molar heat capacity at constant pressure, average molar thermal enthalpy, and standard molar entropy), which were compared with experimental values. A molecular interpretation for the molar heat capacity at constant pressure, as an interesting pedagogical application of Diatomic, was also explored in this paper.
... na qual h ficou conhecida como constante de Planck, cujo valor é 6, 626 × 10 −34 Jůs(MOHR et al., 2012). ...
Article
Full-text available
Resumo Este artigo tem como objetivo apresentar um método experimental para determinar a constante de Planck através do cálculo de potencial de corte V0 provenientes de LED com diferentes comprimentos de onda. O experimento é desenhado utilizando o Arduino como ferramenta central de modo a tornar a atividade experimental mais envolvente e atrativa para os alunos, com o uso das tecnologias digitais. A partir das curvas características de cada LED, a análise gráfica foi utilizada para obter o potencial de corte e, sabendo o comprimento de onda correspondente, foi possível calcular a constante de Planck. Esta constante também foi obtida a partir do ajuste linear do gráfico do potencial de corte pela frequência de cada LED. Dada a relevância da constante de Planck na física, acredita-se que este experimento possa oferecer aos professores a oportunidade de abordar conceitos da física moderna, como a quantização da energia, de maneira mais acessível e aplicada em sala de aula. Isso não apenas enriquecerá a compreensão dos alunos sobre a natureza fundamental da matéria, mas também incentivará um engajamento mais profundo com os princípios da física quântica.
Preprint
Full-text available
We assess a new on-board panoramic polarimeter capability for observing stratospheric aerosol in the water vapor absorption band at 1.378 µm from near-earth orbit. The polarimeter's objective lens irradiation was estimated for solar radiation at 1.378 µm scattered in the stratosphere by aerosol particles and molecules above the tropopause over black and grey Lambertian surfaces. The extinction coefficient, phase function, and degree of linear polarization of radiation scattered by aerosol were calculated using Mie theory for spherical particles that consist of a 75% sulfuric acid solution. Irradiation evaluations were performed for a clear molecular atmosphere and aerosol scenarios with aerosol optical depth values of 0.0001, 0.001, 0.01, 0.1, and 0.5. These estimates covered the scattering angle range of 64.5°–162.5° within the polarimeter's ±30° field of view from the nadir. A sun-synchronous polar orbit at 700 km altitude with 98° inclination was considered as the working orbit for the polarimeter. The polarimeter features an optical channel that separates input radiation into four beams, enabling simultaneous measurement of Stokes parameters across its field of view. This design improves spatiotemporal resolution of a polarimeter compared to filter-based polarimeters like POLDER or 3MI, which should therefore improve the accuracy of aerosol property measurements. The results demonstrate that the polarimeter could serve as a base model for instruments capable of providing precise data on stratospheric aerosol content and properties, enhancing our understanding of their role in climate change.
Article
Full-text available
Human gluttony is having a catastrophic effect on the environment. Since the age of industry and the world wars, modern societies have hygienically depleted most of the earth's resources, thus depleting all the resources that will be essential for future generations. The problem doesn't stop there: greenhouse gas emissions have significantly increased the earth's temperature, causing terrible damage to the climate. The production of green energy with no greenhouse effect seems essential to save the planet. Green hydrogen is a suitable and promising way to generate an energy source that produces H2O molecules instead of CO2. Water electrolysis is a very important technique for producing green H2 using an appropriate electrical current generated by a non-polluting energy source such as wind turbines. This review presents a historical and technical overview of the hydrogen element from its discovery to its current production. Throughout this work, we have tried to deal with the most significant historical periods.
Preprint
We calculate one loop yty_t and λ\lambda dependent corrections to ΓˉZ,Rˉf0\bar{\Gamma}_Z,\bar{R}_f^0 and the partial Z widths due to dimension six operators in the Standard Model Effective Field Theory (SMEFT), including finite terms. We assume CP\rm CP symmetry and a U(3)5\rm U(3)^5 symmetry in the UV matching onto the dimension six operators, dominantly broken by the Standard Model Yukawa matrices. Corrections to these observables are predicted using the input parameters {α^ew,M^Z,G^F,m^t,m^h}\{\hat{\alpha}_{ew}, \hat{M}_Z, \hat{G}_F, \hat{m}_t, \hat{m}_h\} extracted with one loop corrections in the same limit. We show that at one loop the number of SMEFT parameters contributing to the precise LEPI pseudo-observables exceeds the number of measurements. As a result the SMEFT parameters contributing to LEP data are formally unbounded when the size of loop corrections are reached until other data is considered in a global analysis. The size of these loop effects is generically a correction of order %\sim\% to leading effects in the SMEFT, but we find multiple large numerical coefficients in our calculation at this order. We use a MS\rm \overline{MS} scheme, modified for the SMEFT, for renormalization. Some subtleties involving novel evanescent scheme dependence present in this result are explained.
Preprint
Energy levels, wavelengths, lifetimes and hyperfine structure constants for the isotopes of the first and second spectra of radium, Ra I and Ra II have been compiled. Wavelengths and wave numbers are tabulated for 226Ra and for other Ra isotopes. Isotope shifts and hyperfine structure constants of even and odd-A isotopes of neutral radium atom and singly ionized radium are included. Experimental lifetimes of the states for both neutral and ionic Ra are also added, where available. The information is beneficial for present and future experiments aimed at different physics motivations using neutral Ra and singly ionized Ra.
Preprint
Full-text available
The simplest molecules in nature, molecular hydrogen ions in the form of H2+ and HD+, provide an important benchmark system for tests of quantum electrodynamics in complex forms of matter. Here, we report on such a test based on a frequency measurement of a vibrational overtone transition in HD+ by laser spectroscopy. We find that the theoretical and experimental frequencies are equal to within 0.6(1.1) parts per billion, which represents the most stringent test of molecular theory so far. Our measurement not only confirms the validity of high-order quantum electrodynamics in molecules, but also enables the long predicted determination of the proton-to-electron mass ratio from a molecular system, as well as improved constraints on hypothetical fifth forces and compactified higher dimensions at the molecular scale. With the perspective of comparisons between theory and experiment at the 0.01 part-per-billion level, our work demonstrates the potential of molecular hydrogen ions as a probe of fundamental physical constants and laws.
Article
Full-text available
We have applied an optical method to the measurement of the 2S hyperfine interval in atomic hydrogen. The interval has been measured by means of two-photon spectroscopy of the 1S-2S transition on a hydrogen atomic beam shielded from external magnetic fields. The measured value of the 2S hyperfine interval is equal to 177 556 860(15) Hz and represents the most precise measurement of this interval to date. The theoretical evaluation of the specific combination of 1S and 2S hyperfine intervals D_21 is in moderately good agreement with the value for D_21 deduced from our measurement.
Article
Full-text available
An accurate value of the faraday has been determined by the electrolytic dissolution of metallic silver in aqueous solutions of perchloric acid. Standards of electric current, mass, and time as maintained by the National Bureau of Standards were utilized in the determinations. The electric current was measured in terms of the standards of electromotive force and electrical resistance. Silver of high purity, freed from oxygen, was used. The value of the faraday was found to be faraday=96516.5±2.4coulombsgram-equivalent−1(physicalscale),faraday=96490.0±2.4coulombsgram-equivalent−1(chemicalscale).These values were obtained using 107.9028±0.0013 and 107.8731±0.0013, for the atomic weight of silver on the physical and chemical scales, respectively. The electrochemical equivalent of silver was found to be electrochemical equivalent of silver=1.117972±0.000019milligram coulomb−1.This value may be used in an alternate method of defining the ampere in absolute value, namely, that steady current which will dissolve 1.117972 milligrams of silver per second and depends only on the standards of mass and time. The indicated uncertainties are overall limits of error based on 95 percent confidence limits for the mean and allowances for the effects of known sources of possible systematic error.
Article
Full-text available
Oxygen-free high-purity samples were used in a precise determination of the electrochemical equivalent of silver. A comprehensive mass spectrometric analysis for impurities was performed. The authors' value agrees well with prior measurements of the same quantity at the National Bureau of Standards (NBS) by Craig and coworkers. It is found that the electrochemical equivalent of pure silver is 1. 1179648 mg C//N//B//S** minus **1. Attached to this figure is an uncertainty whose random component (standard deviation of the mean of 8 determinations) is 9. 5 multiplied by 10** minus **7 mg C** minus **1 (0. 85 ppm). The root-sum-square of systematic uncertainties of known origin is 1. 07 multiplied by 10** minus **6 mg C** minus **1 (0. 96 ppm).
Article
Full-text available
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.
Article
Full-text available
A technique has been devised which is sufficiently accurate to aid in an electrochemical determination of the Faraday constant using the silver coulometer. The technique is used to recover the silver residue which falls from the anode during operation of the silver coulometer. In contrast to previous efforts at recovery, which involved weighing of the silver residue, the method here described is to convert the silver atoms to ions and then to plate the silver onto a cathode held at constant potential with respect to a reference electrode. The current involved in the electrolysis is integrated electronically. An overall standard deviation of 5 mu g is achieved for samples ranging in size from 400 mu g to 1. 8 mg.
Article
Full-text available
The National Institute of Standards and Technology (NIST) watt balance experiment completed a determination of Planck constant in 1998 with a relative standard uncertainty of 87 × 10-9 (k = 1), concurrently with an upper limit on the drift rate of the SI kilogram mass standard. A number of other fundamental physical constants with uncertainties dominated by this result are also calculated. This paper focuses on the details of the balance apparatus, the measurement and control procedures, and the reference calibrations. The alignment procedures are also described, as is a novel mutual inductance measurement procedure. The analysis summary discusses the data noise sources and esti mates for the Type B uncertainty contributions to the uncertainty budget. Much of this detail, some historical progression, and a few recent findings have not been included in previous papers reporting the results of this experiment.
Article
Full-text available
We report a new determination of the Universal Gas Constant R: (8. 314 471 plus or minus 0. 000 014) J multiplied by (times) mol** minus **1K** minus **1. The uncertainty in the new value is 1. 7 ppm (standard error), a factor of 5 smaller than the uncertainty in the best previous value. The gas constant was determined from measurements of the speed of sound in argon as a function of pressure at the temperature of the triple point of water. The speed of sound was measured with a spherical resonator whose volume was determined by weighing the mercury required to fill it at the temperature of the triple point. The molar mass of the argon was determined by comparing the speed of sound in it to the speed of sound in a standard sample of argon of accurately known chemical and isotopic composition.
Article
Full-text available
High precision measurements of two Zeeman hyperfine transitions in the ground state of muonium in a strong magnetic field have been made at LAMPF using microwave magnetic resonance spectroscopy and a resonance line narrowing technique. These determine the most precise values of the ground state hyperfine structure interval of muonium Δν = 4463302765(53)Hz (12ppb), and of the ratio of magnetic moments μμ/μp = 3.18334513(39) (120ppb), representing a factor of 3 improvement. Values of the mass ratio mμ/me and the fine structure constant α are derived from these results.
Article
Full-text available
We have performed a pure optical frequency measurement of the 2S-12D two-photon transitions in atomic hydrogen and deuterium. From a complete analysis taking into account this result and all other precise measurements (by ourselves and other authors), we deduce optimized values for the Rydberg constant, R∞ = 109737.31568516(84)cm-1 (relative uncertainty of 7.7×10-12) and for the 1S and 2S Lamb shifts L1S = 8172.837(22)MHz and L2S-2P = 1057.8446(29)MHz [respectively, L1S = 8183.966(22)MHz, and L2S-2P = 1059.2337(29)MHz for deuterium]. These are now the most accurate values available.
Article
We calculate vacuum-polarization corrections to the g-factor of a bound electron in the ground state of a hydrogenlike atom. The result is found in a closed analytic form for an arbitrary value of the nuclear charge Z. It is valid for both electronic and muonic atoms. Some useful asymptotics are also presented. The result for the electronic atoms is consistent with published numerical data.
Article
We calculate three-loop radiative-recoil corrections to hyperfine splitting in muonium generated by the diagrams with the first order electron and muon polarization loop insertions in graphs with two exchanged photons. These corrections are enhanced by the large logarithm of the electron-muon mass ratio. The leading logarithm squared contribution was obtained a long time ago. Here we calculate the single-logarithmic and nonlogarithmic contributions. We previously calculated the three-loop radiative-recoil corrections generated by two-loop polarization insertions in the exchanged photons. The current paper therefore concludes calculation of all three-loop radiative-recoil corrections to hyperfine splitting in muonium generated by diagrams with closed fermion loop insertions in the exchanged photons. The new results obtained here improve the theory of hyperfine splitting, and affect the value of the electron-muon mass ratio extracted from experimental data on the muonium hyperfine splitting.
Article
This paper gives the 1998 self-consistent set of values of the basic constants and conversion factors of physics and chemistry recommended by the Committee on Data for Science and Technology (CODATA) for international use. Further, it describes in detail the adjustment of the values of the subset of constants on which the complete 1998 set of recommended values is based. The 1998 set replaces its immediate predecessor recommended by CODATA in 1986. The new adjustment, which takes into account all of the data available through 31 December 1998, is a significant advance over its 1986 counterpart. The standard uncertainties (i.e., estimated standard deviations) of the new recommended values are in most cases about 1/5 to 1/12 and in some cases 1/160 times the standard uncertainties of the corresponding 1986 values. Moreover, in almost all cases the absolute values of the differences between the 1998 values and the corresponding 1986 values are less than twice the standard uncertainties of the 1986 values. The new set of recommended values is available on the World Wide Web at physics.nist.gov/constants.
Article
A cooperative survey between the Soviet Academy of Sciences and the Australian Bureau of Mineral Resources during 1979 successfully measured the acceleration due to gravity using an absolute apparatus at Sydney, Hobart, Alice Springs, Darwin, and Perth in Australia, and at Port Moresby in Papua New Guinea. The measurements have a precision of about 6 micrometre Gal and an accuracy of about 15 micrometre Gal. Gravity ties to earlier stations allow comparisons with GAG-2 gravity meters, OVM pendulums and IGSN71 results. Gravity differences between cities are generally not significant at the 95% confidence level. Gravity differences at individual cities are also not significantly different from zero. The mean difference for all cities could be interpreted as having a component of secular variation of +3.3 +- 1.2 micrometre Gal/yr.-Authors
Article
A more accurate value of the Avogadro constant NA will be a key input parameter to tabulated values of the fundamental constants and a new definition of the unit of mass. The contribution summarizes the activities of the Physikalisch-Technische Bundesanstalt (PTB) in replacing the kilogram artefact by the mass of a certain number of silicon atoms. Defining the unit of mass by such an atomic procedure requires a determination of the Avogadro constant with a relative measuring uncertainty of better than 5 · 10-8. At present, the most limiting factors seem to be the -up to now- unknown density of self-point defects and the precise determination of the isotope composition of the silicon material. In collaboration with the Wacker-Siltronic company in Germany and several other european research institutes, PTB has initiated a scientific program for the improvement of the purity of silicon crystals, especially by a significant reduction of the carbon and oxygen content and by homogeneity investigations of density and lattice parameter with respect to vacancies and Si self-interstitials. As a second independent method for the study of the isotope composition -besides mass spectroscopy- the interaction of the crystal with neutrons producing prompt y-rays was proved to be sensitive enough. This method is now under development at PTB.
Article
The proton gyromagnetic ratio (γ′ p) in water has been obtained by the low-field method using the atomic magnetic resonance in 4He, a multi-current solenoid and an induction technique for the dimensional measurement of the solenoid. The final result is γ′ p (low)=2.675 154 18 × 10 8 s -1 T -1 (0.18 × 10 -6, by K J-90=483 597.9 GHz/V, R K-90=25 812.807 Ω).
Chapter
Publisher Summary This chapter presents the theory of atom interferometry based on optical pulses. The interference of magnetic spin states used in magnetic resonance and later generalized to electronically excited states of atoms is a mature field. Consequently, the wealth of theoretical and experimental techniques that have been developed for over a half century can be exploited for atom interferometry. The fundamental starting point of an atom interferometry based on optical pulses is that light can be used to detect the motion of atoms. Changes in the velocity of individual atoms are registered essentially through changes in the frequency of atomic resonances due to the Doppler effect. This chapter is concerned mainly with the high precision interferometers with long measurement times. It discusses interference of atoms in the ground state and analyzes momentum transfer based on stimulated Raman transitions. The chapter also discusses several applications of these techniques such as in gravitational acceleration, gradiometry, and gyroscopes.
Article
Article
Article
In order to resolve the discrepancies which presently exist between the directly measured values of the absolute or SI ampere and the calculated values obtained indirectly from other fundamental physical constant determinations, one must design an absolute ampere experiment which will produce a result with an uncertainty of one half part per million or less. A new approach recently proposed by Kibble promises such sub-ppm accuracy. Presented here is the design and evaluation of a coil system which will fulfill the requirements of this new approach.
Article
This paper is the second part of the new evaluation of atomic masses Ame2003. From the results of a least-squares calculation described in Part I for all accepted experimental data, we derive here tables and graphs to replace those of 1993. The first table lists atomic masses. It is followed by a table of the influences of data on primary nuclides, a table of separation energies and reaction energies, and finally, a series of graphs of separation and decay energies. The last section in this paper lists all references to the input data used in Part I of this Ame2003 and also to the data entering the Nubase2003 evaluation (first paper in this volume).
Article
The latest evaluation of atomic weight determinations and other cognate data has warranted 16 changes for the standard atomic weights of the elements, A,(E), from those published previously in the 2001 Table of Atomic Weights. The revised standard atomic weights are as follows: A(r)(Al) = 26.9815386(8), A(r)(Bi) = 208.980 40(1), A(r)(Cs) 132.905 4519(2), A(r)(CO) = 58.933 195(5), A(r)(Au) = 196.966 569(4), A(r)(La) 138.905 47(7), A(r)(Mn) = 54.938 045(5), A(r)(Nd) = 144.242(3), A(r)(P) = 30.973 762(2), A(r)(Pt) = 195.084(9), A(r)(Sm) = 150.36(2), A(r)(Sc) = 44.955 912(6), A(r)(Na) = 22.989 769 28(2), A(r)(Ta) = 180.947 88(2), A(r)(Tb) = 158.925 35(2), A(r)(Th) = 232.038 06(2). A recommendation is made that delta C-13 values of all carbon-bearing materials be measured and expressed relative to Vienna Pee Dee Belemnite (VPDB) on a scale normalized by assigning consensus values of -46.6 parts per thousand to L-SVEC lithium carbonate and +1.95 parts per thousand to NBS 19 calcium carbonate.
Article
A study is carried out of the vacuum polarization in a strong Coulomb field. Radiative corrections are neglected. A perturbation calculation is avoided by making use of the explicit solutions of the Dirac equation in a Coulomb field. The Laplace transform of the polarization charge density times r2{r}^{2} is found and used as a basis for further study. It is proved to be an analytic function of the strength of the inducing charge. It is verified that the first-order term in a power series expansion in the strength of the inducing charge just corresponds to the Uehling potential. The third-order term is studied in some detail. The leading term in the polarization potential close to the inducing charge and the space integral of the induced potential divided by r are found to all orders in the strength of the inducing charge. Ambiguities are handled by a method corresponding to regularization.
Article
By using the formalism developed in Part I, we investigated errors in the measurement of the silicon lattice parameter by scanning LLL x-ray interferometry. We show that lattice spacing does not determine uniquely the period of travelling fringes unless crystal motion and form are free from geometrical aberrations. Owing to limited accuracy in manufacturing and operation, crystal movement may change interferometer geometry which, in turn, causes period deviations from the spacing of diffracting planes. We review the special cases of the so-called weak and strong absorptions and, additionally, consider the case of medium absorption, which is of great experimental interest. Finally, we examine how the phase of travelling fringes depends on interferometer design and point out non-linear effects and resonances, so far overlooked, which are related to the oscillatory structure of x-ray diffraction.
Article
Three mechanisms leading to nonlinear tranducer motion in the acoustic interferometer are discussed. Small odd perturbation terms in the transducer restoring force are shown to lead to errors in measured sound velocity and absorption coefficient, but even perturbation terms are found to be entirely innocuous. In cases where the transducer amplitude varies from point to point on its radiating face with a distribution that is itself amplitude dependent, similar errors arise to those found in the odd perturbation case. It is shown how measured corrections may be made where needed to experimental values of sound velocity and absorption. These are based on the observed asymmetries in the admittance plots of the interferometer. Thoughout, the simplifying assumption is made that the fluid loading of the transducer is small compared to its intrinsic impedance as is believed usually to be the case at audio frequencies if nonlinearity is significant. This assumption precludes the application of the corrections to ultrasonic quartz crystal transducers but, if necessary, more general corrections may be derived. The discussion is cast in terms of the theorems on admittance circles in the preceding paper which should be referred to first. This approach enables nonlinearity correction terms to be expressed in a more tractable form than in an impedance analysis.
Article
The wavelength of the Kα1 line from an electron-bombarded natural W anode has been measured in terms of that of an I2-stabilized HeNe laser. This visible laser is a reference point for current Rydberg determinations and for the present-day definition of length. The resulting wavelength value, namely 0.20901 349 Å (0.90 ppm) (energy = 59.319233 keV) appears to resolve historical inconsistencies in the x-ray route to γ wavelengths.
Article
The Newtonian gravitational constant G is determined by means of a high-Q torsion pendulum and the time-of-swing method, in which the period of the pendulum is altered by the presence of two 6.25-kg stainless steel cylinders. The nonlinear fitting method is used to extract the frequencies from the angle-time data of the pendulum. The resulting value of G is (6.6699+/-0.0007)×10-11 m3 kg-1 s-2.
Article
New measurements relating the quantized Hall resistance RH(= h/ie2), International System (SI) Ohm (ΩSI), and the National Physical Laboratory maintained ohm (ΩNPL) have now been completed at NPL in the U.K. with improvements and simplifications in the cryogenic current comparator measurements and 1000-Ω dc resistance measurements. From the measurements over the past four years the relationship between ΩNPL and ΩSI can be described by the equation ΩNPL − ΩSI = −1.049(0.020) − 0.0478(0.0074)[t − 1986.0] μΩ in which t is measured in years. For the previous two years the equivalent relationship between RH and ΩNPL is RH = 25 812.8(1 + 1.452(0.038) × 10 −6 + 0.0694(0.0772) · [t − 1986.0] × 10−6) ΩNPL in which the uncertainties (in parentheses) are one-standard-deviation (1σ) random uncertainties of the least squares fit to the data. Combining the most recent measurements of RH and ΩSI, using a more direct method of measurement RH = 25 812.8106(17) ΩSI in which the relative combined uncertainty is 0.067 × 10−6.
Article
The National Measurement Laboratory (NML) of Australia has maintained an absolute standard of resistance based on a calculable capacitor for more than 20 years. Since its inception, various developments have been incorporated which contribute to a reduction in the overall uncertainty. A reassessment of uncertainties gives a figure now of 6.2 in 108 for the ohm. A systematic error, introduced in 1974, has been identified, and a corrrection of −0.09 ppm should be made to resistances expressed in terms of the NML ohm since that time.
Article
Opitcal interferometry of an Silicon lattice period is an important link between macroscopic and microscopic lengths as well as between low-energy and high-energy spectroscopies. An evident discrepancy between two pre-1982 measurements has limited the effective application of these results. Very recent results, reported here in a preliminary way, appear to further understanding and removing this discrepancy.
Article
An automatic measurement system has been used to determine the values of quantized Hall resistances RH in terms of the National Measurement Laboratory (NML) realization of the International System (SI) ohm. The quantized Hall resistances of two GaAs-AlGaAs heterostructures were measured. The n = 2 step of one heterostructure and the n = 4 step of the other were measured over a seven-month period. A weighted mean of these determinations gave a value for the quantity RH(n = 1) of 0.383 ppm (0.078 ppm one-standard-deviation (1σ) uncertainty) above the nominal 25 812.80 Ω in SI units.
Article
This report summarizes a round table session held last July at the CPEM 2006 to discuss recently proposed redefinitions of some base units of the International System of Units (SI) based on defined values of some fundamental constants. The aim of the session was to inform CPEM delegates of the various proposals and to promote a wide discussion of the issues arising from them. An interdisciplinary panel of six experts from national metrology institutes, the academic community and the industrial metrology community briefly presented their views and their concerns. The presentations were followed by a session in which the panel answered questions and heard comments from the audience.
Article
Measurements of the hyperfine Zeeman transitions (ΔMμ=+/-1, ΔMJ=0) in the ground state of the muonic helium atom (4He++μ-e-) at magnetic fields of 11.5 and 13.6 kG have yielded values for the hfs interval, Δν=4465.004(29) MHz (6.5 ppm), and for the negative-muon magnetic moment, μμ-μp=3.183 28(15) (47 ppm). The theoretical value for Δν, including relativistic, radiative, and recoil contributions, agrees with our measured value but is much less precise because of inadequate knowledge of the Schrödinger wave function.
Article
High resolution laser spectroscopy of the 6sS1/22→6pP1/22 transition ( D1 line) in neutral Cs133 is performed in a highly collimated thermal atomic beam by use of a femtosecond laser frequency comb and narrow-linewidth diode laser. The diode laser is offset locked to a single frequency component of the femtosecond laser frequency comb and probes the optical transitions between selected pairs of ground-state and excited-state hyperfine components. A photodiode detects the excited-state decay fluorescence, and a computerized data acquisition system records the signal. The Doppler shift is eliminated by orienting the laser beam in a direction perpendicular to the atomic beam to within a precision of 5×10-6rad . Optical frequencies for all four pairs of hyperfine components are measured independently, from which the D1 line centroid and excited-state hyperfine splitting are obtained by least-squares minimization with the ground-state splitting as a fixed constraint. We find the D1 line centroid to be fD1=335116048748.1(2.4)kHz , and the 6pP1/22 state hyperfine splitting to be 1 167 723.6(4.8) kHz. These results, in combination with the results of an atom interferometry experiment by Wicht [Phys. Scripta T 102, 82 (2002)], are used to calculate a new value for the fine-structure constant.
Article
A new determination of the magnetic moment of the positive muon in units of the magnetic moment of the proton is presented. The Larmor precession of positive muons in liquid bromine was observed by a stroboscopic technique in a field of 0.75 T and combined with concomitant proton NMR measurements in the same chemical environment. The stroboscopic method allows use of the full muon stopping rate available at the Schweizerisches Institut für Nuklearforschung (SIN) muon channel. Moreover, it permits an intrinsically precise determination of muon Larmor frequency and proton NMR frequency measuring the magnetic field by comparison with the stable reference frequency of the SIN accelerator (ΔΩΩ~10-8). Two different bromine targets were used which allowed an unambiguous determination of the chemical field shift experienced by the muons. One target contained pure and water-free liquid bromine (Br2), where stopped muons form (μ+e-)Br molecules. The other target was slightly contaminated with water; there a chemical reaction chain places the muons into (μ+e-)HO molecules. The diamagnetic shielding of protons in the analogous molecules HBr and H2O in liquid bromine was measured by high-resolution NMR. Values for the isotopic shift of the diamagnetic shielding, when protons are replaced by muons, are available from quantum chemical calculations. After application of the chemical-shift corrections, the results from the two different bromine targets are consistent. The final result is μμμp=3.183 344 1(17)(or +/-0.53 ppm). This value agrees with other recent precision determinations of μμμp. For the muon mass the present result implies mμme=206.768 35(11)(+/-0.53 ppm).