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The Avogadro constant, $N_{\mathbf {A}}$ , is the physical constant that connects microscopic and macroscopic quantities, and is indispensable especially in the field of chemistry. In addition, the Avogadro constant is closely related to the fundamental physical constants, namely, the electron relative atomic mass, fine-structure constant, Rydberg constant, and Planck constant. For several decades, the Avogadro constant has been determined using the x-ray crystal density (XRCD) method, which is currently one of the practical methods to redefine the kilogram based on fundamental physical constants. In this paper, we present the results of mass measurements of 28Si-enriched spheres, performed at the National Metrology Institute of Japan (NMIJ) in 2014, for the determination of the Avogadro constant using the XRCD method. The results of repeatability of the cleaning effect on the mass of the spheres and the determination of the physical adsorption of water vapor on the spheres are shown. These results establish the reliability of the mass measurement at NMIJ. In addition, we report the results of the mass measurements of 28Si-enriched sphere AVO28-S5c conducted in 2016 to participate in the Pilot Study organized by the Consultative Committee for Mass and Related Quantities aiming at the redefinition of the kilogram based on the fixed numerical value of the Planck constant.

A model of the electron is examined, allowing us to obtain its mass, spin and magnetic moment. The electron is represented as a sphere of classical radius (protoelektron) with zero rest mass, the rotating orbit radius of which is reduced value of the Compton wavelength of the electron. The ratio of the radius of the sphere to the radius of the orbit is equal to the fine structure constant. The sphere has a single charge distributed over its surface. Due mutual repulsion of parts of charge sphere acquires a mass equal to half of the rest mass of an electron, rotating mechanical mass protoelektron on orbit provides its characteristic electron spin 1/2 and kinetic energy, which creates 1/4 of the rest mass. Rotation of charge, similar to the ring current generates a magnetic moment equal to the Bohr magneton and magnetic energy, creating 1/4 of the rest mass of an electron. The total energy of the electron is the sum of its electrostatic, magnetic and kinetic energy. Accordingly, the total mass of the electron is the sum of the masses of electrostatic, magnetic and kinetic origin. The model is applicable to the muon and tau leptons. The correct ratio between the mass, spin and magnetic moment for them observed under the condition in the ratio of the radius of the charged sphere to the radius of the orbit equal to the fine structure constant. The model allows us to understand the physical nature of a number of problems: the Heisenberg uncertainty principle, Lorentz transformations and wave properties of the electron. The cause of the orbital rotation proto-particles is a magnetic field which creates self-acting rotation proto-particles around its own axis.

The ratio $h/m_{\mathrm{u}}$ between the Planck constant and the unified atomic mass constant should have a special status in the framework of the future International System of Units. As the Planck constant $h$ will be fixed, the ratio $h/m_{\mathrm{u}}$ will ensure the realization of the new kilogram (quantum kilogram) at the atomic scale. Furthermore, this ratio becomes a key data for the realization of the kilogram at the macroscopic scale using the XRCD method. The ratio $h/m_{\mathrm{u}}$ can be precisely determined from the measurement of the atomic recoil due to the absorption of a photon momentum. In this conference we will present the lastest developments of our experiment in Paris that aims to measure precisely the recoil of rubidium atom using atom interferometry.

The definition of the kilogram, the unit of mass in the International System of Units (SI), has not changed in more than 125 years. The kilogram is still defined by the mass of a Pt–Ir cylinder conserved at the International Bureau of Weights and Measures. Science and technology have progressed to the point where it is likely the kilogram will be redefined in 2018 in terms of a constant of physics—the Planck constant, which is closely linked to the Avogadro and atomic mass constants. In this article, we illustrate by means of a simple experiment on how analytical chemistry is contributing to this project, how the new definition of the kilogram will be put into practice and what it may mean for chemists. Surprisingly, perhaps, this simple experiment allows us to determine the mass of an aluminum-27 atom, the mass of a carbon-12 atom (and the atomic mass constant), the Avogadro constant, and the Planck constant—all with uncertainty less than 1%—in close analogy to the way the most accurate experiment of thi...

The former University of Washington Penning Trap Mass Spectrometer (UW-PTMS), now located at the Max Planck Institute for Nuclear Physics in Heidelberg, Germany, was used in the decade before the move to determine new values for the deuteron atomic mass, M (2H+) = 2.013 553 212 745(40) u, and the deuterium atomic mass, M (2H) = 2.014 101 778 052(40) u, both of which are now more than an order-of-magnitude more accurate than the previous best 1994-MIT measurements of these quantities. The new value for the deuteron's mass can then be used with the accepted 2010-CODATA proton mass and the most recent 1999-measurement of the 2.2 MeV gamma-ray binding energy of the deuteron to refine the neutron's mass to mn = 1.008 664 916 018(435) u which has about half the uncertainty relative to the value computed using that previous 1994-MIT deuterium measurement. As a result, further improvements of mn must now come from a more accurate determination of the wavelength of this gamma ray.In this same period of time, this spectrometer has also been used to determine new values for the helion atomic mass, M (3He2+) = 3.014 932 246 668(43) u, and the neutral helium-3 atomic mass, M (3He) = 3.016 029 321 675(43) u, which are both about 60 times more accurate than the 2006-SMILETRAP measurements, but disagree with the 4.4-times less-accurate 2015-Florida-State measurements by 0.76 nu. It is expected that these helium-3 results will be used in the future 3H/3He mass ratio (to be determined by the Heidelberg, Germany version of the old UW-PTMS) in order to generate a more accurate value for the tritium atomic mass.

We report on the precise measurement of the atomic mass of a single proton with a purpose-built Penning-trap system. With a precision of 32 parts-per-trillion our result not only improves on the current CODATA literature value by a factor of three, but also disagrees with it at a level of about 3 standard deviations.

A very precise measurement of the magnetic moment of a single electron bound to a carbon nucleus, combined with a state-of-the-art calculation in the framework of bound-state quantum electrodynamics, gives a new value of the atomic mass of the electron that is more precise than the currently accepted one by a factor of 13. The atomic mass of the electron is a key parameter for fundamental physics. A precise determination is a challenge because the mass is so low. Sven Sturm and colleagues report on a new determination of the electron's mass in atomic units. The authors measured the magnetic moment of a single electron bound to a reference ion (a bare nucleus of carbon-12). The results were analysed using state-of-the-art quantum electrodynamics theory to yield a mass value with a precision that exceeds the current literature value by more than an order of magnitude. The quest for the value of the electron’s atomic mass has been the subject of continuing efforts over the past few decades1,2,3,4. Among the seemingly fundamental constants that parameterize the Standard Model of physics5 and which are thus responsible for its predictive power, the electron mass me is prominent, being responsible for the structure and properties of atoms and molecules. It is closely linked to other fundamental constants, such as the Rydberg constant R∞ and the fine-structure constant α (ref. 6). However, the low mass of the electron considerably complicates its precise determination. Here we combine a very precise measurement of the magnetic moment of a single electron bound to a carbon nucleus with a state-of-the-art calculation in the framework of bound-state quantum electrodynamics. The precision of the resulting value for the atomic mass of the electron surpasses the current literature value of the Committee on Data for Science and Technology (CODATA6) by a factor of 13. This result lays the foundation for future fundamental physics experiments7,8 and precision tests of the Standard Model9,10,11.

The fine structure constant α has a particular status in physics. Its precise determination is required to test the quantum electrodynamics (QED) theory. The constant α is also a keystone for the determination of other fundamental physical constants, especially the ones involved in the framework of the future International System of units. This paper presents Paris experiment, where the fine structure constant is determined by measuring the recoil velocity of a rubidium atom when it absorbs a photon. The impact of the recent improvement of QED calculations of the electron moment anomaly and the recent measurement of the cesium atom recoil at Berkeley will be discussed. The opportunity to provide a precise value of the ratio h/mu between the Planck constant and the atomic mass constant will be investigated.

Three new mass dimension quantities have been derived by dimensional analysis, in addition to the famous Planck mass mP ~10-8 kg. These masses have been derived by means of fundamental constants-the speed of light (c), the gravitational constant (G), the Plank constant (h) and the Hubble constant (H). The enormous mass m1 ~1053 kg practically coincides with the Hoyle-Carvalho formula for the mass of the observable universe. The extremely small mass m2 ~10-33 eV has been identified with the minimum quantum of energy, which seems close to the graviton mass. It is noteworthy that the Planck mass appears geometric mean of the masses m1 and m2. The mass m3 ~107 GeV could not be unambiguously identified at present time. Besides, the order of magnitude of the total density of the universe has been estimated by this approach.

A high accuracy, non-relativistic wavefunction is used to study nuclear motion in the ground state of three-particle {a+1a+2a-3} electronic and muonic molecular systems without assuming the Born Oppenheimer approximation. Intracule densities and center of mass particle densities show that as the mass ratio mai/ma3, i=1,2, becomes smaller, the localisation of the like-charged particles (nuclei) a1 and a2 decreases. A new coordinate system is used to calculate center of mass particle densities for systems where a1≠a2. It is shown that the nuclear motion is strongly correlated and depends on the relative masses of the nuclei a1 and a2 rather than just their absolute mass. The heavier particle is always more localised and, the lighter the partner mass, the greater the localisation. It is shown, for systems with ma1

International audience; The ratio h/m u between the Planck constant and the unified atomic mass constant should have a special status in the framework of the future International System of Units. Currently (before the redefinition), this ratio allows to compare determinations of h (watt balance) and determinations of m u (XRCD method). In the future SI, as the Planck constant h will be fixed, the ratio h/m u will ensure the realization of the new kilogram (quantum kilogram) at the atomic scale. Furthermore as the Avogadro constant will be fixed, the carbon molar mass M(12 C), which will no longer be equal to 12 g · mol −1 , will be determined from m u. This ratio is also a key data for the realization of the kilogram at the macroscopic scale using the XRCD method. In this paper we present the state of the art on experiments that provide the most precise value of the ratio h/m u. We focus on the one based on the measurement of the atomic recoil due to the photon momentum.

In consideration the radiological properties of materials and studying the scattering processes in atomic and nuclear physics, the effective atomic and mass numbers is widely employed. These numbers have been calculated for any mixed or composite materials in interaction with high energy photons (Linac in radiation therapy). A pair equation in terms of these numbers is obtained. The first equation has been derived from the conservation of mass energy law and the second by minimizing the binding energy from the semiempirical mass formula (Myers and Swiatecki formula) that gives a relation between atomic and mass numbers for stable nuclei approximately. By these equations one can obtain the effective atomic and mass numbers for any compound or mixed materials uniquely. These numbers are calculated for some materials and compared with the other studies.

This article is divided into two parts. In the first part, the atomic unit (au) system is introduced and the scales of time, space (length), and speed, as well as those of mass and energy, in the atomic world are discussed. In the second part, the utility of atomic units in quantum mechanical and spectroscopic calculations is illustrated with examples. It is shown that the system of atomic units can greatly facilitate calculations and unit conversions. In addition, a number of topics that can be fruitfully treated with the au system, including photoelectric effect, hydrogen atom and different Rydberg constants, positronium atom, atomic mass unit, nuclear binding energy, nuclear reaction energetics, annihilation and mass-energy interconversions, femtosecond and attosecond spectroscopies, quantum-size effects, excitons in semiconductors, and so forth are presented and discussed.

An experiment is described for determining the atomic mass constant by accumulating ions from an ion beam up to a weighable mass. It establishes a link between the international prototype of the kilogram, the realization of the associated SI unit and an atomic mass. The items necessary for such an experiment are a high-current ion source, an ion optical system with high transmission, a suitable ion collector and a vacuum balance. With the most recent measurement, a mass of more than 320 mg of bismuth was accumulated and its atomic mass was determined with a relative standard uncertainty of 9.4 × 10−5. Special emphasis is placed on determining the mass loss of the accumulated ions caused through sputter effects in the ion collector.Although work on this experiment at the PTB has now been stopped, we conclude with a number of suggestions that could lead to much smaller relative uncertainty in a future experiment.

For an atomic or molecular system we consider the evaluation of the Thomas--Fermi--Dirac energy functional using an electron density whose value and bounding surfaces differ by small amounts from those of the exact Thomas--Fermi-- Dirac electron density. The resulting energy is shown necessarily to be higher than the true Thomas--Fermi--Dirac energy. If the displacement of the boundary is not small, the conclusion still holds as long as the boundary of the approximate density lies everywhere outside that of the exact density. (auth)

The comparison of mass and energy variation in a nuclear reaction allows an experimental verification of Einstein’s energy - mass equivalence principle. Mass measurements are performed in a high precision Penning trap and yield values in unified atomic mass units. The energies of emitted gamma radiation are determined via Laue-diffraction with perfect crystals. The according values of the gamma ray wave lengths are expressed in units of the crystal lattice constant. The comparison of masses and wave lengths requires a conversion factor, which represents the unified atomic mass unit within the SI unit system. The latter is given by the molar Planck constant N A h, which itself is known via its relation to the fine structure constant. In the present paper we report on measurements carried out until 2003 with an uncertainty level of 4 ⋅ 10-7. We discuss the main limitations of these experiments and outline the possibilities for future measurements at the 10-8 level. Such measurements would allow a direct representation of the unified atomic mass unit in terms of a Compton frequency and are of utmost importance for a future re-definition of the kilogram mass unit.

A short survey is given on mass units and recommendations on the proper use of the notations mass and weight.Whereas mass is an inertial physical quantity in classical mechanics, weight is a force due to the gravitational field and depending on the geographic situation.

The atomic mass difference of (163)Ho and (163)Dy has been directly measured with the Penning-trap mass spectrometer SHIPTRAP applying the novel phase-imaging ion-cyclotron-resonance technique. Our measurement has solved the long-standing problem of large discrepancies in the Q value of the electron capture in (163)Ho determined by different techniques. Our measured mass difference shifts the current Q value of 2555(16) eV evaluated in the Atomic Mass Evaluation 2012 [G. Audi et al., Chin. Phys. C 36, 1157 (2012)] by more than 7σ to 2833(30(stat))(15(sys)) eV/c(2). With the new mass difference it will be possible, e.g., to reach in the first phase of the ECHo experiment a statistical sensitivity to the neutrino mass below 10 eV, which will reduce its present upper limit by more than an order of magnitude.

The definitions of some units of the Systeme International are likely to be revised as early as 2011 by basing them on fixed values of fundamental constants of nature, provided experimental realizations are demonstrated with sufficiently small uncertainties. As regards the kilogram, experiments aiming at linking it to the Planck constant and the atomic mass constant are under way in several laboratories. The other units likely to be redefined are the ampere, the kelvin and the mole. We discuss the advantages and disadvantages of different alternatives for revised definitions of the kilogram and the mole. From physical considerations, metrological consequences and ease of understanding, a definition of the kilogram based on the mass of a particle, such as an atom or the electron, is favoured. One of the proposed definitions fixes the value of the Planck constant through the Compton frequency of a material, though unphysical, particle. Finally, a redefinition of the mole, the counting unit of the amount-of-substance, is proposed which fixes the Avogadro constant as a dimensionless number.

The paper summarises the activities of several national and international Metrology Institutes in replacing the kilogram artefact, the unit of mass, by the mass of a certain number of atoms, in particular the atomic masses of silicon or bismuth. This task is based on two different experiments: a very accurate determination of the Avogadro constant, N A , measuring the density and lattice parameter of an enriched silicon-28 crystal, and the accumulation of decelerated bismuth-209 ions by using a mass separator. The relative measurement uncertainties reached so far are in the first case 2 parts in 10 7 , and in the latter several part in 10 4 . The bismuth experiment is still in an early state of the work. The ratios between the masses of 28 Si or 209 Bi, respectively, and the present atomic mass standard, the mass of 12 C, can be determined with an accuracy now approaching 10 −10 using high precision Penning traps mass spectrometers.

The unified atomic mass unit (unit symbol: u) is a non-SI unit of mass defined as one twelfth the mass of a single 12C atom in its ground state. This definition was agreed upon by both the International Union of Pure and Applied Physics and the International Union of Pure and Applied Chemistry in early 1960s to resolve a longstanding difference between two scales of atomic mass unit. The term “atomic mass unit” (unit symbol: amu) has been used to a unit of mass defined as one sixteenth the mass of a single atom 16O [m(16O)=16 amu] in physics, or as one sixteenth the isotope-averaged atomic mass (equivalent to the atomic weight) of oxygen [Ar(O)=16 amu] in chemistry.It is a common mistake to use the deprecated term “atomic mass unit” and the deprecated unit symbol “amu” for the unit of mass defined as one twelfth the mass of single atom 12C.

The electron’s mass determined from the electronic g factor of 12C5+ is given by m e = 0.000 548 579 909 2 (4) u and has a three times lower error margin than the 1998 CODATA value. We elucidate the influence of the fine-structure constant and the binding energies of the electrons in 12C to this value.

Background: There are no particle models giving theoretical rest mass energy values for the electron or proton, and their internal energy configurations are unknown. Consequently there is no theoretical basis for the proton/electron rest mass ratio mp/me. Previous articles established both electrons and protons consist of quantum loops of the same 6.8MeV base quantum energy, albeit in different relativistic states.Methods: Prior work is extended by considering internal particle energy cross coupling factors to derive detailed theoretical expressions for the internal energy distributions of electrons and protons. These expressions consist of the base quantum energy modified by terms containing only relativistic factors of the fine structure constant, α ~ 1/137. For mp/me the base quantum energy cancels and the derived mass ratio is given by the particle’s internal quantum loop relativistic states. The derived mass ratio is compared to the empirical value. Newton’s gravitational constant, G, is calculated from the electron internal energy configuration.Results: Derived particle energy configurations give proton mass and proton/electron mass ratio values fully consistent with empirical data. The common base quantum loop energy is obtained to 6ppm. Combining particle mass energy expressions gives mp/me to ten digits and consistent with the 2014 CODATA value via an expression containing only the fine structure constant. A theoretical value for Newton’s gravitational constant is obtained to an uncertainty of 6ppb. The Hierarchy problem is resolved, and the Planck scale of matter is adjusted. Conclusions: The particle energy configurations are validated by providing particle mass energy values and a proton/electron mass ratio consistent with empirical data. Newton’s G is shown not a natural constant, and misunderstanding its nature gave rise to the Hierarchy problem and an erroneous value for the Planck scale of matter, both now resolved.

For the first time a direct determination of the atomic mass difference of 187Re and 187Os has been performed with the Penning-trap mass spectrometer SHIPTRAP applying the novel phase-imaging ion-cyclotron-resonance technique. The obtained value of 2492(30stat)(15sys) eV is in excellent agreement with the Q values determined indirectly with microcalorimetry and thus resolves a long-standing discrepancy with older proportional counter measurements. This is essential for the determination of the neutrino mass from the beta-decay of 187Re as planned in future microcalorimetric measurements. In addition, an accurate mass difference of 187Re and 187Os is also important for the assessment of 187Re for cosmochronology.

The mass of a highly charged ion is the sum of the mass of the nucleus, the mass of the electrons and the electronic binding energies. High accuracy mass measurements on highly charged ions in a sequence of different charge states yield informations on atomic binding energies, i.e., the ionisation potentials. In our contribution we discuss the possibility of determining atomic binding energies of highly charged ions to better than 20 eV via cyclotron frequency measurements in a Penning trap. At this level of accuracy different contributions to the binding energies, like relativistic corrections, Breit corrections and QED corrections, can be measured.

The UW Penning trap mass spectrometer has been used to improve the values for the electron's atomic mass and the proton-electron mass ratio. The cyclotron frequency of small clouds of /spl les/15 electrons is compared with the cyclotron frequency of a single trapped carbon ion (C/sup 6+/) in order to determine their relative mass ratio. In these comparisons, a relatively uniform magnetic field is used in order to assure that each particle sees (on the average) the same field. During systematic studies, the trapping potential was changed by more than a factor of two for the electron. In addition, measurements were taken versus axial and cyclotron drive power as well as the size of the electron cloud. Since the detection mechanism is through the nonharmonic content of the trapping potential, this too was varied. Upon correcting for the lost electrons in carbon, the comparison directly yields M/sub e/=0.000 548 579 911 7(1 7) u. Using the accepted value for the proton's atomic mass, we determine m/sub p//m/sub e/=1836.152 6636(58). These values are limited primarily by the present stability of the magnetic field. >

The Penning trap mass spectrometer at the University of Washington is described along with the relevant detection mechanisms and the systematic shifts associated with the finite energies in the normal modes of the trapped particle. The cyclotron frequency for the particle-of-interest is compared with the corresponding frequency of a single trapped carbon ion (usually C6+). Upon correcting for lost electrons and their binding energies, the relative mass ratio then becomes the atomic mass for the particle-of-interest. As a recent example, the value of the electron's "atomic mass" has been measured to be Me = 0.000 548 579 911 7(17) u and the corresponding proton–electron mass ratio becomes mp/me = 1836.152 664 6 (58).

The possibility of detecting neutrinoless double-$\ensuremath{\beta}$-decay (0$\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$-decay) in experiments that are currently in operation or under development provides the exciting opportunity to determine the Dirac or Majorana nature of the neutrino and its absolute mass scale. An important datum for interpreting 0$\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$-decay experimental results is the $Q$ value of the decay. Using Penning trap mass spectrometry we have measured the atomic mass of ${}^{48}$Ca to be $M{[}^{48}$Ca] $=$ 47.952 522 76(21) u which, combined with the mass of ${}^{48}$Ti evaluated by Audi et al. [Nucl. Phys. A 729, 337 (2003)], provides a new determination of the ${}^{48}$Ca $\ensuremath{\beta}\ensuremath{\beta}$-decay $Q$ value: ${Q}_{\ensuremath{\beta}\ensuremath{\beta}}$ $=$ 4262.96(84) keV.

Conventional neutron numbers are based on the approximations that the mass of the electron is zero and that those of the proton and neutron are each equal to unity. It was shown, by using the exact rest masses, that the neutron numbers are actually one or two less than the conventional ones for atomic masses greater than 108. Presented here are new equations for the atomic mass, mass per nucleon and mass defects for the most abundant stable isotope (or the one with the longest half life) of each of the 118 elements of the Periodic Table.

The mass of an atom incorporates all its constituents and their interactions. The difference between the mass of an atom and the sum of its building blocks (the binding energy) is a manifestation of Einstein's famous relation E = mc(2). The binding energy determines the energy available for nuclear reactions and decays (and thus the creation of elements by stellar nucleosynthesis), and holds the key to the fundamental question of how heavy the elements can be. Superheavy elements have been observed in challenging production experiments, but our present knowledge of the binding energy of these nuclides is based only on the detection of their decay products. The reconstruction from extended decay chains introduces uncertainties that render the interpretation difficult. Here we report direct mass measurements of trans-uranium nuclides. Located at the farthest tip of the actinide species on the proton number-neutron number diagram, these nuclides represent the gateway to the predicted island of stability. In particular, we have determined the mass values of (252-254)No (atomic number 102) with the Penning trap mass spectrometer SHIPTRAP. The uncertainties are of the order of 10 keV/c(2) (representing a relative precision of 0.05 p.p.m.), despite minute production rates of less than one atom per second. Our experiments advance direct mass measurements by ten atomic numbers with no loss in accuracy, and provide reliable anchor points en route to the island of stability.

Penning trap mass measurements of 9 Be, 10 Be ( t 1 / 2 = 1.51 My ), and the one-neutron halo nuclide 11 Be ( t 1 / 2 = 13.8 s ) have been performed using TITAN at TRIUMF. The resulting 11 Be mass excess ( ME = 20 177.60 ( 58 ) keV ) is in agreement with the current Atomic Mass Evaluation (AME03) [G. Audi, et al., Nucl. Phys. A 729 (2003) 337] value, but is over an order of magnitude more precise. The precision of the mass values of 9,10 Be have been improved by about a factor of four and reveal a ≈ 2 σ deviation from the AME mass values. Results of new atomic physics calculations are presented for the isotope shift of 11 Be relative to 9 Be, and it is shown that the new mass values essentially remove atomic mass uncertainties as a contributing factor in determining the relative nuclear charge radius from the isotope shift. The new mass values of 10,11 Be also allow for a more precise determination of the single-neutron binding energy of the halo neutron in 11 Be.

The accurate determination of atomic masses and the high-precision measurement of the bound-electron g factor are prerequisites for the determination of the electron mass, which is one of the fundamental constants of nature. In the 2002 CODATA adjustment [P. J. Mohr and B. N. Taylor, Rev. Mod. Phys. 77, 1 (2005)], the values of the electron mass and the electron-proton mass ratio are mainly based on g factor measurements in combination with atomic mass measurements. In this paper, we briefly discuss the prospects for obtaining other fundamental information from bound-electron g factor measurements, we present some details of a recent investigation of two-loop binding corrections to the g factor, and we also investigate the radiative corrections in the limit of highly excited Rydberg S states with a long lifetime, where the g factor might be explored using a double resonance experiment., Comment: 13 pages, LaTeX; dedicated to Prof. H.-J. Kluge on the occasion of his 65th birthday, to appear in Int. J. Mass. Spectrometry

A new independent value for the electron's mass in units of the atomic mass unit is presented, ${m}_{e}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.0005485799092(4)\mathrm{u}$. The value is obtained from our recent measurement of the $g$ factor of the electron in ${}^{12}{\mathrm{C}}^{5+}$ in combination with the most recent quantum electrodynamical (QED) predictions. In the QED corrections, terms of order ${\ensuremath{\alpha}}^{2}$ were included by a perturbation expansion in $Z\ensuremath{\alpha}$. Our total precision is three times better than that of the accepted value for the electron's mass.

This paper gives the 2010 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. The 2010 adjustment takes into account the data considered in the 2006 adjustment as well as the data that became available from 1 January 2007, after the closing date of that adjustment, until 31 December 2010, the closing date of the new adjustment. 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 2010 set replaces the previously recommended 2006 CODATA set and may also be found on the World Wide Web at physics.nist.gov/constants., Comment: 94 pages, 8 figures, 48 tables

There are about a dozen quantities in atomic and nuclear physics that are fundamental to our current understanding of science. One is the speed of light and another is the fine-structure constant, which governs the spectra of atoms. A third is the mass of the lightest atomic particle – the electron.

This chapter discusses the relative atomic masses, molecular masses, and the mole concept. The relative atomic mass of an element is defined as the weight in grams of the number of atoms of the element contained in 12.00 g of carbon-12. To calculate the relative atomic mass of chlorine, the average mass of one atom of chlorine is found by considering 100 atoms of chlorine. 75.53 of these atoms each have a mass of 35 atomic mass units (AMU), and 24.47 atoms each have a mass of 37 AMU. The word mole has been adopted to represent the Avagadro number of atoms of an element, that is, the relative atomic mass of an element. Thus, one mole of sodium weighs 23.0 g or one tenth of a mole of sodium weighs 2.3 g.

The system of a single-mode field interacting with a -type three-level atom in a harmonic trap is investigated. The linear entropy of the field, the atomic internal states and the atomic mass center motion are explored. It is shown that the atomic mass center motion not only can affect the linear entropy of the field and the atomic internal states, but also effectively changes their relationship.

On the basis of the improved averaged atomic model, the distribution of the free electrons is dealt with by the partial-wave method to improve the precision of determination of the energy level, electron populations and atomic inner energy. The obtained results of atomic energy for ground state are in rather good agreement with that of Hartree-Fock method. As samples, the total electron energies of W, Au, Rn and Am are calculated respectively.

The authors describe techniques which allow the study in undergraduate laboratories of the spectrum of atomic hydrogen. The Rydberg constant, the electron-proton mass ratio, and the fine-structure constant are evaluated from the measurements. The key to the series of experiments is a discharge tube in which atomic lines dominate over the molecular lines.

The ground-state energy of an atomic nucleus with asymmetryβ is considered to be equivalent to the energy of a perfect sphere made up of the infinite nuclear matter of the same asymmetry plus a residual energyη called the local energy,η represents the energy due to shell, deformation, diffuseness and exchange Coulomb effect etc. Using this picture and the generalized Hugenholtz- Van Hove theorem of many-body theory a new mass formula has been developed. Based on this, a mass table containing the mass excesses of 3481 nuclei in the range 18 ⩽A ⩽ 267 has been made. This mass formula is compared with other mass models.

A comparison is made of theoretical values of various authors for the fine structure constant, for the proton-electron and muon-electron mass ratios, and for the gravitational constant. It is shown that a lattice ether theory developed by Aspden gives the best overall agreement with experiment.

We use geochronological and cosmological data to obtain upper limits on the rates of change of the following “constants”: proton mass, neutron mass, fine structure constant, weak interaction constant, strong interaction constant, and “range” of nuclear forces. If the rates of change of all these constants are correlated, then the available data permit changes much in excess of the limits that have been obtained by Dyson and others from the assumption that only one or two constants change. As an application of our results, we note that the disagreement between atomic time and ephemeris time reported by Van Flandern can be explained by a change in an atomic constant (magnetic moment of proton or, equivalently, pion mass) rather than a change in the gravitational constant.

If the problem of the hydrogen-like atom is done with the assumption that the nucleus is at rest, the resulting energy levels are proportional to the Rydberg constant for infinite mass. It is traditional to obtain the Rydberg constant for finite mass of the nucleus by a simple substitution of the reduced mass of the system for the electron mass in the expression for the Rydberg constant for infinite nuclear mass. Realization that such a substitution (which is drawn from classical mechanics) does not give a correct transformation to the center-of-mass coordinate system in the case of charged particles, leads one to significant corrections for the Rydberg constants of finite nuclear masses. The corrections are drawn from classical, non-relativistic physics. Also, an interesting conjecture about the energy levels of hydrogen-like atoms, under the assumptions of Bohr theory and classical physics, is obtained.

A brief description is given of the mass spectroscopic methods in current use for the determination of atomic masses. The agreement between atomic masses so-derived and those obtained by studying the energy balance in nuclear reactions is also lightly touched upon, with particular reference to the mass of C/sup 12/. Finally, a table is given of the atomic mass differences which have been obtained table supepplements (and occasionally amends) a similar table which appeared in the October, 1954, issue of this Journal. (auth)

The potential of the uranium atom and ions are calculated on the statistical model, allowing for exchange interaction and electron correlation. It is demonstrated that due allowance for electron correlation is essential in calculating the integral atomic characteristics. The ionization energies I1, I2, I3 are calculated from the curves obtained for the atomic and ionic potentials. Theoretical results are compared with experiment.

The Paper contains a mathematical deduction of a simple formula for the combined mass of two electrical charges when in proximity to each other. This mass is not the sum of their individual masses when far apart, if it be supposed that all mass of positive electricity, like that of electrons, is of electromagnetic origin. Applications are made of the formula to questions of atomic constitution and of radioactivity. A discussion is given of the evidence leading to the conclusion that the nuclei or cores of positive electricity in atoms are complex structures of electrons and even smaller positive nuclei. On this basis, emission of an α-particle by an atom does not decrease its atomic mass by 4, a correction being necessary for the "mutual mass" of the α-particle and the rest of the core. Estimates of the magnitude of this correction, in the case of radium and thorium passing into lead by the emission of particles, are given. From the value given by Soddy for the atomic weight of thorite lead we can deduce the average distance apart of the components in a radium nucleus. It is of the same order as the radius of an electron. Suggestions of further interesting applications of the precise formula for mutual mass are also contained in the Paper.

For pt.I see ibid., vol.7, no.12, 1506 (1974). The leading term in an asymptotic expansion of the resonant ionization probability in the interaction of slow hydrogen-like atoms with solid state surfaces is obtained in closed form. A procedure for calculation of the subsequent terms is also outlined.

An experimental search was made for a frequency shift produced by conducting-plate confinement of the cesium beam in an atomic clock. The ratio of experimental to theoretical plate separation dependence is -0.023 ± 0.036, consistent with no shift.