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.

/pdf/codata-recommended-values-of-the-fundamental-physical-4bsdant71c.pdf

CODATA Recommended Values of the Fundamental Physical Constants: 2006

Inertial sensors relying on atom interferometry offer a breakthrough advance in a variety of applications, such as inertial navigation, gravimetry or ground- and space-based tests of fundamental physics These instruments require a quiet environment to reach their performance and using them outside the laboratory remains a challenge Here we report the first operation of an airborne matter-wave accelerometer set up aboard a 0g plane and operating during the standard gravity (1g) and microgravity (0g) phases of the flight At 1g, the sensor can detect inertial effects more than 300 times weaker than the typical acceleration fluctuations of the aircraft We describe the improvement of the interferometer sensitivity in 0g, which reaches 2 x 10-4 ms-2 / \surdHz with our current setup We finally discuss the extension of our method to airborne and spaceborne tests of the Universality of free fall with matter waves

https://hal.archives-ouvertes.fr/hal-00834705/document

Detecting inertial effects with airborne matter-wave interferometry

Measurements of air density determined gravimetrically and by using the CIPM-81/91 formula, an equation of state, have a relative deviation of 6.4 ? 10?5.This difference is consistent with a new determination of the mole fraction of argon xAr carried out in 2002 by the Korea Research Institute of Standards and Science (KRISS) and with recently published results from the LNE. The CIPM equation is based on the molar mass of dry air, which is dependent on the contents of the atmospheric gases, including the concentration of argon. We accept the new argon value as definitive and amend the CIPM-81/91 formula accordingly. The KRISS results also provide a test of certain assumptions concerning the mole fractions of oxygen and carbon dioxide in air. An updated value of the molar gas constant R is available and has been incorporated in the CIPM-2007 equation. In making these changes, we have also calculated the uncertainty of the CIPM-2007 equation itself in conformance with the Guide to the Expression of Uncertainty in Measurement, which was not the case for previous versions of this equation. The 96th CIPM meeting has accepted these changes.

/pdf/revised-formula-for-the-density-of-moist-air-cipm-2007-3wpf3e22n3.pdf

Revised formula for the density of moist air (CIPM-2007)

A detailed analysis of the most relevant sources of phase noise in an atomic interferometer is carried out, both theoretically and experimentally. Even a short interrogation time of 100 ms allows our cold atom gravimeter to reach an excellent short term sensitivity to acceleration of 1.4×10-8g at 1 s. This result relies on the combination of a low phase noise laser system, efficient detection scheme and good shielding from vibrations. In particular, we describe a simple and robust technique of vibration compensation, which is based on correcting the interferometer signal by using the ac acceleration signal measured by a low noise seismometer.

https://hal.archives-ouvertes.fr/hal-00203007/document

Limits to the sensitivity of a low noise compact atomic gravimeter

The measurement of the Planck constant, h, is entering a new phase. The CODATA 2010 recommended value is 6.626 069 57 × 10(-34) J s, but it has been a long road, and the trip is not over yet. Since its discovery as a fundamental physical constant to explain various effects in quantum theory, h has become especially important in defining standards for electrical measurements and soon, for mass determination. Measuring h in the International System of Units (SI) started as experimental attempts merely to prove its existence. Many decades passed while newer experiments measured physical effects that were the influence of h combined with other physical constants: elementary charge, e, and the Avogadro constant, N(A). As experimental techniques improved, the precision of the value of h expanded. When the Josephson and quantum Hall theories led to new electronic devices, and a hundred year old experiment, the absolute ampere, was altered into a watt balance, h not only became vital in definitions for the volt and ohm units, but suddenly it could be measured directly and even more accurately. Finally, as measurement uncertainties now approach a few parts in 10(8) from the watt balance experiments and Avogadro determinations, its importance has been linked to a proposed redefinition of a kilogram unit of mass. The path to higher accuracy in measuring the value of h was not always an example of continuous progress. Since new measurements periodically led to changes in its accepted value and the corresponding SI units, it is helpful to see why there were bumps in the road and where the different branch lines of research joined in the effort. Recalling the bumps along this road will hopefully avoid their repetition in the upcoming SI redefinition debates. This paper begins with a brief history of the methods to measure a combination of fundamental constants, thus indirectly obtaining the Planck constant. The historical path is followed in the section describing how the improved techniques and discoveries in quantum mechanics steadily reduced the uncertainty of h. The central part of this review describes the technical details of the watt balance technique, which is a combination of the mechanical and electronic measurements that now determine h as a direct result, i.e. not requiring measured values of additional fundamental constants. The first technical section describes the basics and some of the common details of many watt balance designs. Next is a review of the ongoing advances at the (currently) seven national metrology institutions where these experiments are pursued. A final summary of the recent h determinations of the last two decades shows how history keeps repeating itself; there is again a question of whether there is a shift in the newest results, albeit at uncertainties that are many orders of magnitude less than the original experiments. The conclusion is that there is room for further development to resolve these differences and find new ideas for a watt balance system with a more universal application. Since the next generation of watt balance experiments are expected to become kilogram realization standards, the historical record suggests that there is yet a need for proof that Planck constant results are finally reproducible at an acceptable uncertainty.

https://iopscience.iop.org/article/10.1088/0034-4885/76/1/016101/pdf

History and progress on accurate measurements of the Planck constant

A new Watt balance project is now in progress at the Bureau National de Metrologie (BNM), Paris, France. In this paper, the general configuration and the main parts of the experimental setup currently in development are presented. The aim is to contribute to the international effort in monitoring the kilogram toward a new definition of the mass unit with a relative accuracy of 10/sup -8/ or better.

The BNM Watt balance project

In 2000, the Bureau National de Metrologie (BNM, France) decided to develop a new watt balance experiment. Among numerous design studies, the choice of the transfer mass is particularly important. Because of the proximity to a source of high magnetic intensity, this mass must have a magnetic susceptibility as weak as possible. Gold–platinum alloy seems to meet this requirement, as well as additional requirements for density and hardness values, making it a possible candidate for mass standard realization. Five different gold–platinum alloys were studied, their volume magnetic susceptibility ranging from −2.8×10−5 to −2.1×10−5 for two of them and from +1.1×10−5 to +8.8×10−5 for the other three.

https://iopscience.iop.org/article/10.1088/0026-1394/40/4/305/pdf

Volume magnetic susceptibility of gold–platinum alloys: possible materials to make mass standards for the watt balance experiment

The mole fraction of argon in ambient dry air has been measured using gas phase chromatography calibrated with gravimetric gas standards prepared at the Laboratoire National de Metrologie et d'Essais. Different air samples, operators and gas standards were used to obtain a value of 0.9330 × 10−2 mol mol−1 ± 0.0032 × 10−2 mol mol−1. This value is significantly different from the conventional value (0.917 × 10−2 mol mol−1) used in the 81/91 formula of the Comite International des Poids et Mesures (CIPM) (Davies 1992 Metrologia 29 67–70) for the determination of air density during comparisons of mass standards.This value confirms the result obtained by the Korea Research Institute of Standards and Science, which found a concentration of 0.9332 × 10−2 mol mol−1 ± 0.0006 × 10−2 mol mol−1 by mass spectrometry in 2004.This new value explains the difference between the CIPM formula method and the artefact method used for the determination of air density.

https://iopscience.iop.org/article/10.1088/0026-1394/44/6/003/pdf

Determination of the argon concentration in ambient dry air for the calculation of air density

Today, the determination of the density of air is the main source of uncertainty (10??g) in a comparison of a platinum?iridium alloy national prototype with a stainless steel reference standard. The method currently recommended by the BIPM is to calculate this density, using a formula developed in 1981 and revised in 1991 by the CIPM, from the measured values of the pressure, temperature, hygrometry and molar fraction of CO2 in air. Recent work has found significant differences between the values given by this formula and those given by a method using artefacts having identical masses and very different volumes (6.4 ? 10?5 with a relative uncertainty of 1.2 ? 10?5). To investigate this difference, the BIPM asked the member laboratories of the Consultatitve Committee for Mass (CCM) to investigate two lines of approach: check the composition of the air, in particular the argon content, which may explain the discrepancies found; this is the object of a study by the chemical metrology unit of LNE (see the article by Sutour et al in this issue), study the behavior of artefacts during the air?vacuum transfer in a comparator that can work both in a controlled atmosphere and in a vacuum, to confirm or not confirm the discrepancies; this latter study is the object of this paper.

https://iopscience.iop.org/article/10.1088/0026-1394/44/6/002/pdf

Determination of the density of air: a comparison of the CIPM thermodynamic formula and the gravimetric method

Le kilogramme est la seule unite de base du Systeme International d'unites (SI) encore definie par un artefact materiel. En regard des evolutions passees du SI et du peu de connaissance de la stabilite du prototype international, la definition en est insatisfaisante. Il serait preferable de lui substituer, a terme, une definition basee soit sur des proprietes atomiques, soit sur des constantes fondamentales. Parmi les diverses recherches en cours dans les laboratoires de metrologie, une des voies les plus prometteuse semble etre celle de la « balance du watt ». Son principe consiste a effectuer la comparaison d'une puissance mecanique a une puissance electromagnetique. Elle resulte d'une mesure effectuee en deux etapes: une phase statique au cours de laquelle la force de Laplace s'exercant sur un conducteur parcouru par un courant et place dans un champ d'induction est comparee au poids d'une masse etalon, et une phase dynamique ou l'on determine la tension induite aux bornes du meme conducteur lorsqu'il est deplace dans le meme champ d'induction a vitesse connue. La determination des grandeurs electriques par comparaisons a l'effet Josephson et a l'effet Hall quantique permet alors de relier l'unite de masse a la constante de Planck. Bien que le principe de l'experience reste simple et direct, l'obtention d'une incertitude relative suffisamment faible (1.10 -8 ) suppose la mise en oeuvre, au meilleur niveau, de dispositifs relevant de divers champs de la physique. L'article fait le point sur les developpements en cours sur le plan national.

André Gosset

Papers

The BNM Watt balance project

Volume magnetic susceptibility of gold–platinum alloys: possible materials to make mass standards for the watt balance experiment

Determination of the argon concentration in ambient dry air for the calculation of air density

Determination of the density of air: a comparison of the CIPM thermodynamic formula and the gravimetric method

La balance du watt : vers une nouvelle définition de l'unité de masse ?