Ernest G. Kessler

Determination of the Avogadro constant by counting the atoms in a 28Si crystal.

The Avogadro constant links the atomic and the macroscopic properties of matter. Since the molar Planck constant is well known via the measurement of the Rydberg constant, it is also closely related to the Planck constant. In addition, its accurate determination is of paramount importance for a definition of the kilogram in terms of a fundamental constant. We describe a new approach for its determination by counting the atoms in 1 kg single-crystal spheres, which are highly enriched with the 28Si isotope. It enabled isotope dilution mass spectroscopy to determine the molar mass of the silicon crystal with unprecedented accuracy. The value obtained, NA = 6.022,140,78(18) × 10(23) mol(-1), is the most accurate input datum for a new definition of the kilogram.

Michelson interferometry with 10 pm accuracy

We demonstrate a new heterodyne Michelson interferometer design for displacement measurements capable of fringe interpolation accuracy of one part in 36 000. Key to this level of accuracy are the use of two acousto-optic modulators for heterodyne frequency generation and digital signal processing demodulation electronics. We make a direct comparison of our interferometer to a commercial interferometer based on a Zeeman-stabilized laser, and show that the residual periodic errors in ours are two orders of magnitude lower than those in the commercial unit. We discuss electronically induced optical cross talk and optical feedback as sources of periodic error. Our new interferometer is simple, robust, and readily implemented.

Counting the atoms in a 28Si crystal for a new kilogram definition

This paper concerns an international research project aimed at determining the Avogadro constant by counting the atoms in an isotopically enriched silicon crystal. The counting procedure was based on the measurement of the molar volume and the volume of an atom in two 1 kg crystal spheres. The novelty was the use of isotope dilution mass spectrometry as a new and very accurate method for the determination of the molar mass of enriched silicon. Because of an unexpected metallic contamination of the sphere surfaces, the relative measurement uncertainty, 3 × 10−8 NA, is larger by a factor 1.5 than that targeted. The measured value of the Avogadro constant, NA = 6.022 140 82(18) × 1023 mol−1, is the most accurate input datum for the kilogram redefinition and differs by 16 × 10−8 NA from the CODATA 2006 adjusted value. This value is midway between the NIST and NPL watt-balance values.

Remeasurement of γ-Ray reference lines

Abstract Over the last several years, we have established a new and significantly improved measurement chain connecting γ-ray lines with visible reference standards. This chain has three links: First, a Si lattice repeat distance is determined by combined X-ray and optical interferometry. Second, this crystal calibration is transferred to other specimens suited to γ-ray diffraction. Finally, these crystals are used in a transmission double-crystal instrument to determine γ-ray wavelengths via the Bragg-Laue equation. To obtain the required precision and accuracy, the spectrometer is fitted with angle interferometers of considerable sensitivity (∼0.05 marcsec) and these are calibrated by summing to closure the external interfacial angles of a 72-sided optical polygon. This report focuses on the apparatus and methodology of the third step but includes descriptions of the first two also. Results are presented from tests of closure using cascade-crossover relations and inter-order comparisons. Energies for γ-transitions in 198Au, 192Ir, 170Tm, 169Yb, together with the X-ray transition W Kα1 are included. γ-Ray wavelength accuracies are estimated to be near 0.5 ppm.

Present Status of the a Vogadro Constant Determination from Silicon Crystals with Natural Isotopic Composition

The determination of the Avogadro constant from two selected silicon crystals is described. The density, molar mass, and lattice spacing of the two crystals were measured at NMU, PTB, IRMM, IMGC, and NIST. When all the data are combined, it leads to the Avogadro constant of 6.022 1353 (21) times 1023 mol-1 with a relative combined standard uncertainty of 3.4 times 10-7

World Year of Physics: A direct test of E=mc2

One of the most striking predictions of Einsteins special theory of relativity is also perhaps the best known formula in all of science: E=mc2. If this equation were found to be even slightly incorrect, the impact would be enormous — given the degree to which special relativity is woven into the theoretical fabric of modern physics and into everyday applications such as global positioning systems. Here we test this mass–energy relationship directly by combining very accurate measurements of atomic-mass difference, Δm, and of γ-ray wavelengths to determine E, the nuclear binding energy, for isotopes of silicon and sulphur. Einsteins relationship is separately confirmed in two tests, which yield a combined result of 1−Δmc2/E=(−1.4±4.4)×10−7, indicating that it holds to a level of at least 0.00004%. To our knowledge, this is the most precise direct test of the famous equation yet described.

A curved crystal spectrometer for energy calibration and spectral characterization of mammographic x‐ray sources

Clinical efficacy of diagnostic radiology for mammographic examinations is critically dependent on source characteristics, detection efficiency, image resolution and applied high voltage. In this report we focus on means for evaluation of source-dependent issues including noninvasive determination of the applied high voltage, and characterization of intrinsic spectral distributions which in turn reflect the effects of added filtration and target and window contamination. It is shown that a particular form of x-ray curved crystal spectrometry with electronic imaging can serve to determine all relevant parameters within the confines of a standard clinical exposure.

The deuteron binding energy and the neutron mass

Abstract A new value for the deuteron binding energy of S(d)=2.38817007(42)×10−3 u is reported based on an absolute wavelength determination of the 2.2 MeV n–p capture gamma-ray using a crystal diffraction spectrometer. A new more precise value for the neutron mass mn=1.00866491637(82) u is obtained by summing this binding energy and the 2 H− 1 H mass difference.

A high energy resolution X-ray spectroscopy synchrotron radiation beamline for the energy range 800–5000 eV

A beamline for X-ray spectroscopy of atomic and molecular gases and condensed matter has been designed and installed at the National Synchrotron Light Source. The beamline is UHV compatible to allow windowless operation for improved flux at low photon energies. A double axis crystal monochromator is employed with a collimating premirror and a focusing postmirror. Paris of beryl, quartz or silicon crystals define an energy band width of <0.4 eV at an arbitrary energy above 0.8 keV. The premirror acts as a tuneable low-pass filter to minimize heat loading on the first monochromator crystal. At the present operating parameters of NSLS, a flux of 109–1013 photons/s of highly monochromatic X-rays can be focused onto a 1 mm diameter spot. Initial experimental results are presented.

The GAMS4 flat crystal facility

Abstract A high-resolution flat-crystal gamma-ray facility, GAMS4, has been constructed at the high-flux reactor at the Institut Laue-Langevin (ILL), Grenoble, France. The facility is located at the exit of a through-tube equipped to place sources in a neutron flux of ≈5.5×10 14 n cm −2 s −1 . Considerable care has been exercised to provide a precision gamma-ray metrology station including vibration isolation, temperature control, environmental monitoring, background suppression, and remote and automatic spectrometer control. The diffraction angles are controlled and measured interferometrically and absolute angle calibration is established with a relative uncertainty of ≈3×10 −7 . The crystals are nearly perfect specimens of Si and Ge whose lattice spacings are measured in meters and have a relative uncertainty of ≈5×10 −8 . The resolution obtained with this facility closely approaches dynamical diffraction predictions. Examples of measurements performed using this facility include (1) absolute wavelengths standards and neutron binding energies, (2) lifetimes of nuclear exited states, (3) determination of interatomic potentials, and (4) crystal structure factors. GAMS4 is a scheduled ILL instrument with beamtime being awarded through the ILL proposal process.