A direct test of E=mc2

Deuteron-to-Proton Mass Ratio from Simultaneous Measurement of the Cyclotron Frequencies of H_{2}^{+} and D^{+}

By simultaneously measuring the cyclotron frequencies of an H_{2}^{+} ion and a deuteron in a coupled magnetron orbit we have made an extended series of measurements of their cyclotron frequency ratio. From the observed changes in H_{2}^{+} mass energy we have followed the decay of three H_{2}^{+} ions to the vibrational ground state. We are able to assign some of our measured ratios to specific rovibrational levels, hence reducing uncertainty due to H_{2}^{+} rotational energy. Assuming the most probable assignment, we obtain a deuteron-to-proton mass ratio, m_{d}/m_{p}=1.999 007 501 272(9). Combined with the atomic mass of the deuteron [S. Rau et al., Nature (London) 585, 43 (2020).NATUAS0028-083610.1038/s41586-020-2628-7] we also obtain a new value for the atomic mass of the proton, m_{p}=1.007 276 466 574(10)  u.

Defocused travelling fringes in a scanning triple-Laue X-ray interferometry setup

This paper investigates both analytically and experimentally the effect of the defocus (the difference between the splitter-to-mirror and analyser-to-mirror distances) on the phase of the travelling fringes in a separate-crystal triple-Laue X-ray interferometer.

The measurement of the silicon lattice parameter by a separate-crystal triple-Laue X-ray interferometer is a key step for the realization of the kilogram by counting atoms. Since the measurement accuracy is approaching nine significant digits, a reliable model of the interferometer operation is required to quantify or exclude systematic errors. This paper investigates both analytically and experimentally the effect of the defocus (the difference between the splitter-to-mirror and analyser-to-mirror distances) on the phase of the interference fringes and the measurement of the lattice parameter.

A different perspective on the forensic science crisis

Recurrent mentions of a forensic science crisis are reported in the literature. Some 15 years ago, the discussion was focused on the backlog problem. Other issues have been regularly debated since then, including the risk of error, need for independence, importance and risk of contextualisation, increasing fragmentation into separate processes and specialisations. Proposed solutions to solve one problem often led to other issues in other parts of the process. This paper attempts to address the apparent crisis using a different perspective, through a comparison with established disciplines, namely material science, medicine and historical science. The comparison with material science shows that, despite the varied organisational and legal models and the interdisciplinary nature of the field, a common element to all forensic science endeavours exists: the trace. A greater focus on the trace might thus help the development of a holistic approach in forensic science. The comparison with medicine demonstrates that, through the overall process, the main risk shifts from the risk to overlook important hypotheses or traces at the beginning of the process (e.g. problems in the detection of traces/symptoms and formulation of hypotheses) to the risk of supporting the wrong hypothesis at the end of the process (e.g. erroneous test of the hypotheses/diagnostic). Further, in medicine, symptoms are rarely evaluated in isolation, while traces are often evaluated separately. By analogy, epidemiology illustrates forensic science's critical role in preventing crime through forensic intelligence, supporting a more extensive and more collaborative application of forensic science in security issues. The comparison with historical science also indicates that a single trace (i.e. the observed effect) is rarely sufficient to reason on its cause. Retrodiction (abduction) is proposed as an alternative reasoning approach to reconstruct events from the past based on signs uncovered in the present. Finally, the impact of science in investigating crimes is presented as an evolving process. A new trace or information can bring an entirely different light on the reconstruction of past events or prevention of future issues. Thus, issues or challenges in the first stages of the process (i.e., crime scene investigation) should be addressed in priority for subsequent stages to function correctly.

Mass-Difference Measurements on Heavy Nuclides with an eV/c^{2} Accuracy in the PENTATRAP Spectrometer

First ever measurements of the ratios of free cyclotron frequencies of heavy, highly charged ions with Z>50 with relative uncertainties close to 10^{-11} are presented. Such accurate measurements have become realistic due to the construction of the novel cryogenic multi-Penning-trap mass spectrometer PENTATRAP. Based on the measured frequency ratios, the mass differences of five pairs of stable xenon isotopes, ranging from ^{126}Xe to ^{134}Xe, have been determined. Moreover, the first direct measurement of an electron binding energy in a heavy highly charged ion, namely of the 37th atomic electron in xenon, with an uncertainty of a few eV is demonstrated. The obtained value agrees with the calculated one using two independent, different implementations of the multiconfiguration Dirac-Hartree-Fock method. PENTATRAP opens the door to future measurements of electron binding energies in highly charged heavy ions for more stringent tests of bound-state quantum electrodynamics in strong electromagnetic fields and for an investigation of the manifestation of light dark matter in isotopic chains of certain chemical elements.

Matter-Energy Equivalence

Over the last two centuries, thermodynamics has contributed significantly to technical and industrial progress. According to phenomenological thermodynamics developed by Rudolf Clausius and Josiah Willard Gibbs, properties such as volume or interface represent energetic qualities of a real body. In the present work, the energy concepts of thermodynamics and special relativity are connected with each other. The plausibility of complete mass-energy equivalence is evaluated within the thermodynamic context. Einstein’s interpretation of the well-known equation E = mc 2 as complete mass-energy equivalence results as a special case for idealized moving point masses – according to the assumptions of the theory of special relativity. It is shown that mass is one energy-equivalent property of matter, but not the only one, because complete mass-energy equivalence contradicts the principle of conservation of energy. Thermodynamics suggests matter-energy equivalence. In accordance with the two main laws of thermodynamics and corresponding with experimental facts, it forms the basis of an in-depth understanding of nature and provides impetus for the research in quantum physics, thermodynamics and astrophysics.

A quartz amplifier for high-sensitivity Fourier-transform ion-cyclotron-resonance measurements with trapped ions

Single-ion sensitivity is obtained in precision Penning-trap experiments devoted to light (anti)particles or ions with low mass-to-charge ratios, by adding an inductance coil to an amplifier connected to the trap, both operated at 4 K. However, single-ion sensitivity has not been reached on heavy singly or doubly charged ions. In this publication, we present a new system to reach this point, based on the use of a quartz crystal as an inductance, together with a newly developed broad-band (BB) amplifier. We detect the reduced-cyclotron frequency of ⁴⁰Ca⁺ ions stored in a 7-tesla open-ring Penning trap. By comparing the detected electric signal obtained with the BB amplifier and the fluorescence signal obtained by collecting the photons emitted by a trapped ion cloud, we show a detection limit below 110 ions. Adding the crystal, the electrical signal increases by a factor of about 30 at room temperature, which combined with the measured equivalent resistance and voltage noise, proves the feasibility of the system to reach single-ion sensitivity at 4 K.

High-Precision Atomic Mass Measurements for Fundamental Constants

Atomic mass measurements are essential for obtaining several of the fundamental constants. The most precise atomic mass measurements, at the 10−10 level of precision or better, employ measurements of cyclotron frequencies of single ions in Penning traps. We discuss the relation of atomic masses to fundamental constants in the context of the revised SI. We then review experimental methods, and the current status of measurements of the masses of the electron, proton, neutron, deuteron, tritium, helium-3, helium-4, oxygen-16, silicon-28, rubidium-87, and cesium-133. We conclude with directions for future work.

Rotational Energy as Mass in H_{3}^{+} and Lower Limits on the Atomic Masses of D and ^{3}He

We have made precise measurements of the cyclotron frequency ratios H_{3}^{+}/HD^{+} and H_{3}^{+}/^{3}He^{+} and observe that different H_{3}^{+} ions result in different cyclotron frequency ratios. We interpret these differences as due to the molecular rotational energy of H_{3}^{+} changing its inertial mass. We also confirm that certain high J, K rotational levels of H_{3}^{+} have mean lifetimes exceeding several weeks. From measurements with the lightest H_{3}^{+} ion we obtain lower limits on the atomic masses of deuterium and helium-3 with respect to the proton.

Highly sensitive superconducting circuits at ∼700 kHz with tunable quality factors for image-current detection of single trapped antiprotons

We developed highly sensitive image-current detection systems based on superconducting toroidal coils and ultra-low noise amplifiers for non-destructive measurements of the axial frequencies (550-800 kHz) of single antiprotons stored in a cryogenic multi-Penning-trap system. The unloaded superconducting tuned circuits show quality factors of up to 500 000, which corresponds to a factor of 10 improvement compared to our previously used solenoidal designs. Connected to ultra-low noise amplifiers and the trap system, signal-to-noise-ratios of 30 dB at quality factors of >20 000 are achieved. In addition, we have developed a superconducting switch which allows continuous tuning of the detector's quality factor and to sensitively tune the particle-detector interaction. This allowed us to improve frequency resolution at constant averaging time, which is crucial for single antiproton spin-transition spectroscopy experiments, as well as improved measurements of the proton-to-antiproton charge-to-mass ratio.

Rotational spectroscopy of isotopologues of silicon monoxide, SiO, and spectroscopic parameters from a combined fit of rotational and rovibrational data

Pure rotational transitions of silicon monoxide, involving the main ((28)Si(16)O) as well as several rare isotopic species, were observed in their ground vibrational states by employing long-path absorption spectroscopy between 86 and 825 GHz (1 ≤ J" ≤ 18). Fourier transform microwave spectroscopy was used to study the J" = 0 transition frequencies in the ground and several vibrationally excited states. The vibrational excitation of the newly studied isotopologues extend to between υ = 9 and 29 for (28)Si(17)O and (30)Si(16)O, respectively. Data were extended for some previously investigated species up to υ = 51 for the main isotopologue. The high spectral resolution allowed us to resolve the hyperfine structure in (28)Si(17)O caused by the nuclear electric quadrupole and magnetic dipole moments of (17)O for the first time, and to resolve the much smaller nuclear spin-rotation splitting for isotopic species containing (29)Si. These data were combined with previous rotational and rovibrational (infrared) data to determine an improved set of spectroscopic parameters of SiO in one global fit which takes the breakdown of the Born-Oppenheimer approximation into account. Highly accurate rotational transition frequencies for this important astronomical molecule can now be predicted well into the terahertz region with this parameter set. In addition, a more complete comparison among physical properties of group 14/16 diatomics is possible.

The role of the international prototype of the kilogram after redefinition of the International System of Units

Since 1889, the international prototype of the kilogram has served to define the unit of mass in what is now known as the International System of Units (SI). This definition, which continues to serve mass metrology well, is an anachronism for twenty-first century physics. Indeed, the kilogram will no doubt be redefined in terms of a physical constant, such as the Planck constant. As a practical matter, linking the quantum world to the macroscopic world of mass metrology has, and remains, challenging although great progress has been made. The international prototype or, more likely, a modern ensemble of reference standards, may yet have a role to play for some time after redefinition, as described in this paper.

The Avogadro constant: determining the number of atoms in a single-crystal ²⁸Si sphere

The Avogadro constant, the number of entities in an amount of substance of one mole, links the atomic and the macroscopic properties of matter. Since the molar Planck constant--the product of the Planck constant and the Avogadro constant--is very well known via the measurement of the Rydberg constant, the Avogadro constant is also closely related to the Planck constant. In addition, its accurate determination is of paramount importance for a new definition of the kilogram in terms of a fundamental constant. Here, we describe a new and unique approach to determine the Avogadro constant from the number of atoms in 1 kg single-crystal spheres that are highly enriched with the (28)Si isotope. This approach has enabled us to apply isotope dilution mass spectroscopy to determine the molar mass of the silicon crystal with unprecedented accuracy. The value obtained, N(A)=6.022 140 82(18)×10(23) mol(-1), is now the most accurate input datum for a new definition of the kilogram.

Direct measurement of the free cyclotron frequency of a single particle in a Penning trap

A measurement scheme for the direct determination of the free cyclotron frequency ν(c) of a single particle stored in a Penning trap is described. The method is based on the dressed states of mode coupling. In this novel measurement scheme both radial modes of the single trapped particle are simultaneously coupled to the axial oscillation mode.

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.

High-accuracy mass spectrometry for fundamental studies

Mass spectrometry for fundamental studies in metrology and atomic, nuclear and particle physics requires extreme sensitivity and efficiency as well as ultimate resolving power and accuracy. An overview will be given on the global status of high-accuracy mass spectrometry for fundamental physics and metrology. Three quite different examples of modern mass spectrometric experiments in physics are presented: (i) the retardation spectrometer KATRIN at the Forschungszentrum Karlsruhe, employing electrostatic filtering in combination with magnetic-adiabatic collimation-the biggest mass spectrometer for determining the smallest mass, i.e. the mass of the electron anti-neutrino, (ii) the Experimental Cooler-Storage Ring at GSI-a mass spectrometer of medium size, relative to other accelerators, for determining medium-heavy masses and (iii) the Penning trap facility, SHIPTRAP, at GSI-the smallest mass spectrometer for determining the heaviest masses, those of super-heavy elements. Finally, a short view into the future will address the GSI project HITRAP at GSI for fundamental studies with highly-charged ions.