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Precise measurement of deuteron mass raises hopes of solving the nuclear-mass puzzle

Contradictory values for the masses of atomic nuclei have cast doubt on the reliability of these widely used quantities. A new mass measurement of the deuteron, the second-simplest atomic nucleus, clarifies the situation.
Jeroen C. J. Koelemeij is in the Department of Physics and Astronomy, Vrije Universiteit Amsterdam, Amsterdam 1081, the Netherlands.
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Precise values for the masses of the nuclei of the simplest atoms, such as hydrogen and helium, are crucial for experiments targeting big unsolved problems in physics. A technique known as Penning-trap mass spectrometry has produced some of the most precise nuclear-mass values obtained so far, but the various results do not seem to be consistent with each other. Writing in Nature, Rau et al.1 report an astonishingly precise measurement of the mass of the deuteron — the nucleus of a hydrogen isotope called deuterium. Remarkably, this result also deviates widely from previous values. The authors therefore carried out a clever auxiliary measurement revealing that their findings back up those parts of the ‘nuclear-mass puzzle’ that initially seemed to be discrepant.

The mass values for atomic nuclei represent a rich source of information for research in physics and chemistry. For example, atoms can bind together to form molecules, and when they do, their bonds resemble vibrating springs rather than stiff rods (Fig. 1a). Molecular vibrations drive biological processes in cells and define properties of solids, but the frequencies of these vibrations ultimately depend on the masses of the atomic nuclei.

Figure 1 | The importance of nuclear masses for physics research. a, The rotating molecule HD+ comprises a deuteron — the nucleus of a hydrogen isotope called deuterium — and a proton. These two particles are bound by an electron, which acts like a vibrating spring. The rotational and vibrational frequencies of HD+ reflect the deuteron and proton masses, as well as fundamental laws of physics7,8. But the interpretation of these laws has been hampered by inconsistent mass measurements. b, A triton (the nucleus of a hydrogen isotope known as tritium) decays into a helion (the nucleus of a helium-3 atom), an electron and an elementary particle called a neutrino. The unknown neutrino mass could, in principle, be determined from the energy of the decay products2. However, doubt could be cast on the outcome of this approach if the helion mass is not known precisely — and measurements of the helion mass have been contradictory6. Rau et al.1 have obtained ultraprecise measurements of the deuteron and HD+ masses that will help to resolve these issues.

Nuclear masses also provide information through Einstein’s famous energy–mass relationship, E = mc2, where c is the speed of light in a vacuum. Some nuclei are radioactive, meaning that they will decay into a lighter atomic nucleus while producing a few lightweight (and highly energetic) elementary particles, such as electrons and the ghostly neutrinos. If the mass difference between the parent and daughter nuclei, ∆m, is precisely known, the total energy and mass available for the elementary particles produced can be predicted by computing ∆mc2. This principle underpins experiments aimed at answering one of today’s biggest questions in physics2: what is the mass of the elusive neutrino?

Clearly, precise nuclear-mass values are useful, but how can they be measured? An atomic nucleus is a charged particle, which implies that its motional path can be deflected by a magnetic field. An extreme version of this principle forms the basis of devices known as Penning traps, as used by Rau and colleagues. A Penning trap consists of an extremely strong magnet, which can capture a single deuteron in perpetual orbital motion, together with a vacuum chamber containing a stack of ring-shaped electrodes, all placed inside the magnetic field generated by the magnet.

The measurement principle makes use of tiny alternating currents, called image currents, that are induced at the inner surfaces of the electrodes by the charge of the moving deuteron. From these image currents, the orbital frequency of the deuteron is determined, which scales inversely with its mass. Next, the deuteron is replaced with a carbon nucleus, the orbital frequency of which is also measured. The key step now involves taking the ratio of the two measured frequencies so that the common magnetic-field dependence cancels out. The deuteron mass, md, is then found in atomic mass units, where one atomic mass unit is defined as one-twelfth the mass of the carbon atom.

In previous such mass measurements, the precision was limited by deviations of the magnetic field from its ideal form, resulting in imperfect magnetic-field cancellation. Rau et al. therefore used an adjustable superconducting electromagnetic coil to measure these deviations and suppress them by a factor of 100. This suppression enabled md to be determined at a remarkable precision of eight parts per trillion (p.p.t.), making it the most precisely known particle mass so far. However, the deuteron mass measured by Rau and colleagues is smaller than the previous state-of-the-art value of md by about 100 p.p.t. — five times its specified precision3 of 20 p.p.t. This situation is reminiscent of similar large discrepancies in observed values of the proton mass4,5, mp, and the mass of the helium-3 nucleus, also known as the helion6, mh.

This unfolding nuclear-mass puzzle seriously hinders experiments at the forefront of physics and chemistry. For example, the simplest molecules in nature are the molecular hydrogen ions H2+ and HD+ (a proton and a deuteron, bound by an electron). Studies of these ions attempt to verify whether quantum electrodynamics — a theory that has been extremely successful at explaining the behaviour of particles and atoms — is also valid for molecules. However, the precision of this theory’s predictions of rotational and vibrational frequencies of molecular hydrogen ions is severely hampered by the observed mass discrepancies7,8. Likewise, the contradictory mass values could impair the outcome of an experiment to determine the neutrino mass by studying the nuclear decay of tritium2, a radioactive isotope of hydrogen (Fig. 1b).

To remedy this situation, Rau and colleagues also measured the mass of the HD+ ion using their Penning-trap set-up. From this measurement, the authors extracted the value of the sum mp + md, and found it to be in excellent agreement with their values of mp and md obtained from single protons4,4 and deuterons, respectively. In addition, all the results were consistent with a recent and precise measurement of the deuteron–proton mass ratio9, md/mp, as well as with experimental results from rotational7 and vibrational8 spectroscopy of HD+. These successful consistency checks suggest that the authors’ precise value of mp and the current value of md, both of which might have seemed discrepant at first, are reliable, after all.

Despite Rau and colleagues’ major advance, one piece of the mass puzzle still stands. Multiple ways of determining the mass difference mp + md − mh have produced inconsistent results depending on whether the newer mass values or older reference values are used. The authors’ work suggests that the mass of the helion, mh, might be the source of this remaining inconsistency, and it provides strong motivation for new mass measurements of this particle. But perhaps the most valuable lesson to be learnt from this work is that, in the art of precision measurement, no result stands completely on its own.

Nature 585, 35-36 (2020)

doi: 10.1038/d41586-020-02474-3

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Competing Financial Interests

The author is co-founder and shareholder of OPNT bv. (Additional information: OPNT bv is a private company (a term abbreviated in Dutch to 'bv'), which emerged from one of the author's research lines at VU University Amsterdam. The company provides time- and frequency-distribution solutions based on laser precision measurements in fiber-optic telecommunications networks. The author owns significant stock in the company.)

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