A cunning addition for the determination of nuclear masses provides world-leading sensitivity for accurate measurements. This is already opening up new physics and applications.

It may sound simple to weigh an atomic nucleus, but there is more to it than you might think, especially when the nucleus is very unstable. Finding out the properties of such fleeting nuclei, perhaps surviving for only a few milliseconds, can solve long-standing science problems. Short-lived nuclei are key to our understanding not only of how neutrons and protons bind together in nuclei, but also of the way that explosive events in the cosmos tell us about the life-cycle of stars.

At first sight, a measured mass gives us just a number with units such as kg. Nuclear physicists like to use keV or MeV, where 1 eV corresponds to 1.6 × 10^-19 J, or, equivalently, 1.8 × 10^-36 kg, after factoring in Einstein's relation E = mc². The trick is to work out differences. Take the case of odd-odd ¹⁰²Rh, with 45 protons and 47 neutrons. It weighs in at about 95,000 MeV. But look at its radioactive decay products ¹⁰²Ru (44 protons, 48 neutrons) and ¹⁰²Pd (46 protons, 46 neutrons): these two even-even isobars average out at about 2 MeV lighter - a difference of only 2 parts in 100,000 - but it's a systematic effect, applying to other comparable cases. The origin of the 2 MeV difference is due to pairing. In ¹⁰²Rh there are two unpaired nucleons (neutrons and protons) while in ¹⁰²Ru and ¹⁰²Pd, all nucleons are nicely paired up, and this gives extra binding. The point is that, by looking at mass differences, subtle effects such as pairing can be found that depend on the internal structure of the nuclei, and that makes it worthwhile to measure nuclear masses very carefully - and very accurately.

A powerful technique for measuring the masses of unstable (radioactive) nuclei is first to produce them with a high-energy beam of heavy ions, as has been done at the Institute of Modern Physics in Lanzhou, China. An international collaboration of physicists, led by Meng Wang from IMP Lanzhou, used a beam of ⁵⁸Ni ions at an energy of 25,000 MeV, which struck a target of ⁹Be. The beam nuclei fragmented, and all sorts of radioactive products flew forwards from the reaction. The beam energy was high enough so that the produced nuclei were “bare”, with all their atomic electrons removed. After electromagnetic filtering, nuclei of interest were stored in a large electromagnetic ring with a circumference of 129 m. Their masses could be obtained by passing them through a carbon foil that serves as a time-of-flight (TOF) detector, and measuring their circulation frequencies.

A vital requirement for accurate masses is to choose ion energies that satisfy the isochronous condition of the storage ring, so that slightly faster ions of a given mass-to-charge ratio (A/Z for fully ionised nuclei) which go round in larger orbits, have equal orbital periods, with precise compensation for their greater velocity. But this compensation only works over a very small A/Z range, as shown by the black squares in Fig. 1 [1]. The cunning addition in the new work was to double-up on the number of TOF detectors, with an 18 m straight section between them. By measuring the ion flight time between the two, a velocity correction could be made. In this way, the blue circles of Fig. 1 were obtained, showing far better precision, and opening up a new range of measurements [1-3].

Fig. 1Full-screen View

Standard deviations of the TOF data (black squares, left scale) shown as a function of mass-to-charge ratio. Also shown are the corrected data (blue circles). The right scale gives the absolute accuracies of the mass-to-charge ratios. The figure is from Ref. [1].

First up [1] was fundamental physics: testing the unitarity of the Cabibbo-Kobayashi-Maskawa quark mixing matrix [4], and hence testing the standard model of particle physics. The nuclear physics input comes partly from precision mass measurements, and the new results were for the masses of ⁴⁶Cr, ⁵⁰Fe and ⁵⁴Ni, with half-lives of 232 ms, 152 ms and 114 ms, respectively. Such short half-lives don’t give a lot of time to make mass measurements, but in fact the technique only needs about 0.1 ms, giving unprecedented access to precision masses of highly unstable nuclei. In 0.1 ms, ions in the storage ring circulate about 150 times, passing through the TOF detectors every orbit and providing time stamps from which the masses are derived. The mass-to-charge ratio of a single ion can be determined with a precision of about 5 keV (see Fig. 1), where the charge of fully ionised nickel, for example, is q = 28, so the mass precision would be about 140 keV for a single ion of nickel. The new results have extended the possibilities to test the unitarity of the CKM matrix with heavier nuclei than was previously possible.

Next the Lanzhou team used a high-energy beam of ⁷⁸Kr ions to produce a different range of fragment nuclei. The radioactive isotopes that they studied included ⁶⁵As and ⁶⁶Se, for which they measured new mass values. These two isotopes had been predicted to provide the most sensitive tests of astrophysical model calculations. They analysed their data to extract mass differences in a way that revealed proton binding energies [2], enabling them to work out when the number of protons (for a given number of neutrons) becomes too great for the last proton to stay bound to the nucleus. This matters for the most common type of X-ray bursts (type-I) which are some of the brightest astrophysical events that can be observed by space-based telescopes. (The X-rays get absorbed by the Earth's atmosphere, preventing them being seen by ground-based telescopes.) The bursts are understood to occur when material, mainly hydrogen and helium, falls onto the surface of a neutron star from an orbiting companion. Every so often the material ignites in a nuclear explosion, creating a burst of X-rays, powered by the capture of hydrogen nuclei (protons) and creating a whole range of highly unstable proton-rich nuclei. One of the team's definitive findings [2] is that ⁶⁵As is proton unstable: when ⁶⁴Ge tries to capture a proton, it will not stick. Nevertheless, it survives long enough, 190 ms on average, for its mass to be measured. This leads to ⁶⁴Ge being called a waiting-point nucleus, because the explosive sequence of proton captures ends there and the X-ray burst stalls. With the new data on nuclear masses, the model calculations are better able to make sense of the X-ray observations.

Further new results have now been published [3] based on a different analysis of the data from the fragmented ⁷⁸Kr beam, this time focussing on basic nuclear physics and the role of three-body forces. Such forces originate from the substructure of nucleons, composed of quarks and gluons, but three-body forces are poorly characterised in heavy nuclei with many nucleons. Taking double differences of nuclear binding energies, it has been possible to extract residual proton-neutron interactions for heavy N = Z nuclei from ⁵⁶Ni up to ⁷²Kr. Surprisingly, the gently decreasing residual interactions, found as a function of increasing proton number for even-even nuclei, change to steeply increasing residual interactions for odd-odd nuclei, confounding the usual model calculations. However, by adding three-nucleon forces, the experimental data can be reproduced, albeit qualitatively. While there is room for improvements in the theory, the new analysis [3] marks a milestone in appreciating the role of three-body forces in heavy nuclei.

These three sets of results, based on accurate mass measurements of short-lived nuclei, show beautifully the power of the technique, which has been augmented by including velocity measurement along with the circulation time of ions in a storage ring. Many ions circulate in the ring at any one time, some of which already have accurately known masses. It is then possible to measure the orbits a single “unknown” ion and to determine its mass in as little as 0.1 ms, to an accuracy in mass-to-charge ratio down to 5 keV. This innovation opens up the capability for many further discoveries in fundamental physics and applications.

The double TOF technique will be adopted at other storage rings being planned or under construction, including at the HIAF facility in China [5], and the FAIR facility in Germany [6]. Indeed, the concept was discussed by the ILIMA collaboration [7] at FAIR, foreseeing the possibilities at the Lanzhou storage ring. Its implementation is a most welcome development.