Light nuclei, such as carbon and oxygen, typically have about the same number of protons and neutrons. But in heavier elements, Coulomb repulsion between protons starts to overcome the strong-force attraction between protons and neutrons, so extra neutrons are needed to form a stable nucleus.

Tin-100 is one of the heaviest nuclides with an equal number of protons and neutrons, and with 50 of each, it’s doubly magic—both its proton and neutron shells are full. Those features make ¹⁰⁰Sn particularly interesting for studying proton–neutron pairing interactions and, through its decay products, unpaired-nucleon states. Measurements of its properties would improve ab initio nuclear structure calculations, which have only recently begun to tackle such large nuclei (see the article by Filomena Nunes, Physics Today, May 2021, page 34).

But ¹⁰⁰Sn exists at the edge of proton stability. It’s produced in such small quantities that even one of its most basic properties, its mass, can only be measured indirectly. Instead, its mass has been derived from measurements of its β-decay energy and the mass of its daughter, indium-100. To help nail down the ¹⁰⁰Sn mass, CERN researcher Maxime Mougeot and colleagues used the ISOLTRAP spectrometer at CERN’s Isotope Separator On Line (ISOLDE) facility, shown above, to measure the mass of ¹⁰⁰In. Facing a low production rate and significant contamination, the researchers had to use the most advanced mass-spectrometry and separation techniques available—including a multireflection time-of-flight device, the fastest and most sensitive type of mass spectrometer for nuclear measurements. The experiments reduced uncertainty in the ¹⁰⁰In mass by a factor of 90 compared with previous observations.

With their ¹⁰⁰In mass in hand, the researchers faced a question- What value for the β-decay energy should they use to calculate the ¹⁰⁰Sn mass? Two literature values exist. The first, published in 2012 using data from the GSI Helmholtz Centre for Heavy Ion Research in Darmsdadt, Germany, was based on 250 ¹⁰⁰Sn atoms. The second, published in 2019, included 2500 atoms generated at the RIKEN Nishina Center for Accelerator-Based Science in Wako, Japan. Nearly two standard deviations separate the measurements, and that difference is reflected in the disparate ¹⁰⁰Sn masses that Mougeot and colleagues calculated using the two β-decay energies.

To glean more insight, the researchers calculated the two-neutron empirical shell gap Δ_2n, a quantity used to describe nuclear structures, and compared it with the values for other nuclides that have 50 neutrons but fewer protons (Z). The results with the GSI (pink) and RIKEN (blue) energies are shown in the figure; vertical lines indicate one standard deviation. The calculations based on the GSI value generally follow the trend set by the lighter nuclides, whereas the ones based on the RIKEN value exhibit a sharp jump at 50 protons, which is difficult to justify with nuclear-structure models.

Similar divergences from established trends in other quantities appeared in calculations using the RIKEN β-decay energy. Mougeot and colleagues therefore concluded that their new measurements favor the GSI value. Still, without a higher-precision β-decay energy or a precise direct measurement, the question of ¹⁰⁰Sn’s mass remains unresolved. (M. Mougeot et al., Nat. Phys. 17, 1099, 2021.)