Although the helium nucleus has just four nucleons—two neutrons and two protons—theoretical models fail to replicate some of its properties. Or so Sonia Bacca, now at Johannes Gutenberg University Mainz in Germany, and her colleagues discovered in their 2013 calculations. Helium nuclei, also known as alpha particles, are a popular testing ground for nuclear models because they are relatively simple while still capturing essential nuclear phenomena, and theory replicates their ground state pretty well.
Early nuclear models were phenomenological, and their uncertainties were hard to assess. But that changed with the introduction of chiral effective field theory (ChEFT) in the early 1990s. ChEFT correctly predicts the helium nucleus’s ground-state properties to within 1%. But the 2013 ChEFT calculations of a quantity related to how the nucleons are arranged in the alpha particle’s first excited state didn’t match the values inferred from electron-scattering experiments. Those studies were primarily from the 1970s, however, and the uncertainties were large. In the intervening decades, the techniques and technologies—particularly detector sensitivity—had improved dramatically, but that excited-state property of the humble helium nucleus hadn’t been explored since 1983.
In light of the apparent disagreement between theory and experiment, Concettina Sfienti, also of Johannes Gutenberg University Mainz, and her colleagues decided that a new and improved experimental investigation was warranted. Now they and their theory colleagues have confirmed the disagreement and charted theoretical and experimental paths to suss out its origin.
Day and night for three weeks in 2018, the Mainz Microtron’s A1 collaboration shot electrons at helium gas in an aluminum cell. Only one in every 10 000 electrons that hit helium excited the nucleus, and that signal needed to be distinguished from the large background created by elastic scattering off helium and scattering off aluminum—a difficult task. Over several years, Sfienti and her colleagues meticulously processed the data to track the fate of the scattered electrons and painstakingly subtract out the unwanted signal.
The measured scattering cross section of the excited state was then converted to what’s known as the transition form factor, which captures information about the shape of the nucleus. The results, the blue and red data points in the graph, agree with older experiments (gray data and error bars), although with dramatically reduced uncertainty. But theoretical calculations (red curve) predict a form factor as much as twofold larger than is observed.
“It’s possible that we missed some piece of the nuclear force,” says Bacca, “or that this observable is so sensitive to some detail of the nuclear force that it’s almost impossible to get it right.” The ChEFT calculation has around 25 parameters, none of which were varied in the current study but will be in the future. On the experimental side, the Mainz team is constructing a new facility that can perform electron-scattering measurements on gases without the aluminum cell—and its pesky background—by instead using a continuous flow of gas.
Understanding the disagreement between ChEFT and electron-scattering experiments could have implications beyond the field of nuclear physics. Neutron stars, for example, have hot, dense nuclear matter at their cores that prevents their collapse into a black hole (see the article by Jorge Piekarewicz and Farrukh Fattoyev, Physics Today, July 2019, page 30). ChEFT is extensively used to predict and understand the nature of that exotic stellar matter. (S. Kegel et al., Phys. Rev. Lett. 130, 152502, 2023.)