In 2013, Bacca used this effective field theory to predict how much an excited helium nucleus would swell. But when she compared her calculation to experiments performed in the 1970s and 1980s, she found a substantial discrepancy. She’d predicted less swelling than the amounts measured, but the experimental error bars were too big for her to be sure.

Ballooning Nuclei

After that first hint of a problem, Bacca encouraged her colleagues at Mainz to repeat the decades-old experiments — they had sharper tools at their disposal and could make more precise measurements. Those discussions led to a new collaboration: Simon Kegel and his colleagues would update the experimental work, and Bacca and her colleagues would try to understand the same intriguing mismatch, if it emerged.

In their experiment, Kegel and his colleagues excited the nuclei by shooting a beam of electrons at a tank of cold helium gas. If an electron zipped within range of one of the helium nuclei, it donated some of its excess energy to the protons and neutrons, causing the nucleus to inflate. This inflated state was fleeting — the nucleus quickly lost grasp of one of its protons, decaying into a hydrogen nucleus with two neutrons, plus a free proton.

As with other nuclear transitions, only a specific amount of donated energy will allow the nucleus to swell. By varying the electrons’ momentum and observing how the helium responded, scientists could measure the expansion. The team then compared this change in a nucleus’s spread — the form factor — with a variety of theoretical calculations. None of the theories matched the data. But, strangely, the calculation that came closest used an oversimplified model of the nuclear force — not the chiral effective field theory.

“This was totally unexpected,” said Bacca.

Other researchers are equally mystified. “It’s a clean, well-done experiment. So I trust the data,” said Laura Elisa Marcucci, a physicist at the University of Pisa in Italy. But, she said, the experiment and theory contradict one another, so one of them must be wrong.

Bringing Balance to the Force

In hindsight, physicists had several reasons to suspect that this simple measurement would probe the limits of our understanding of nuclear forces.

First, this system is particularly persnickety. The energy needed to produce the transiently inflated helium nucleus — the state researchers want to study — lies just above the energy needed to expel a proton and just below that same threshold for a neutron. That makes everything hard to calculate.

The second reason has to do with Weinberg’s effective field theory. It worked because it allowed physicists to ignore the less important parts of the equations. Van Kolck contends that some of the parts deemed less important and routinely ignored are in fact very important. The microscope provided by this particular helium measurement, he said, is illuminating that basic error.

“I cannot be too critical because these calculations are very difficult,” he added. “They’re doing the best they can.”

Several groups, including van Kolck’s, plan to repeat Bacca’s calculations and find out what went wrong. It’s possible that simply including more terms in the approximation of the nuclear force might be the answer. On the other hand, it’s also possible that these ballooning helium nuclei have exposed a fatal flaw in our understanding of the nuclear force.

“We exposed the puzzle, but unfortunately we have not solved the puzzle,” Bacca said. “Not yet.”