A new experiment challenges the leading theory of the nucleus

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A The new measurement of the strong nuclear force, which binds protons and neutrons together, confirms earlier hints of an inconvenient truth: We still don’t have a solid theoretical understanding of even the simplest nuclear systems.

To test the strong nuclear force, physicists turned to the helium-4 nucleus, which has two protons and two neutrons. When helium nuclei are excited, they grow like a balloon that inflates until one of the protons detaches. Surprisingly, in a recent experiment, helium nuclei didn’t inflate according to plan: They inflated more than expected before bursting. A measure describing that expansion, called the form factor, is twice as large as theoretical predictions.

The theory should work, said Sonia Bacca, a theoretical physicist at the Johannes Gutenberg University in Mainz and author of the paper describing the discrepancy, published inPhysical Review Letters. We were puzzled.

The inflating helium core, the researchers say, is a kind of mini-lab for testing nuclear theory because it’s like a microscope: It can magnify deficiencies in theoretical calculations. Physicists think that certain peculiarities of that bulge make it extremely sensitive to even the weakest components of nuclear force factors, so small they are usually ignored. How much the nucleus swells also corresponds to the softness of the nuclear matter, a property that offers insights into the mysterious hearts of neutron stars. But before explaining the crushing of matter in neutron stars, physicists must first understand why their predictions are so far off.

Bira van Kolck, a nuclear theorist at France’s National Center for Scientific Research, said Bacca and his colleagues have exposed a significant problem in nuclear physics. They found, she said, a case where our best understanding of nuclear interactions, a framework known as chiral effective field theory, fell short.

This transition amplifies the problems [with the theory] which in other situations are not so relevant, said van Kolck.

The strong nuclear force

Atomic nuclei, protons and neutrons are held together by the strong force. But the strong force theory wasn’t developed to explain how nucleons stick together. Instead, it was first used to explain how protons and neutrons are made of elementary particles called quarks and gluons.

For many years, physicists didn’t understand how to use the strong force to understand the viscosity of protons and neutrons. One problem was the bizarre nature of the strong force: it gets stronger with increasing distance, instead of slowly dying out. This feature prevented them from using their usual calculation tricks. When particle physicists want to understand a particular system, they typically break down a force into more manageable approximate contributions, sort those contributions from most important to least important, then simply ignore the less important contributions. With the strong force, they couldn’t do it.

Then, in 1990, Steven Weinberg found a way to connect the world of quarks and gluons to sticky nuclei. The trick was to use effective field theory, a theory that is only as detailed as necessary to describe nature at a particular dimensional (or energy) scale. To describe the behavior of a nucleus, it is not necessary to know quarks and gluons. Instead, at these scales, a new effective force emerges, the strong nuclear force, transmitted between nucleons by the exchange of pions.

Weinberg’s work has helped physicists understand how the strong nuclear force emerges from the strong force. He also allowed them to perform theoretical calculations based on the usual method of approximate contributions. Effective chiral theory is now widely considered to be the best theory we have, Bacca said, for calculating the forces governing the behavior of nuclei.

In the body image
THE PUZZLE: Sonia Bacca, a physicist at the Johannes Gutenberg University in Mainz, has found that our best theoretical understanding of the strong nuclear force runs counter to experimental results. Photo by Angelika Stehle.

In 2013, Bacca used this powerful field theory to predict how much an excited helium nucleus would swell. But when he compared his calculation to experiments performed in the 1970s and 1980s, he found a substantial discrepancy. He had predicted less swelling than the measured amounts, but the experimental error bars were too large to be sure.

Balloon cores

After that first hint of trouble, Bacca encouraged his Mainz colleagues to repeat the decades-old experiments: They had sharper tools and could make more precise measurements. Those discussions led to a new collaboration: Simon Kege and his colleagues would update the experimental work, and Bacca and his colleagues would try to understand the same intriguing discrepancy if it emerged.

In their experiment, Kegel and his colleagues excited nuclei by firing a beam of electrons at a reservoir of cold helium gas. If an electron whizzed within range of one of the helium nuclei, it donated some of its excess energy to the protons and neutrons, causing the nucleus to swell. This inflated state was fleeting: the nucleus quickly lost the grip 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 inflate. By varying the momentum of the electrons and observing the response of the helium, the scientists were able to measure the expansion. The team then compared this change in a diffuse form factor in the core to a variety of theoretical calculations. None of the theories matched the data. But, strangely, the calculation that came closest used a simplified model of the nuclear force, not chiral effective field theory.

This was completely unexpected, Bacca said.

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

Bring balance to strength

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

First, this system is particularly insightful. The energy required to produce the transiently inflated helium nucleus that the state researchers want to study lies just above the energy required to eject a proton and just below the same threshold for a neutron. This makes everything difficult 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 argues that some of the parts thought to be less important and routinely ignored are actually very important. The microscope provided by this particular helium measurement, he said, is illuminating that basic error.

I can’t be too critical because these calculations are very difficult, he added. They are doing their best.

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

We exposed the puzzle, but unfortunately we didn’t solve the puzzle, Bacca said. Not yet.

This article was originally published onQuantum abstractionsblog.

Main image: Excited helium nuclei inflate like balloons, giving physicists the ability to study the strong nuclear force, which binds the protons and neutrons in the nucleus. Credit: Kristina Armitage/Quanta Magazine.

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