Physicists trying to understand the stability of some heavy atomic nuclei are drawing inspiration from the fluid motion of giant flocks of birds.

Some nuclei behave like a collection of individual protons and neutrons, each interacting as individuals like birds in a tree. Other nuclei are more like a flock on the wing, moving and interacting collectively like a murmuration of starlings.

“I like the bird analogy,” explained Tim Gray, recent PhD graduate from the Department of Nuclear Physics at ANU. “We can understand each individual bird quite well, and we can also describe a flock’s behaviour like a kind of fluid. The really interesting part is how you connect those two levels of understanding — how to shift from individual to collective behaviour.”

Gray is lead author on a study published in Physical Review Letters in January 2020, in which the researchers glimpsed the onset of collective nuclear behaviour by examining a pair of almost identical nuclei that straddle the line between flock and bird.

The international research team, including Gray and Professor Andrew Stuchbery from ANU, analysed the nuclear structure of tin-128 and antimony-129, which differ by just a single proton.

While the tin nucleus acts as a group of individual protons and neutrons, the researchers found that antimony’s one extra proton gives it a surprisingly large amount of collective, fluid behaviour.

The results make the tin-antimony pair an excellent testing ground to study the emergence of nuclear collective behavior, according to Gray.

“In the nucleus, we know how the individual protons and neutrons interact,” he explains. “And then we have models for the collective behaviour of lots of nucleons, describing changes in shape, or rotations and vibrations.

“We want to understand how this collective behaviour emerges from the individual particle interactions.”

The model of the collective behaviour is known as the liquid drop model, where the protons and neutrons are treated like molecules in a drop of water. It accurately describes many properties of heavier nuclei, which can rotate, vibrate, squish and wobble — all collective behaviours that involve coordination between large numbers of protons and neutrons.

But experiments have long shown that the liquid drop model fails badly for nuclei where the number of protons or neutrons equals one of a set of “magic numbers”: 2, 8, 20, 28, 50, 82 and 126.

These special numbers occur when the nuclear particles organise into patterns of particular energies, called shells. When a shell is completed, the nucleus becomes more stable. This nuclear shell model is analogous to the filled electron shells that define the chemically inert noble gases, such as helium, argon and neon.

A nucleus with a magic number of protons or neutrons tends to be more tightly bound than predicted by the liquid drop model. Nuclei like helium-4, calcium-40 and tin-132, which have magic numbers of both protons and neutrons, are “doubly magic” and get an extra dose of stability.

“Tin-132 appears to be one of the most robust examples of a doubly-magic nucleus,” explains Dr Gray. “So exploring nuclei that are just a little different from tin-132 allows us to test shell-model predictions and investigate the emergence of collectivity.”

Gray and his colleagues focused their research on tin-128 and antimony-129, two isotopes differing by just a single proton. Both are close enough to doubly-magic tin-132 to test the limits of the shell model, and tin-128 still has a magic number of protons.

“The shell model suggests that the one extra proton in antimony-129 shouldn’t make much difference,” explained Dr Gray. “You would expect it to behave much like a single proton interacting with a core of tin-128.”

To look for signs of emerging collective behaviour, the physicists examined data from experiments at Oak Ridge National Laboratory in 2004 that fired beams of energetic antimony-129 nuclei at a titanium target. The collisions sent the antimony nuclei into a range of different energy states.

Gray and his colleagues compared the probabilities of those energy transitions with shell model calculations to look for discrepancies. One set of these transitions, known as electric quadrupole transitions, are known to be closely associated with collective nuclear behaviour.

They were surprised to find that the chance of antimony making these electric quadrupole transitions was 40% higher than they first predicted. Their best shell-model calculations accounted for some of the extra proton’s impact, but left a large amount to be explained.

“The extra proton in antimony-129 has a disproportionate effect,” Dr Gray said. “It looks much more collective than we would expect.”

The result gives the physicists confidence that exploring the landscape around doubly-magic nuclei will help to close the gap between the two distinct descriptions of nuclear behaviour.

“The tin and antimony pair sits in an ideal place to test these sorts of effects,” explained Dr Gray. "It's close enough to tin-132 that the shell-model descriptions still apply, but far enough away that collective effects are starting to be relevant. 

“There are several other nucleus pairs to examine — a few more around tin-132, and some others close to lead-208, which is also doubly-magic. So we have a lot more of the landscape to explore.”