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New “Magic Number” inside Atoms Discovered

At the frontiers of high-energy physics, picking “34” is like hitting the lottery
The DALI2 gamma-ray detector array at the Radioactive Isotope Beam Factory in Japan



Satoshi Takeuchi

“Magic numbers” of protons and neutrons can make an atomic nucleus exceptionally stable—and a new one has just been added to the existing menagerie that helps sketch a fuller picture of the complicated inner workings of atoms. By smashing beams of nuclei together at high speeds, researchers have discovered that when a calcium atom has 34 neutrons in its nucleus, things stay pretty quiet—at least for a few milliseconds. The discovery overturns some of scientists’ previous notions about magic numbers and opens up a new line of inquiry for nuclear physics.

Inside nuclei, protons and neutrons fill up separate buckets—called shells—with each shell characterized by a different energy level that can accommodate only a certain number of particles. A nucleus holds a magic number of protons or neutrons when the particles completely fill its shells without any room left for adding more, rendering it stable and longer-lived than other nuclei. But magic numbers don’t behave quite as expected when too many neutrons are packed in relative to the number of protons. (Most stable versions of elements, called isotopes, have roughly equal numbers of protons and neutrons.)

In this alternative realm of radioactive isotopes magic numbers aren’t what they seem. For example, 20 is thought to be a standard magic number for neutrons. But the isotope 32magnesium, with 12 protons and 20 neutrons, turns out to be unstable, without any of the properties expected of magic nuclei. The same is true of 28oxygen —with eight protons and 20 neutrons it was expected to be bound tight but, on further inspection, turns out not to be. “Nobody would have bet an iota some years ago that it would be this way, but it is,” says nuclear physicist Robert Janssens of Argonne National Laboratory. “That’s part of the challenge for us to understand at the moment.”

There was much uncertainty about the stability of 54calcium, which has 20 protons and 34 neutrons. With such an overabundance of neutrons, this isotope is not regularly found in nature. Instead, it was created at the Radioactive Isotope Beam Factory operated jointly by the RIKEN Nishina Center and the University of Tokyo’s Center for Nuclear Study in Japan. The researchers projected a high-intensity beam of 55scandium nuclei (which have 21 protons) toward a target of beryllium, which knocked a proton off the scandium nuclei to create 54calcium. “The only place where that really can be done at the moment is this machine in Japan, which can produce the most intense beams of primary particles in the world,” says Janssens, who was not involved in the research, but called it a “major development.”

To determine whether 54calcium merits magic nucleus status (that is, whether it has a magic number of protons and neutrons), the scientists needed to dig deep. When it comes to neutron-heavy isotopes, having full shells isn’t enough to make a magic number; it is the difference in energy between one shell and another—its energy gap—that determines whether a full shell bestows stability. A larger energy gap makes it harder to excite the nucleus and raise a neutron to the next available shell, giving it incentive to stay the way it is—in other words, stability.

For neutrons in a calcium atom, 34 was predicted to attain magic status by some groups but models from other researchers predicted the opposite. “We weren’t really sure if there was going to be this magic number or not,” says research leader David Steppenbeck of the University of Tokyo. The team zapped the 54calcium to get it up to the next shell, called an excited state, then let it decay back to its lower-energy shell, in the process emitting a gamma ray. The energy of these gamma rays revealed how much of an energy gap separated the two states. “In the case of 54calcium the first excited state lies at quite a high energy,” Steppenbeck says, meaning 34 is indeed a magic number—a fact the team reports the October 10 issue of Nature. (Scientific American is part of Nature Publishing Group.)

Whereas that means 54calcium is slightly more stable than isotopes with one more or less neutron, the nucleus is still radioactive and tends to decay in a matter of milliseconds. That’s a relatively long time inside the center of a star, however, where nuclear reactions take place at much shorter timescales. Its longer survival than other isotopes means that 54calcium could play an outsize role in the reactions that create the heavy elements in the universe.

The discovery allows scientists to probe how interactions between protons and neutrons affect the energy gaps between shells and make nuclei more or less stable. “From the beginning of the field of nuclear structure physics, we were stuck with only being able to make detailed studies of the 350 or so stable isotopes—the ones we could dig out of the ground,” says Paul Cottle, a nuclear physicist at The Florida State University. “It has only been since the 1990s that we've been able to look carefully at some of the thousands of known short-lived radioactive isotopes. The big issue addressed in this experiment is developing a detailed understanding of how protons and neutrons talk to each other in nuclei.”

Scientists hope eventually to map the limits of stability and determine which nuclei can and can’t exist. “Scientifically, this is extremely interesting,” says Eric Scerri, a chemist and philosopher of chemistry at the University of California, Los Angeles. “The nuclear magic numbers are kind of giving way—the dogma begins to break down and the rules of the game have to be expanded. When you push things to a more extreme domain, new science comes out.”

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