New “Magic Number” inside Atoms Discovered

At the frontiers of high-energy physics, picking “34” is like hitting the lottery

The “magic number” is a quantity of protons or neutrons that makes an atomic nucleus unusually stable. Protons and neutrons fill up separate shells inside nuclei and each shell can accommodate only a certain number of particles. A nucleus holds a ‘magic number’ of protons or neutrons when the particles completely fill the shells without any room left for adding more. This renders the nucleus more stable and longer-lived than other nuclei.

Researchers smashed beams of nuclei together at high speeds and discovered that calcium-54, which has 20 protons and 34 neutrons in its nucleus is stable – for a few milliseconds. This isotope is a radioactive variant of calcium and is not regularly found in nature. The new magic number could help scientists understand how atomic nuclei are formed in stars.

“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.)