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Divining the mysteries of the atomic nucleus

New research at the edge of the nuclear landscape is illuminating the most powerful force in the universe and teaching scientists how elements are forged in stars

by Katherine Bourzac, special to C&EN
January 28, 2024 | A version of this story appeared in Volume 102, Issue 3
A researcher stands behind a metal pipe covered with electrical cords and gauges.

Credit: Facility for Rare Isotope Beams | A researcher works on a device at the Facility for Rare Isotope Beams. This part of the facility provides low-energy radioactive beams.


In brief

More than 100 years after scientists began studying the atomic nucleus, they still don’t understand what holds it together. The nuclear force is the strongest force in the universe, yet it remains mysterious. Scientists can’t reliably predict the structure and behavior of nuclei. New research with more powerful tools is bringing surprises and scientific insights. By making and observing rare isotopes in the lab, scientists are learning more about the structure of the nucleus and the glue that holds it together. This work should help nuclear theorists fill in the missing pieces in their models. It’s also helping astrophysicists understand the details of how elements are made in the universe and the physics of neutron stars.

Oxygen is the most abundant element in Earth’s crust and the third-most-common element in the entire universe. It sustains life as we know it on this planet, making it possible to take a breath, light a match, and manufacture plastics and steel.

But even this extremely common and well-studied element is still poorly understood at its very core, the atomic nucleus. More than 100 years after the birth of nuclear physics, scientists still can’t reliably predict how the oxygen nucleus—or any other nucleus—will behave when pushed to its limits.

Results that Takashi Nakamura, a nuclear physicist at the Tokyo Institute of Technology, has been working on for years and published late last summer brought this home for him. Nakamura is part of the team that made the first observations of the long-sought isotope oxygen-28. According to what 20th-century physicists knew about the laws of the atomic nucleus, 28O should have been stable, even though it has 12 more neutrons than the common form, 16O. But Nakamura and his colleagues found that 28O fell apart as soon as they made it. In fact, its parts held together so weakly and for such a short time that the association they formed can’t even be called a nucleus at all. “I was surprised,” Nakamura says.


Twentieth-century theories about the physical structure and energy levels of the nucleus hold up well when it comes to abundant isotopes. But the rules break down in unpredictable ways in rare isotopes with outsize ratios of neutrons to protons or vice versa. Scientists now know that they simply can’t predict what will happen in these nuclei—so they’re working to fill in their understanding of the nuclear force, the strongest force in the universe.

“A piece of the nuclear force is missing,” says Robert Janssens, a nuclear physicist at the University of North Carolina at Chapel Hill.

New research is helping scientists understand what they’re missing in this powerful force—and should help nuclear theorists better predict subatomic behavior. It’s also giving astrophysicists insight into how elements are made in the universe and the physics of neutron stars.

The nuclear landscape

In the 20th century, physicists and chemists settled on a basic picture of the atom. At the dawn of the 1900s, the electron had been discovered. Since scientists knew atoms were electrically neutral, they pictured atoms as blobs with electrons and positively charged particles all mixed up and packed together. Ernest Rutherford and his collaborators proved this wrong. They fired α particles (which are helium-4 nuclei) at a metal foil, and while some passed through, many deflected at large angles. That wouldn’t happen if nuclei were homogeneous mixtures. The findings suggested to Rutherford a dense nugget of positive charge at the center of the atom.

For decades, scientists pictured this dense nucleus as a roughly spherical ball of protons and neutrons, held together by the strongest force in the universe, with swarms of electrons orbiting at a distance.

The other way of considering the nucleus is in terms of energy. Protons and neutrons fill up energy “shells” to reach stable configurations. These are analogous to the shells occupied by an atom’s electrons. Just as certain numbers of electrons can snugly fill up these energy shells and make for extremely stable and nonreactive noble gases, certain numbers of neutrons and protons fit just so in the energy levels of the nucleus. For that reason, they are called magic numbers.

Black-and-white photo of a woman looking up and to the right. Behind her is a chalkboard with isotope symbols written on it. She holds a wooden slide rule.
Credit: Nobel Prize Outreach
Maria Goeppert Mayer shared the 1963 Nobel Prize in Physics for her work on nuclear structure and magic numbers.

Maria Goeppert Mayer was one of a trio of physicists who devised the nuclear shell theory and described magic numbers in the late 1940s—and shared the 1963 Nobel Prize in Physics for the discovery. While researching the origins of the elements in the universe, Goeppert Mayer noticed that nuclei that were particularly abundant tended to have magic numbers of protons or neutrons or both. Those numbers are 2, 8, 20, 28, 50, 82, and 126. Some of the stablest and most abundant isotopes are doubly magic, with filled shells of both protons and neutrons. Those include helium-4 (two protons and two neutrons) and oxygen-16 (eight protons and eight neutrons).

“That nuclei of this type are unusually abundant indicates that the excess stability must have played a part in the process of the creation of elements,” Goeppert Mayer wrote in her 1963 Nobel lecture.

But scientists are finding that these 20th-century ideas about the physical and energy structure of the nucleus are not universal. They can’t be used to make predictive models—especially when it comes to rare isotopes. These may be uncommon on Earth outside the lab, but they’re abundant in stars, the element factories of the universe.

The first time scientists observed an isotope in flagrant violation of the known laws of nuclear physics was in the mid-1980s. Scientists at Lawrence Berkeley National Laboratory (Berkeley Lab) measured the radius of lithium-11, a stable and relatively light nucleus, which has only three protons and eight neutrons. It was huge. Instead of a small, compact sphere, the physicists saw a giant halo as large as that of much heavier nuclei, such as lead.

A photo taken from above shows a cluttered space including two large blue metal structures and two shiny metallic spheres with holes in them. Also visible are pipes running along the wall, wooden crates, tables, a dolly, and a pile of long, skinny cardboard boxes.
Credit: Courtesy of Katherine Bourzac
Inside Lawrence Berkeley National Laboratory’s cyclotron building, physicists and engineers are constructing a highly sensitive γ-ray detector. When it’s assembled, the blue metal structures will hold the aluminum sphere in place at the beamline at the Facility for Rare Isotope Beams. The large, round holes in the sphere will be filled with crystalline detectors.

“It was the biggest surprise,” says Rituparna Kanungo, an experimental subatomic physicist at Saint Mary’s University in Halifax, Nova Scotia. “People were left wondering, What is going on?”

An illustration shows the structure of the nucleus of beryllium-10. Two clusters, each with two protons and two neutrons, are circled by two individual neutrons.
Credit: C&EN
Beryllium-10 is what’s called a halo nucleus. Two neutrons (blue ) orbit two clusters, each of which is an α particle containing two protons (red) and two neutrons.

Lithium-11 is what’s called a halo nucleus. At its core sits a tight cluster of three protons and six neutrons. Orbiting at a distance are two neutrons. Since this observation, scientists have found other halo nuclei. For instance, last year, physicists found that beryllium-10 consists of four pieces. Two neutrons orbit a pair of what looks like two helium-4 nuclei (Phys. Rev. Lett. 2023, DOI: 10.1103/PhysRevLett.131.212501).

Halo nuclei are “at the edge of the nuclear landscape,” Kanungo says. Their discovery sparked a renewed interest in exploring rare isotopes, particularly those that are overloaded with neutrons.

Besides finding nuclei with strange physical shapes, scientists have observed nuclei that don’t conform to the magic-number rules, indicating that the nuclear shells may not be where Goeppert Mayer and other scientists thought they ought to be. Oxygen has provided multiple examples of this unexpected behavior. As physicists have made ever-more-neutron-rich isotopes of the element, there have been twists and turns that don’t follow the magic-number map.

Oxygen’s doubly magic flavors should include 16O and 28O, and scientists wouldn’t expect the isotopes in between to be particularly stable. But in 2009, Kanungo was part of a team whose experiments showed that oxygen-24 is surprisingly stable, which suggests that its 16 neutrons can fill a previously unseen shell. Sometimes, 16 can be a magic number too. And 28O wasn’t stable, as physicists learned last year—so 20 neutrons don’t always fill a shell.

A calcium-48 beam hits a beryllium target, leading to fluorine-29 and other fragments. The fluorine-29 becomes oxygen-28, which leads to oxygen-24 and four separate neutrons.
Credit: Adapted from Nature 2023, DOI: 10.1038/d41586-023-02485-w
To make oxygen-28, scientists started with a beam of calcium-48. After the beam hit various targets, the rare oxygen isotope appeared for a fraction of a second. But the nucleus immediately fell apart into 24O and four neutrons. Empty circles in the nuclei represent places where protons or neutrons were knocked loose as part of the experiment.

“Shells seem to be disappearing, and we find new ones appearing,” Kanungo says. The nuclear rules in neutron-rich nuclei are tricky. “If you give me a nucleus that is somewhat standard, I can compute what the levels look like,” Florida State University theoretical physicist Alexander Volya says. “But not at those extremes.”

The nuclear force is the glue that holds the nucleus together. “This glue changes its properties once you are far from the stable nuclei,” says Miguel Madurga, a nuclear physicist at the University of Tennessee, Knoxville.

Those extremes may not be part of daily life on Earth, but they’re part of our history. Most of the elements heavier than iron, including those that came to be part of the solar system, were forged in extreme, neutron-rich reactions in stars. And this process is going on today in other stars. Understanding rare isotopes is key to understanding the basic science of the atomic nucleus and what goes on in stars—neutron stars, in particular.

Star stuff

In the beginning, there were hydrogen and helium. Those were the only elements produced in any great quantity in the early moments of the universe after the big bang, when protons and neutrons bumped into one another and formed these light elements.

The next cohort of elements is made by nuclear fusion in stars like our sun. Stars are giant gas balls hot enough to overcome the electrostatic repulsion between nuclei. And light nuclei can slam into one another with great speed, fusing into heavier nuclei. But this process can reach only so deep into the periodic table. Making elements as heavy as iron by nuclear fusion releases energy; making heavier ones by fusion requires an input of energy.

So where do the heavier elements come from? Over 50% of the total mass of heavier elements such as neodymium, gold, and uranium are made by what’s called the rapid neutron-capture process, or r-process. It occurs when lighter elements are bombarded with tremendous numbers of neutrons during spectacular astronomical events. As the name suggests, this process happens quickly. These unstable, neutron-rich isotopes repeatedly undergo β decay, spitting out an electron and turning one neutron inside the nucleus into a proton. This process forges heavier and heavier elements. The universe is about 13.7 billion years old, and our solar system is about 4.5 billion years old. That interim provided plenty of time for younger stars to make the heavy elements that ended up in the material that condensed to form Earth and our neighbors.

Astrophysicists believe the r-process occurs in supernovas and in neutron star collisions. But they can’t see the details of this process at a distance. “We don’t have an instrument capable of measuring that in space,” Madurga says. “You need to have the USS Enterprise slide into a neutron star to get a sample,” he jokes, referring to a spaceship in Star Trek.

From an Earth perspective, neutron stars are strange. They have about the same mass as our sun, contained in a space about the size of a city. As the name suggests, they are almost entirely made up of neutrons. They are the second-densest objects in the universe, after black holes. The tremendous pressure in these stars converts most electrons and protons to neutrons. Given their composition, “when they collide, this is an ideal place to have huge numbers of neutrons banging into nuclei,” says Andrew Levan, an astrophysicist at Radboud University.

In recent years, Levan says, astrophysicists have been able to observe heavy elements in neutron star mergers—providing evidence for the r-process as a driver of element production in the universe.

An illustration shows a small burst of whitish yellow surrounded by a large, oblong aura of blurred and wavy pink lines. At the top and bottom of the pink region are two blue waves spreading outward. The background shows the blackness of space sprinkled with faint stars.
Credit: NASA/CXC/M. Weiss
This artist’s conception shows a kilonova, the violent aftermath of a neutron star merger. During a kilonova, there’s a bright burst of light, and heavy elements can form by the rapid neutron-capture process and then jet out into space.

Neutron stars are faint and challenging to find with conventional telescopes. Scientists spotted a neutron star merger for the first time in 2017, when gravitational-wave observatories heard a characteristic rumble in space-time. Scientists raced to locate this event with telescopes and were able to observe the last stages of this collision, an explosion called a kilonova. During a kilonova, the r-process burns brightly, and gas dust and light are flung out into the universe. In the 2017 kilonova, scientists spotted absorption lines characteristic of strontium and yttrium (Nature 2019, DOI: 10.1038/s41586-019-1676-3).

In the 2017 event, scientists noticed that the gravitational waves were accompanied by a γ-ray burst. So now scientists on the hunt for kilonovas use γ rays as a guide. They have to act quickly. Neutron stars might circle one another for billions of years before merging, but the final act—the element-forging kilonova—is visible for only a few days. Last March, Levan was part of a team that followed up on one of these γ-ray bursts to find another kilonova. The scientists used a suite of instruments, including the infrared eye of the James Webb Space Telescope. The team saw evidence of tellurium and of lanthanides, the group of elements that includes key ingredients used in high​-​performance magnets (Nature 2023, DOI: 10.1038/s41586-023-06759-1).

Nuclear shrapnel

Scientists can’t sample neutron stars, at least not yet. But they can learn the basics about the kinds of reactions that happen in stars by studying rare isotopes, particularly those loaded with neutrons. “Stars produce nuclei that are so neutron rich we won’t have access to them,” says Heather Crawford, a nuclear chemist at Berkeley Lab. Making rare isotopes that are less extreme than those found in stars but still relatively neutron rich can help physicists validate models of what happens during kilonovas and other stellar events.

In these experiments, instead of adding neutrons onto a nucleus—which would take a huge amount of energy—physicists typically start with a beam of a heavier nucleus. They collide this beam with a series of targets to knock it to pieces, eventually carving out the rare isotope of choice for observation. Suites of sensitive detectors, including powerful mass spectrometers, γ-ray detectors, and neutron detectors, monitor these beamlines.

The oxygen-28 study was done at the Riken Radioactive Isotope Beam Factory in Wakō, Japan. This facility provides intense primary beams of nuclei, including calcium-48. Nakamura’s team fired this beam at a spinning beryllium target, blasting it into fragments including fluorine-29, which the scientists separated with the help of a spectrometer. That nucleus then collided with a sheet of liquid hydrogen, knocking a proton out of some of the F nuclei to leave behind oxygen-28.

A square metal structure houses a concave sphere made up of metal rectangles. Also shown in the image are various bundles of wires attached to the central sphere. Nearby are a metal pipe, scaffolding, and a scientist wearing a mask.
Credit: Yasuhiro Togano
This structure houses a new detector array being developed for the Riken Radioactive Isotope Beam Factory. The Caesium Iodide Array for γ-ray Transitions in Atomic Nuclei at High Isospin Asymmetry detector uses 140 crystals to detect protons and γ rays. These crystals are inside the metal rectangles at the center of the detector.

To prove that 28O had come to the edge of existence before falling apart, the team had to measure the pieces it left behind. The biggest challenge was to simultaneously detect the four neutrons 28O emitted as it disintegrated into 24O. Scientists had never before been able to detect so many of these extremely elusive, electrically neutral particles at the same time.

The Riken study used a battery of neutron detectors, and data analysis was intense. Nakamura says this is why there were nearly 8 years between the 2015 experiments and the publication of the results (Nature 2023, DOI: 10.1038/s41586​-023-06352-6). Plus, the team wanted to ensure it had really observed such a blatant defiance of the magic-number system in 28O, a nucleus presumed to be especially stable and have filled nuclear shells. Instead, it proved unstable, and its shells didn’t seem to be filled.

The way unstable nuclei fall apart is not the same as the way radioactive materials decay. In fact, unstable nuclei such as 28O don’t stick around long enough to undergo radioactive decay. Their constituents have some fleeting quantum association, something on the margins near existence. Physicists call this signal a resonance—it’s quasi-bound, something with a fleeting, measurable energy.

The timescales at play here are mind boggling. For scientists to talk about chemistry, an atom has to stick around long enough for an electron cloud to form around the nucleus. According to the International Union of Pure and Applied Chemistry (IUPAC), an element exists if it holds together for 10–14 s, a bit longer than a femtosecond. To qualify as a nucleus, it must persist for about 10–20 s. Any less than that, and a surface can’t form. Oxygen-28 resonates for only about a zeptosecond, 10–21s.

Scientists are also probing the limits of nuclear existence on the proton-rich side. Last year, researchers reported a strange occurrence: the fleeting observation of nitrogen-9 (Phys. Rev. Lett. 2023, DOI: 10.1103/PhysRevLett.131.172501). This entity comprises seven protons and just two neutrons, exists for about 10–21 s, and decays by spitting out five protons in stages. First it comes apart into one proton and carbon-8, which decays to two protons and beryllium​-6, which splinters into two protons and helium-4, an extremely stable nucleus. “That was a tour de force,” Janssens says of the measurements of these nested nuclei.

This work on the proton side can provide insights into less common element-forming nuclear reactions. Not all heavy elements can be made by neutron enrichment in the r-process or other neutron-addition processes. Scientists believe that some heavy elements form by proton addition. Where this happens in the universe is not yet clear. Conditions must be extreme for the nuclear force to overcome the intense charge repulsion between protons in a nucleus with few neutrons to smooth things out.

Astrophysical origins
The big bang produced mostly hydrogen and helium. The other elements were made, and continue to be made, in stars. Lighter elements can be made by nuclear fusion; others are made in the end stages of dying stars or when stars collide.
A version of the periodic table color coded to show which elements were made in the big bang, neutron star collisions, dying low-mass stars, cosmic-ray fission, exploding massive stars, and exploding white dwarfs.
Credit: Adapted from NASA/AASNova

Robert Charity, a nuclear chemist at Washington University in St. Louis and part of the team that observed the strange phenomenon of 9N, says this research can also help scientists understand nuclear structure. Nitrogen-9 brings up deep questions about the boundary between the existence and nonexistence of the nucleus.

The protons bounce around inside a few times before they come out. They’re exploring.
Robert Charity, nuclear chemist, Washington University in St. Louis

Nitrogen-9 is not a nucleus, but in the energy measurements, Charity’s team sees something. They’re just not sure what it is. “There’s some barrier. The protons bounce around inside a few times before they come out. They’re exploring,” he says. “That’s why I think we can call it an isotope and not just a bunch of particles flying apart,” he says.

Intensely weird

Studying how rare isotopes such as 28O and 9N fall apart is the best way to push the nuclear physics to its breaking point and shake loose some information about the nuclear force. And nuclear physicists and chemists are excited to be able to push these experiments further with new instruments in the coming years.

When it comes to looking for rare events in a beam of ions, the best way to improve your odds is to increase the beam’s intensity. The Facility for Rare Isotope Beams (FRIB) in East Lansing, Michigan, which opened to users in May 2022, has beam intensities on par with those at the Riken source, with a power of about 10 kW. As early as 2028, when running at full power, it will provide primary beams with 400 kW. “This will allow us to make more-neutron-rich, heavier isotopes,” says Alexandra Gade, FRIB’s scientific director.

A corridor shows rows of machinery and wires on both sides of the walkway.
Credit: Facility for Rare Isotope Beams
The Facility for Rare Isotope Beams uses this linear accelerator to generate beams of high-energy ions for experiments.

This increase in beam power is thanks to the higher-energy particle accelerator at the heart of FRIB. Instead of a cyclotron, which runs ions in a circle while pumping energy into them, FRIB is built on a linear accelerator.

Witek Nazarewicz, chief scientist at FRIB, is excited about the potential for the facility to create heavy isotopes of calcium. Calcium has 20 protons, a magic number. Nazarewicz wants to know what calcium​-70 will be like. It could be doubly magic, since 50 is a magic number. But that’s a tremendous number of neutrons to cram into one nucleus. “It’s a very bizarre system,” he says. “But many theorists suspect it will live a long time.” Nazarewicz says making 70Ca and determining how it behaves could potentially disprove some theoretical models of the nucleus—and provide evidence for others.

Charity wants to use FRIB to observe more nuclei that decay by emitting multiple protons, as 9N does. He wants to study silicon-20, which may decay by emitting six protons, though he says he’s not yet sure how his team will detect six protons at once.


Beam intensity is important, and so is having great detectors. Interpreting data from rare isotope experiments is like being handed a million-piece jigsaw puzzle with no picture on the box to guide you and many pieces missing. Nakamura’s team members hope to learn more about the nucleus that preceded 28O in their experiments. They want to find the nuclear information encoded in the proton that was knocked out of 29F. CATANA (Caesium Iodide Array for γ-ray Transitions in Atomic Nuclei at High Isospin Asymmetry), a γ-ray and proton detector made up of 140 crystals, will help measure the energy and direction of this proton (Nucl. Instrum. Methods Phys. Res., Sect. B 2020, DOI: 10.1016/j.nimb.2019.05.049).

Berkeley Lab’s Crawford is leading construction of an upgraded γ-ray detector for FRIB. There’s a lot to keep up with. The more intense the source beam, the more γ rays are produced. To get the maximum amount of information about what’s happening, scientists want to know the energy of the γ rays and their direction. GRETA (γ-Ray Energy Tracking Array) is an aluminum sphere that will surround the beamline with 30 modules, each of which contains four soda-can-size germanium crystals segmented into 36 subdetectors. When it’s complete at the end of the year, GRETA will provide 4,800 channels of data. “From the patterns we see, we can infer something about the shape of the nucleus,” Crawford says.

Nature can always surprise you. You have to be diligent and keep an open mind.
Miguel Madurga, nuclear physicist, University of Tennessee, Knoxville

“The better your instrumentation, the better your chances,” Janssens says. Better sources and detectors will help nuclear scientists observe rare isotopes and see in enough detail how they behave. He hopes FRIB will help physicists discern “subtleties that we totally missed before.”

“Nature can always surprise you,” Madurga says. “You have to be diligent and keep an open mind.”

Katherine Bourzac is a freelance journalist in San Francisco.


This story was updated on Feb. 8, 2024, to correct the timing of when the Facility for Rare Isotope Beams’ improvements will be completed. They will be completed as early as 2028, not necessarily by 2028. In addition, the story was updated to correct a description of Witek Nazarewicz’s comments about making 70Ca. He says determining how the isotope behaves, not determining whether it’s stable, could help potentially disprove some theoretical models of the nucleus.


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