Physicist Wolfgang Pauli called her “The Onion Madonna,” after she discovered that the nucleus of the atom has an onionlike layered structure. Maria Goeppert Mayer, the last woman to win a Nobel Prize in Physics, claimed that honor in 1963.

Since then many other women have been widely considered worthy, too: Vera Rubin, who died last year, was regarded as a strong candidate for uncovering the existence of dark matter. Jocelyn Bell Burnell played a major role in discovering pulsars but was left off the relevant 1974 Nobel Prize snagged by her (male) graduate advisor. In 2014 Slate published a longer list of women contenders. But to date, Mayer and Marie Curie are the only women who have been named for this particular prestigious prize. That could change October 3 when the Nobel committee announces this year’s winner—but who knows?

With the Nobel announcements approaching yet again, I decided to look deeper into the life and work of Mayer, who is far from a household name. I drove to the sunny campus of the University of California, San Diego, where Mayer was a professor for the 12 years leading up to her death in 1972. At the university’s futuristic-looking Geisel Library, I pored through some of the hundreds of documents from Mayer’s life stored at the Special Collections department: hand-written letters, typed correspondence, notebook pages, postcards, invitations, certificates, photos, newspaper clippings—even the Western Union telegram informing Mayer of her Nobel win. They reveal a life of achievements as well as frustrations, ultimately filled with scientifically minded friends and great discovery.

The Family Business

Mayer was born in the German town of Kattowitz, now Katowice, Poland. An only child, she came from a long line of academics and would become the seventh-generation university professor in her family. She earned a PhD at the University of Göttingen in 1930, under the tutelage of Max Born, who would go on to win a physics Nobel himself. Many handwritten letters to Mayer in the archival boxes are from Born, spanning decades.


After graduating, Mayer moved with her husband, chemist Joseph Mayer, to the U.S. When her husband worked at Johns Hopkins University and later at Columbia University, Mayer pursued physics research at both institutions but received a full salary at neither. According to a short biography written at the time of her prize, “no university would think of employing the wife of a professor.” Another sign of the times: the archive has a 1941 typed letter informing Mayer that she was elected as a fellow of the American Physical Society—addressed “Dear Sir.” During World War II she worked on separating uranium isotopes for the Manhattan Project.

After the couple moved to Chicago in the mid-1940s, Mayer held a “voluntary” position at the University of Chicago, and a part-time senior physicist position at Argonne National Laboratory. During these Chicago years Mayer explored the topics for which she would achieve scientific fame. Knowing this, I excitedly flipped through pages of notes and equations scrawled in a small 1947 notebook with a giant letter Q on the front above the name “M. G. Mayer”—Q for quantum mechanics, of course.

A Fast Waltz

Mayer’s began her pioneering work by noticing a correlation between how abundant different chemical elements are in nature and the particular numbers of neutrons and protons in their nuclei. Examining other properties of the elements, it became clear to her there were “magic numbers” (a term physicist Eugene Wigner is said to have coined) of nuclear particles linked to stable atomic structures. Elements with “magic” numbers of protons or neutrons were more stable, and therefore more prevalent in nature.

Scientists already knew at the time electrons orbit the nucleus in spherical shells, but Mayer determined the nucleus itself has layered, closed shells of protons and neutrons that orbit a common center of mass. The notion that the nucleus had some kind of shell structure had percolated in the 1930s, but Mayer was able to support and refine it with lots of new experimental data, says David Kaiser, a historian of science at Massachusetts Institute of Technology. The shell model also flew in the face of ideas that the nucleus is like a soup or blob of protons and neutrons.

Mayer realized an atom with completely full proton shells has a “magic number” of protons; one with full neutron shells has a “magic number” of neutrons, and if both types of shells are full—as is the case with oxygen 16 and calcium 40, for example—the nucleus is “doubly magic.”

But where did the magic numbers come from? At the suggestion of physicist Enrico Fermi, Mayer explored the idea of “spin-orbit coupling.” This meant the orbits of neutrons and protons within their shells are connected to these particles’ spins. The concept of spin-orbit coupling was already known in physics but it had never been applied to the “magic numbers” problem in nuclei before.

Mayer described it this way to her daughter, according to The San Diego Union–Tribune: “All the couples on the ballroom floor go one way, and that’s your orbit. Then each couple is also circling in the dance step, and that’s your spin. Everyone who has ever danced a fast waltz knows that it’s much easier if all the couples are dancing in one direction. It’s the same in the nucleus: Each particle spins in the same direction that all are traveling in orbits. And that’s spin-orbit coupling.”

How did this explain magic numbers? In quantum mechanics a neutron or proton has two possible spins: up or down. The combination of spin and orbital motion within the nucleus is called total angular momentum. Mayer found that when the orbital and spin motions align to produce a maximum total angular momentum, the energy of the particle shifts down. Conversely, when orbital and spin motions oppose each other, the energy of the particle shifts up. The “magic numbers” correspond to the greatest gaps in energy between all such shifted energy levels, demarcating where shells end and begin.


Another physicist Mayer didn’t know personally, Hans Jensen, independently reached similar conclusions about the structure of the atomic nucleus with his colleagues. The two became close friends, according to an account from Mayer’s student Robert Sachs (pdf), and jointly published the 1955 book Elementary Theory of Nuclear Shell Structure. Eight years later they shared the physics Nobel Prize, along with Wigner. In one of Mayer’s archived letters, she addresses Jensen as “My Nobel Shell Brother.”
Working on her seminal ideas was more exciting than finding out she got the prize, Mayer told a group of 400 high school girls in 1964. “And one afternoon I found the clue, and after a day of work I found that all the data, everything I had hoped to be able to explain was indeed predicted by the theory I had worked out,” she wrote in the speech, printed in a pamphlet in one of the archival folders. She added, “At such moments, one does not think of the Nobel Prize.”

The prize drew a lot of attention to her, though. Mayer told the Union–Tribune that she received some 700 letters after the Nobel announcement. Her U.C. San Diego archive houses a montage of thank-you notes for such gifts as a chrysanthemum bouquet and red roses. Frank Westheimer, a chemist at Harvard University, and his wife Jeanne must have sent bubbly, because she wrote to them, “Champagne is really the only thing that enables one to survive the onslaught of the press.”

Mayer finally received the title of full professor from U.C. San Diego, and began teaching there in 1960, just three years before her big award. A report to the regents of the University of California, a booklet with a 1968 seal on the back, describes her as “direct and unpretentious in manner,” notes her passion for growing orchids and mentions she and her husband had just taken their second trip around the world.

Privately, challenges loomed. Mayer had suffered a stroke after the move to California, Sachs wrote, and had continual health problems thereafter. But she still taught at the university, worked on the nuclear shell model and “gave as much attention to physics as she could” for the rest of her life. U.C. San Diego’s Mayer Hall was later named for her.

The Shell Model Lives On

In 1964 Mayer told high school girls that the only women she knew of who continued in science after marriage were married to scientists—but also that generally opportunities for women in science are “very good,” and urged them to learn as much science as they could. “Become fully educated women and promote the understanding of science in any way you can,” she said. “Our country needs your help. My generation has played its part. It is up to you to carry on.” According to the American Institute of Physics (pdf), the number of women receiving physics PhDs has been on the uptick in the last 40 years or so, and is at an all-time high (pdf) these days. Even so, women still represent only 20 percent of physics doctorate degrees awarded.

Scientific progress has carried on, however, building off the legacy Mayer left behind. Although the nuclear shell model is now more than 50 years old, physicists are still digging into its mysteries. “We’re motivated by the success of the shell model to try to understand its origins,” says James Vary, professor of physics at Iowa State University.

The shell model is also informing cutting-edge research into exotic particles. The existence of the long-sought tetraneutron, a system of four neutrons, was hinted at by a French-led group in the early 2000s, and further corroborated in 2016 via an experiment at the RIKEN Radioactive Ion Beam Factory in Japan. Further, physicists at Iowa State used simulations based on our present understanding of the shell model to corroborate the particle’s observed properties, Vary says.

Scientists including Vary also recently used the shell model to address the longstanding puzzle of why carbon 14, a special radioactive form of carbon used in dating ancient objects and bones, has a half-life of nearly 6,000 years. The shell model by itself does not predict this isotope would last that long. But in 2011 researchers showed an interaction involving three nuclear particles, akin to three people simultaneously exchanging Frisbees, could explain its longevity. “It’s a very curious thing, something I don’t think maybe in Maria Goeppert Mayer’s era they would have even imagined,” Vary says.

The shell model is additionally important in the ongoing search for the elusive “neutrinoless double beta decay,” a long-sought particle decay process that could help solve the mystery of whether neutrinos are their own antiparticles. The model may also hold clues to how neutrons are packed together in exotic ways inside the superdense remnants of dead stars called neutron stars.

Mayer’s discovery turns out to underpin some of the deepest questions scientists have about what we are made of and where we came from. Let us celebrate her not just for being a rarity as a female Nobel-winning scientist, but as a pioneering thinker whose ideas are still at the core of our cosmic search for our origins.