Maria Goeppert–Mayer: Cracking the Nucleus Shell


The German physicist and mathematician, Maria Goeppert-Mayer is prominent for her numerous contributions to the field of physics for which she earned the Nobel Prize in 1963. She was the first woman to win the Nobel Prize for theoretical physics, and second woman in history to win a Nobel Prize after Marie Curie. She is most famous for proposing the nuclear shell model of the atomic nucleus—a model of the atomic nucleus that provides a detailed description of the structure of the nucleus in terms of energy levels.

After attending public school and a college preparatory academy for girls, in 1924, Maria joined the University of Göttingen, at first intending to study mathematics; however, after attending Max Born’s quantum mechanics seminar, she switched her focus to physics. She married the physical chemist Joseph Mayer, and after completing her PhD in 1930, with a thesis on double photon reactions, they travelled together to the USA.

She worked as a volunteer at Johns Hopkins University in Baltimore, continuing her own research, most of which involved applying quantum mechanics to chemical problems. She then worked at Columbia University, where she worked on calculations of the properties of transuranic elements at first; she later worked with Harold Urey on a photochemical method for isotope separation.

In 1946, she was employed half time at the University of Chicago’s Institute for Nuclear Studies and half time at Argonne National Laboratory. There, she began working with Edward Teller on a project to determine the origin of the elements; the work involved creating a list of isotope abundances. While making this list, it became clear to Goeppert–Mayer that nuclei with 2, 8, 20, 28, 50, 82, or 126 protons or neutrons were especially stable. These numbers became known as “magic numbers”, a term thought to have been coined by Eugene Wigner, who was somewhat skeptical about the shell model.

This observation led her to suggest a shell structure for nuclei, analogous to electron shell structure in atoms. In the nuclear shell model, each nucleon moves in a central potential well created by other nucleons, just as the electrons orbit a potential well created by the nucleus in the atomic shell model. The orbits form a series of shells of increasing energy; nuclei with completely filled outer shells are most stable.

The fact that nuclei with certain numbers of nucleons were especially stable had in fact been noticed before, but physicists were so certain that a shell model could not be correct, in part because an alternative model—the liquid drop model, which treats the nucleus as a homogeneous blob—had been quite successful in explaining fission. Moreover, physicists assumed that the interactions between nucleons would be too strong for the nucleus to be accurately described by a shell model, which treats nucleons as independent particles. Goeppert-Mayer, who had less formal training in nuclear physics, was less biased by evidence for the liquid drop model.

Goeppert–Mayer then considered other nuclear properties, and found they all pointed to more support for magic numbers. In August 1948, her first paper summarizing the evidence for a shell model of the nucleus was published in Physical Review. Although Goeppert–Mayer had collected evidence for the nuclear shell model, at first she could not explain the specific sequence of magic numbers. Standard quantum mechanics and a simple central potential could not account for the magic numbers higher than 20.

The key insight came to Goeppert–Mayer when Enrico Fermi happened to ask her if there was any evidence of spin-orbit coupling; she immediately realized this was the answer. As she was sending her paper off to the Physical Review for publication, she became aware of a paper by Hans Jensen and colleagues, who had independently reached the same result. She asked that her paper be delayed to be published in the same issue as theirs, though hers ended up being published in the issue after theirs, in June 1949.

Goeppert–Mayer had not met Jensen at the time, but later the two met; they became friends and collaborators, and wrote a book together on the nuclear shell model. Jensen and Goeppert–Mayer won the Nobel Prize in 1963 for their work on the shell model; they shared the prize with Eugene Wigner, for unrelated work. Maria Goeppert–Mayer was appointed a full professorship at the University of California, San Diego, in 1960, but suffered a stroke soon after; she never fully recovered and passed away in 1972.


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