Snapshots from Physics History

Maria Goeppert Mayer and the Nuclear Shell Model

Maria Goeppert Mayer, who made important discoveries about nuclear structure, is one of only two women to have won the Nobel Prize in physics. But during her early career, she was forced to spend many years in unpaid positions before she was able to obtain a professorship in physics. Nonetheless, she persevered in her research. In August 1948, Goeppert Mayer published her first paper detailing the evidence for the nuclear shell model, which accounts for many properties of atomic nuclei.

Goeppert Mayer was born in 1906 in Kattowitz, which was part of Germany at the time. When she was 4 years old, her family moved to Gottingen, where her father was a professor of pediatrics. In fact, he was the sixth-generation university professor in the family, and Goeppert Mayer was later proud of being the seventh-generation academic. Her father always encouraged her to grow up to be more than a housewife. It was assumed that Maria would get an education, and she did, even though it was difficult for women at the time.

After attending public school and a college preparatory academy for girls, in 1924, she entered the University of Gottingen, at first intending to study mathematics. But after attending Max Born’s quantum mechanics seminar, she switched her focus to physics.

She completed her Ph.D. in 1930, with a thesis on double photon reactions. While at Gottingen, she met her husband, physical chemist Joseph Mayer. After she completed her Ph.D., the couple moved to the U.S., where he got a job at Johns Hopkins University in Baltimore. Nepotism rules prevented the university from hiring her as a professor, so she worked as a volunteer, continuing her own research, most of which involved applying quantum mechanics to chemical problems. She encountered a similar situation in 1939 when her husband got a job at Columbia University. Goeppert Mayer was given office space, but no salary. At first, she worked on calculations of properties of transuranic elements; later, she worked with Harold Urey on a photochemical method for isotope separation (the method was abandoned as impractical).

In 1946, Goeppert Mayer and her husband moved to Chicago, where she was employed half time at the University of Chicago’s Institute for Nuclear Studies and half time at Argonne National Laboratory. At the lab, 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. In addition, 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 couldn’t explain the specific sequence of magic numbers. Standard quantum mechanics and a simple central potential couldn’t account for the magic numbers higher than 20.

The key insight came to Goeppert Mayer when Enrico Fermi happened to ask her if there were any evidence of spin-orbit coupling. She immediately realized this was the answer. Goeppert Mayer was now able to calculate energy levels and magic numbers.

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 come up with 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 did meet. 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.

Goeppert Mayer was appointed to a full professorship at the University of California, San Diego in 1960, but suffered a stroke soon after. She never fully recovered and died in 1972.