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| Maria Goeppert Mayer, linocut, 11" x 14", by Ele Willoughby, 2025 |
The first thing that came to mind when I thought about lead for the next #PrinterSolstice2425 prompt is how it is the end of many chains of nuclear transmutations. Lead is particularly stable. The woman who figured out why was the second woman to win the Nobel Prize for physics: German-American theoretical physicist Maria Goeppert Mayer (1906-1972, née Göppert). Another woman would not win the physics prize until Canadian Donna Strickland in 2018.
Maria Göppert was born in Kattowicz, a Silesian city then part of Prussia, now part of Poland, the only child of father, pediatrician and sixth generation professor Frederich Göppert and mother Maria (née Wolfe). Maria would grow up, proud to be a seventh generation academic. The family moved to Göttingen when she was four when her father got a position at the university. She was closer to her father, reasoning, he was more interesting, "He was after all a scientist." He encouraged her to aim for more than a life as a housewife. She went to schools for girls intending to pursue higher eduction. When her suffragette-run private prep school closed before she completed the three year program, she took and passed the university entrance examination at 17, a year early. She entered the University of Göttingen, where Emmy Noether was a professor, to study mathematics, in 1924, spending a term in Cambridge before completing her degree. The prestigious university was known for its world class math and physics departments. Renown mathematician David Hilbert was a neighbour and like famed physicists Max Born and James Franck, a family friend of the Göpperts. There were other female students but the others were studying to become mathematics teachers for girls. Göppert on the other hand became interested in physics and decided to pursue her doctorate with Max Born, himself later a Nobel laureate. In her 1930 thesis, she studied two-photon absorption by atoms - something which was virtually impossible to verify until 1961 with the invention of the laser. Year later, her fellow Nobel laureate Eugene Wigner called her thesis, "a masterpiece of clarity and concreteness" and today the two-photon absorption cross-section is named the Goeppert-Mayer (GM) unit.
She met American physical chemist Joseph Edward Mayer, a Rockefeller Fellow who was working for Göttingen physicist (and later Nobel laureate) James Franck, who boarded with the Göppert family. The two fell in love and married in 1930 after she completed her PhD. They moved to the United States, where he got a faculty job at John Hopkins, at the height of the Depression. They had two children: Maria Ann and Peter Conrad. Like many women scientists married to scientists, she found anti-nepotism rules prevented her from getting a professorship at John Hopkins, but she was hired as an assistant dealing with German correspondence. The job had a small salary, but allowed her access to the facilities and she was able to teach courses. She collaborated with her husband and with Karl Herzfeld, a fellow German theoretical physicist at John Hopkins, on applying quantum mechanics to the chemistry of organic molecules. She also made several visits back to Göttingen to collaborate with Max Born in 1931, 1932 and 1933, before the nazis came to power and Born and Franck lost their jobs. She and Herzfeld became involved with refugee efforts, horrified to see academics of Jewish descent driven out of university jobs. She became an American citizen in 1933. She published a landmark paper on double beta decay in 1935. In 1935 Edward Teller got a position at the nearby George Washington University and they would discuss developing theoretical physics. In 1937, her husband was fired; he believed this was because of Maria's presence in the lab and the dean of science's hatred of women. Herzfeld agreed, but also noted the anti-German sentiment that greeted him, Maria and Franck who were all now at John Hopkins. Mayer got a job at Columbia n 1937, where Maria took an unpaid position. Harold Urey and Enrico Fermi arrived at Columbia in 1939 and the three became good friends. In 1940, Joe and Maria published their textbook Statistical Mechanics. Fermi asked her to work on the valence-shell of transuranic elements, which she correctly predicted would form a new series similar to rare earth elements. In 1941 she was elected a fellow of the American Physical Society; the letter from APS was address, "Dear Sir," as if they had not considered an other possible greeting might be appropriate for fellows. She still had no salary, until later that year when she was hired by Sarah Lawrence College, initially part-time, to teach mathematics, physics, physical chemistry and general science courses.
In 1942, she was recruited to work for the Manhattan Project. First she worked part-time for Urey at Columbia's Substitute Alloy Materials Laboratories trying to separate the fissile uranium-235 which could be used for weapons from natural uranium. She looked at uranium hexafluoride and investigated whether photochemical reactions could be used; while unfeasible in the 1940s, now lasers can be used to separate isotopes. Joe was working on conventional weapons at the Aberdeen Proving Grounds in Maryland five days a week. It was a challenging time for the family. The children had a nanny while their parents were occupied with war work. She was vehemently anti-nazi but found feared the consequences of producing a weapon which would harm friends and family in German if it were deployed there. She had taught her students at Sarah Lawrence that, "Man's scientific discoveries and inventions might very likely destroy him." She was stretched pretty thin and suffered several illnesses and on top of her full time teaching duties and childcare so negotiated reduced hours working for Urey. Teller recruited her to work on the Opacity Project on the properties of matter and radiation at extremely high temperature; Teller was working on his "Super" bomb, which would become the basis of the H-bomb. Her husband Joe was sent to fight in the Pacific; Maria decided to leave the children in New York and join Teller's team at Los Alamos. When Joe came back early they returned together to New York in 1945.
After the war her husband got a job at the University of Chicago; as did she, but it was as a voluntary professor of physics. When Teller joined the university she continued working on the Opacity Project and on the origin of elements. She was offered a part-time senior theoretical physicist job at the nearby Argonne National Laboratory. She responded that she didn't "know anything about nuclear physics" when offered the job. It was a shift in focus which laid the ground for her most impactful discoveries. She programmed the Aberdeen Proving Grounds ENIAC early computer to solve criticality problems of their liquid metal cooled reactor using Monte Carlo methods (that is, with statistical models you might use if trying to calculate gambling odds at the casinos in Monte Carlo). With Jacob Bigeleisen she derived the Bigeleisen-Mayer equation, also known as the Urey model (who independently arrived at the idea), of approximate isotope fractionation in isotope exchange reactions used in quantum chemistry and geochemistry.
She began working on her mathematical model of the nucleus to explain why nuclei with certain numbers of nucleons (protons and neutrons) are more stable. As you grow nuclei from hydrogen (one proton) to the hundreds in transuranic elements by adding nucleons there are points where the binding energy of the next nucleon is a lot lower than the last and the nuclei are more stable and common in nature. The numbers of nucleons producing very stable nuclei: 2, 8, 20, 28, 50, 82 and 126 were dubbed "magic numbers" by Wigner. For protons these nuclei are helium, oxygen, nickel, tin, lead and the theoretical unbihexium. From her work on the origin of elements she recognized that these were all more common than their periodic table neighbours. You can also get nuclei with magic numbers of neutrons or "doubly magic" nuclei with magic numbers of protons and of neutrons. In 1932 Ivanenko and Gapon were the first to propose that perhaps nucleons were distributed in shells. But in 1937, Niels Bohr and Kalcar proposed the useful "liquid drop" model of the nucleus. The liquid drop model helped physicist comprehend binding energies, and was for instance, how Lise Meitner and her nephew Otto Frisch explained nuclear fission. But the model did not explain the relative stability of different nuclei or the nature of magic numbers. Because Goeppert Mayer had not come from a nuclear physics background she was less biased in favour of the liquid drop model.
In 1948 she published her first paper summarizing the support for a shell model, but she did not yet have an explanation for the distribution of magic numbers. Fermi suggested she look at spin coupling, and she had a flash of insight. She realized that magic numbers could be explained by a nested sequence of closed nuclear shells where pairs of protons and neutrons would couple together. In 1949, Maria Goeppert Mayer build her nuclear shell model (green diagram) where the magic of these numbers is explained by a nested sequence energy levels (determined by spin and angular momentum & like with electrons beyond the nuclei, the Pauli exclusion principe) of filled shells. Pauli himself called her “The Onion Madonna” for her model’s onion-like layers.
In quantum mechanics nucleons have two possible spins: up or down. If you combine spin with their orbital motion you get total angular momentum. She’d found that if orbital and spin motions align to produce a maximum total angular momentum, nucleon energy level shifts down but when they go opposite directions nucleon energy level shifts up. The largest gaps between these shifted energy levels explain the “magic numbers” and these points mark the shells boundaries. Further, her model explained the ground state spins and magnetic moment of nuclei, for which there had been no previous explanation.
Very shortly thereafter, other physicists (Haxel, Jensen & Suess) independently developed the same idea and & she started collaborating with them & co-authored a book: Elementary Theory of Nuclear Shell Structure with Jensen in ‘50. In ’63, she & Jensen shared half the Nobel "for their discoveries concerning nuclear shell structure" with Wigner awarded other half. In a letter, she addressed Jensen as "My Nobel Shell Brother."
She was finally appointed a full professor of physics at a major university in 1960, at UCSD, where her husband was also offered a position. She suffered a stroke but continued teaching and working despite health problems. In 1971 she suffered a heart attack that left her comatose and she died in February 20, 1972.
The American Physical Society now awards the Maria Goeppert Mayer award to women in physics at the beginning of their careers. In 2018 they named Argonne National labs an APS Historic Site in recognition of her work. A crater on Venus has been named in her honour. In 1996 she was inducted in the National Women's Hall of Fame. The UCSD physics department is named Mayer Hall after her and Joe.
References
August, 1948: Maria Goeppert Mayer and the Nuclear Shell Model, APS News, August 1, 2008
Buntar, Simran, Maria Mayer - The First Woman to Win the Nobel Prize for Nuclear Physics, Secrets of the Universe blog, accessed January, 2025
Maria Goeppert Mayer, Wikipedia, accessed January, 2025
Maria Goeppert Mayer: Revisiting Science at Sarah Lawrence College, Sarah Lawrence College Archives Exhibit, accessed January, 2025
Landau, Elizabeth. The Last Woman to Win a Physics Nobel, Scientific American, September 26, 2017.
Magic number (physics), Wikipedia, accessed January, 2025
Nuclear shell model, Wikipedia, accessed January, 2025
Sachs, Robert G. Maria Goeppert Mayer, 1906-1972, National Academy of Sciences, 1979.
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