MAYER, MARIA GOEPPERT

(b. Kattowicz, Upper Silesia [now Katowice, Poland], 28 June 1906: d. La Jolla, California, 20 February 1972)

physics.

Mayer was a mathematical physicist with a facility for the matrix manipulations of group theory and quantum mechanics and a chemist’s appreciation for the accumulation and analysis of large quantities of physical data. She is best known for the work in nuclear physics that won her the Nobel Prize, but this was done relatively late in her career, when she had recently come to the field on nuclear physics she had recently come to the field of nuclear physics from atomic and chemical physics. Her earlier work, which is not as well known, demonstrates Mayer’s unusual physical intuition. Much of this work has remained unchanged since the 1930’s and provides theoretical bases for several important developments in laser physics, laser isotope separation, double-beta decay, and molecular orbital calculation.

Maria Gerturd Käte Goeppert was the only child of Maria Wolff Goeppert and Friedrich Goeppert, both from old German professional families that included several university professors. Friedrich Goeppert was professor of pediatrics at Georgia Augusta University in Göttingen, the sixth generation of his family to be a university professor. He actively encouraged his daughter to develop her scientific curiosity. Maria Goeppert attended public elementary school and a private girls’ school for college preparation before entering Georgia Augusta University in 1924, with the intention of studying mathematics.

Goeppert studied mathematics for three years at Göttingen before she was attracted by quantum mechanics and decided to take her degree in physics instead. The physics department at Göttingen was led by James Franck and Max Born: Goeppert developed close relationships with both of them, particularly Born. From them she learned to apply the mathematical techniques of quantum mechanics to the interpretation of spectra. The strict mathematical formalism of the Göttingen style of physics, was well suited to Goeppert’s tastes. Of his many talented students. Born later described Goeppert as one of the best.

Goeppert was young enough when she first encountered quantum mechanics to find it easy to accept. Her first mechanics to find it easy to accept. Her first systematic exposure to the theory came through reading proofs for Born and Pascual Jordan’s Elementare Quantenemechanik. She also wrote the section in the book on P. A. M. Dirac’s theory of radiation.

Goeppert’s doctoral dissertation (1930) was an extension of Dirac’s theory of radiation and matter to the case of two-photon processes, which required calculating the second-order time-dependent perturbation in addition to the first. Goeppert recognized that double-photon emission and absorption are analogous to the Raman effect: the dispersion formula of Kramers and Heisenberg could be applied to this process, but with only qualitative results. She estimated from it that the transition probabilities for such processes would be very low. Since the Raman effect can be analyzed as a case of dispersion, Goeppert used Dirac’s theory for dispersion to calculate the transition probabilities. Using a suggestion made by Tatiana Ehrenfest, she added a term to the Lagrangian that is a total differential with respect to time, and derived a Hamiltonian in which the second-order term is much smaller than the first. That made the perturbation a feasible calculation. The probability of double-photon emission or absorption came out so low that it seemed to have no physical significance. As Eugene Wigner pointed out forty years later, however, her doctoral thesis was clear and mathematically elegant.

While completing her work at Göttingen, Goeppert met and married Joseph Edward Mayer, an American chemist who had taken a degree with Gilbert Newton Lewis at Berkeley and who was in Göttingen on a Rockefeller International Education Board fellowship for the years 1929 and 1930. Joseph Mayer was trained as an experimentalist but, in part owing to his wife’s influence, came to be known for the application of theoretical physics, particularly quantum mechanics and statistical mechanics, to chemistry. After their marriage in January 1930, Mayer completed her doctoral degree. Then she and her husband moved to America, where Joseph Mayer took up a position as associate professor of chemistry at Johns Hopkins University. While in Baltimore, the Mayers had a daughter and a son. Maria Mayer became an American citizen in 1933.

Maria Mayer had no regular academic appointment at Johns Hopkins for the nine years she was there. She taught occasional courses, particularly in the chemistry department, and collaborated with her husband and the theoretical chemical physicist Karl F. Herzfeld. Most of her research during the years 1930 to 1939 was therefore in the fields of chemical physics and physical chemistry. The common thread that runs through Herzfeld and Mayer’s joint work is the problem of explaining the existence of a stable phase (a liquid) between a state of complete disorder (the gas) and a state of complete geometrical order (the crystal). Mayer and Herzfeld wrote several articles in which they attempted to analyze the liquid phase in terms of the energetics of the transition from a liquid to a solid. By examining the pressure-volume curve for the equation of state for a simple lattice, they were able to show that there is a temperature at which every crystal breaks down (melts), resulting in a stable liquid phase.

Maria Mayer’s work with Joseph Mayer centered on the application of quantum mechanics to chemistry. In one paper they developed a general method for determining the entropy of a polyatomic molecule from spectroscopic data. By generalizing a method for diatomic molecules and determining the number of rotational states from the symmetry number of a molecule, they described a method that is generally valid for polyatomic molecules, applying it in particular to the calculation of the entropy of ethane. In a second paper the Mayers looked at methods of calculating the polarizability of ions from spectral data. While considering several different methods, they demonstrated the general validity of the Born Heisenberg relation for polarizability, derived in 1924 on the basis of the old quantum theory. These collaborations exposed Mayer to the use of experimental data in theory, and taught her to apply her talents with theory to specific physical situations.

The research for which Mayer was best known before 1949 was a paper she wrote with Alfred Lee Sklar, a student of Herzfeld’s at the Catholic University of America, where Herzfeld taught after 1936. Herzfeld was interested in how chemical structure determines optical properties such as color and suggested this as a thesis topic for Sklar. Because of the complexity of the mathematical techniques involved. Mayer assisted Sklar in the analysis. In calculating molecular energy levels, they used the Heitler-London-Slater-Pauling approsimation and the Hund-Mulliken method. The first ivolves constructing wave functions for the molecule from linear combinations of orbitals of its individual constituent atoms. Sklar used this method in his dissertation, published in 1937.

About a year later Sklar and Mayer published a paper on the spectrum of benzene based on the Hund-Mulliken approximation. They built their Hamiltonian for the molecule by summing the contributions of the individual atoms and added the interaction energy between atoms as a correction. This was one of the first calculations of energy levels for a complex molecule from strictly theoretical principles. The only empirical parameter used in the calculation was the carbon-carbon distance in benzene. This work was elaborated in 1939 when Sklar collaborated with Hertha Sponer, Lothar Nordheim, and Edward Teller on a systematic analysis of the benzene spectrum. This was subsequently the method most commonly used in the construction of molecular orbitals for conjugated systems, and the primary reason that Mayer was generally regarded, between 1939 and 1949, as a specialist in the analysis of the spectra of complex systems.

Mayer also applied the techniques developed in her doctoral dissertation to a problem in nuclear physics, wigner suggested that she calculate the probability of double-beta decay, since Enrico Fermi had recently demonstrated that beta decay can be treated in the same way that Dirac had treated radiation: the emission of an electron and its accompanying neutrino is analogous to the emission of light by an excited atom. Mayer determined how likely it would be that a nucleus would emit two electrons accompanied by two neutrinos. She set up an expression for the probability that came directly from the one she derived for double-photon emission. Using a Thomas-Fermi potential to describe the number 31 would have a half-life greater than 10¹⁷ years for double-beta disintegration. This result, like her calculation of the probability of doublephoton decay, was regarded as a clear and competent analysis of a situation with little likelihood of ever being tested.

During their last years at Johns Hopkins, Mayer and her husband completed the textbook Statistical Mechanics, which grew out of their collaboration in teaching the quantum mechanical basis of statistical mechanics to chemists. The book, published in 1940, became a standard; it went through ten printings by 1963; a second edition, with few changes, appeared in 1977.

In 1939, when Joseph Mayer’s contract at Johns Hopkins was not renewed, the Mayers went to Columbia University, where Joseph Mayer was hired as associate professor of chemistry. Maria Mayer again had no official appointment, although she was asked by Harold Urey to give lectures in the chemistry department, and after the beginning of the Manhattan Project in 1941, she was asked, on twenty-four hours’ notice, to take over Fermi’s class in the physics department.

Mayer’s first research project at Columbia was a problem suggested by Fermi. In 1939 Emilio Segrè had shown that the chemical behavior of one of the radioactive decay products of uranium indicated that it was one of the rare earths. A year later, however, Edwin McMillan and Philip Abelson suggested that the element was instead a transuranic element. Fermi recommended that Mayer test this hypothesis by calculating the expected energy levels for several of the rare earth elements and for the transuranic elements, in order to determine if the expected chemical behaviors were similar. Using a statistical (Thomas-Fermi) potential, Mayer calculated the energy and spatial extension of the 4f eigenfunctions for the rare earth elements and the 5f eigenfunctions for the transuranic elements. In both cases she found that the binding energy increased dramatically and the radii of the orbitals decreased abruptly at the beginning of each series, supporting the hypothesis that the transuranic elements would have chemical behavior similar to the rare earths.

After the outbreak of World War II, Mayer was asked to join Harold Urey’s group, the Substitute Alloy Materials Laboratory (SAM), devoted to solving the problem of isotope separation for the Manhattan Project. Since Urey considered several alternatives to the gaseous diffusion method of separation. Mayer’s work during the war was not all directed toward a single method. In fact, the first method she examined was photochemical separation. This required a thorough understanding of the differences between the spectra of U²³⁵ and U²³⁸. The problem was ideal for Mayer, since her primary expertise was in spectroscopy. She compiled all available data on the spectra of the uranium compounds and then determined where further measurement was needed; the chemists in the experimental group then filled in the gaps. The results of this work were published in 1949 by Gerhard Dieke and Albert Duncan, who edited Spectroscopic Properties of Uranium Compounds. Mayer found that she could account for the high number of closely spaced electronic states in the uranyl ion by assuming that it has three fundamental vibrations: a symmetric stretching, an asymmetric stretching, and a bending vibration. The analysis showed that photochemical separation of uranium was not promising, and the project was phased out.

Mayer moved on to study chemical separation. With Jacob Bigeleisen she found a function describing the separability of two compounds of uranium that was related to the partition-function ratio. Again the outcome of the analysis was that the method would not be effective for uranium, and the possibility was dropped. Mayer did, however, make a contribution to a successful method, gaseous diffusion. She analyzed the structure of uranium hexafluoride (UF₆) from measurements of the Raman spectrum carried out by Bigeleisen.

Mayer’s work at the SAM Laboratory marked a turning point in her career. She was working for the first time without her husband’s emotional support (Joseph Mayer was working for the Naval Ordance Laboratory at Aberdeen. Maryland, throughout most of the war, and was home in New York only one day each week), and was responsible for the first time for the work of other people. Later she regarded this period as the beginning of her career as an independent professional scientist.

In 1945 Joseph and Maria Mayer were offered positions at the University of Chicago, she as voluntary associate professor. They were also both invited to join the new Institute for Nuclear Studies, and in 1946 Maria Mayer was offered a half-time position as research physicist in the theoretical division of the new Argonne National Laboratory. Mayer at this time knew very little about the physics of the nucleus: she developed her knowledge of the field not from books but from discussions with colleagues about current problems. She did not gain a comprehensive background in the subject, and so had what proved to be the advantage of unfamiliarity with many of the traditional beliefs of nuclear physics.

In 1945 the common understanding of nuclear structure was based on Niels Bohr’s compound-nucleus interpretation of nuclear reactions and the assumption that the nucleus behaves like a liquid drop. In Bohr’s view, it was impossible to assign different energy and momentum values to individual nucleons because of the intensity and short range of the nuclear force. Bohr’s authority and the success of the liquid-drop model in accounting for such phenomena as nuclear fission combined to discourage attempts to explain the nucleus as a collection of discrete particles. In addition, Hans Bethe, in his very influential review articles of 1936 and 1937, which served as the primary textbook of nuclear physics for more than a decade, argued against treating nucleons as discrete particles.

Early in 1947 Mayer began to look carefully at data for isotopic abundances in conjunction with a theory she and Teller were proposing to explain the origin of the elements. Mayer noticed that nuclei with fifty and eighty-two neutrons were particularly abundant. This phenomenon could not be explained by the liquid-drop model, which predicted an essentially smooth curve for the binding energy as a function of neutron number. The discrepancy prompted Mayer to look even more closely at abundances, and she found that a marked pattern emerged. Nuclei having 2, 8, 20, 50, or 82 neutrons or protons or 126 neutrons were unusually stable. This conclusion was borne out not only by isotopic abundances but also by delayed-neutron emission and neutron-absorption cross sections. Mayer was convinced that these numbers indicated something special about the structure of the nucleus, and soon took to calling them “magic numbers,” a phrase she had picked up from Wigner, who thought the whole idea was charming nonsense.

Pronounced periodicities in the abundance and stability of various nuclei obviously suggested a corresponding periodic structure in the nucleus, and an analogy to the electronic shell structure was almost inevitable. Mayer recognized this analogy and published her results in 1948, in a paper entitled “On Closed Shells in Nuclei,” in which she summarized all of the data leading to the conclusion that nucleons occupy discrete energy levels in the nucleus. This paper contained no theory to account for the phenomenon, however, because quantum theory applied to a standard central potential, either harmonic oscillator or square well, did not predict the same numbers of nucleons in closed shells as those indicated by experimental data.

This difficulty had been noted much earlier by Walter Elsasser and Karl Guggenheimer, who discovered the phenomenon of the magic numbers in data similar to Mayer’s. In 1933 and 1934 they pointed out the evidence for some sort of nuclear shell structure and attempted to account for shell closure at particular numbers of nucleons. No theory proposed, however, could adequately predict the magic numbers above nucleon number 20. Many physicists were aware of the failure of the older nuclear shell models, which Bethe had discussed at length in the “Bethe Bible.” Mayer was unaware of this history until Bethe pointed it out to her in 1948, but she felt that the more recent evidence for nuclear shells was sufficiently compelling to warrant publishing in spite of the view held by the majority of nuclear physicists.

The publication of Mayer’s paper on closed shells in nuclei, which included much new evidence, prompted several other physicists to try their hands at new sell models. From preprints of such paper by Eugene Feenberg and Lothar Nordheim, Mayer learned about Theodore Schmidt’s technique of assigning an angular momentum value to the last (odd) nucleon in a nucleus, based on the measured spin and the total nuclear magnetic moment j. For Mayer, this method for determining nucleon spins supplied one of the missing pieces of the puzzle.

Sometime early in 1949 Mayer was discussing this question with Fermi when he asked, “Is there any evidence of spin-orbit coupling?” She immediately recognized that there was, and by taking it into account, she found that the energy-level splitting occurred at exactly the magic numbers. For a fermion with a given value of l, there are two possible total angular-momentum values, j = l + ½ and j = l – ½. For electrons, the energy difference between these two levels is small compared with the energy difference between adjacent l-values, and it had been assumed for several reasons that the same was true for nucleons. Mayer saw that if she used Schmidt’s technique for spin assignments to nucleons, then the j = l + ½ level must actually lie below the j = l − ½ level (an inverted doublet), and if the energy due to spin-orbit coupling was proportional to a (l · s) term, then the magnitude of the splitting would be greater for greater l-values. This immediately explained why the square-well potential yields correct energy-level spacings for nuclei up to a neutron or proton number equal to 20, but not above. For low l-values the spin-orbit splitting is not large enough to alter the standard square-well spacing, but for high l-values the magnitude of the separation is at least as large as the separation between adjacent l-levels. Mayer’s postulation of this nuclear spin-orbit interaction was strictly phenomenological. The effect was clearly

not electromagnetic in origin because the magnitude of the spin-orbit energy level separation had to be much greater for nucleons than for electrons and was of the opposite sign.

The remarkable simplicity of the scheme immediately convinced Mayer that she had found the solution to her problem. With the assumption of strong spin-orbit coupling, a simple square well gave level spacings at exactly the right places without the need to assume ad hoc crossing of energy levels (see Table I). Mayer first published her theory in a brief letter to Physical Review that appeared in the same issue as Feenberg’s and Nordheim’s papers on the same subject. Her note was so brief that it convinced almost no one, and appeared to be simply another alternative shell model. By the time she published a longer exposition in April 1950, however, Mayer’s model had gained a large number of influential adherents. It had great value to experimental nuclear physicists because it could account for nuclear spins and magnetic moments, for which there was a tremendous amount of new data in the 1950’s, In spite of this phenomenological success, however, there remained some problems with the shell model. There was no direct experimental evidence that spin-orbit coupling is a strong effect for nucleons until 1952, when George Freier and M. Heusinkveld at the University of Minnesota demonstrated that the widely spaced p_3/2–p_1/2 doublet in Li⁵ was inverted, as Mayer had assumed. There was also no good explanation of how nuclear shells could exist separately in the strong nuclear potential. This problem was not adequately addressed until the mid 1960’s, when a strict shell model of the nucleus had given way to the collective model.

One possible reason that Mayer’s model was accepted so readily by physicists who had recently believed that discrete particles could not exist in the nucleus was that the same model was proposed simultaneously and independently by Otto Haxel, J. Hans D. Jensen, and Hans Suess in Germany. Jensen was the nuclear theorist of the group. He and Mayer formed a close friendship when they met in 1951. Mayer and Jensen worked together to develop various theoretical aspects of the shell model. (Mayer also worked with Nordheim and Steven Moszkowski on a shell-model analysis of betadecay.) The ultimate result of Mayer’s friendship with Jensen was their collaboration on the first textbook devoted entirely to the nuclear shell model, Elementary Theory of Nuclear Shell Structure, published in 1955.

Mayer remained at the University of Chicago and Argonne Laboratory for five years after the publication of Elementary Theory of Nuclear Shell Structure. She published little during those years but was active in the physics department. In 1959 the University of California established a new graduate research program at San Diego and offered both Mayers full (paid) professorships. Although the University of Chicago countered by offering Maria Mayer a salary, the Mayers preferred California, and moved to La Jolla in September 1960. Less than a month after they arrived, Mayer suffered a stroke. Although she continued her work, her health was never good again, and she channeled her diminished energies into teaching until her death in 1972. In 1963 Mayer and Jensen shared half the Nobel Prize for physics for their work on the nuclear shell model.

Mayer’s approach to physical problems changed considerably during her career. Her early work was extremely mathematical, but her later work was much more physical in character. She learned to approach data in the manner of a chemist—to compile and collate large amounts of information in search of patterns. This step was one of the keys to her success with the shell model—the extensive experimental evidence convinced her to continue searching for a theoretical explanation. This same step was taken in Germany by a chemist (Suess) and not a physicist. The role of the physicist (Jensen) became important only after the pattern had been established on the basis of the experimental data. Mayer’s great strength was in her ability to assume both roles.

The single most remarkable aspect of Mayer’s work is the way that her mathematically derived theories retained their physical validity and, in many cases, were far ahead of their time. The theory of double-decay could not be tested experimentally until the 1960’s. With lasers to provide a sufficiently high intensity source of radiation, however, Mayer’s predictions were verified. This led to the development in the 1970’s of the double-photon absorption technique in laser spectroscopy as a means of eliminating the Doppler broadening of an absorption line. Mayer’s prediction of the half-life for double beta-decay served as a guide for its eventual detection in 1987. The theoretical model most commonly used in describing the rare earth elements derives from the work of Fermi and Mayer. With the development of very-high-resolution lasers, photochemical isotope separation has become a standard technique, even for uranium compounds. In all of these cases, Mayer’s early work served as a solid theoretical basis for later developments.

Mayer was remembered by her students as a demanding teacher. She was not a particularly good lecturer, since she spoke very softly and expected students to supply many of the logical connections. She was known at the University of Chicago for keeping the attention of her audience, though, because of her habit of chain-smoking while lecturing, No matter how often she switched chalk and cigarette from hand to hand, no student ever saw her smoke the chalk or write with the cigarette. Mayer had only a few graduate students during her career, but they included some very talented physicists: Robert Sachs (at Johns Hopkins) and Steven Moszkowski and Dieter Kurath (at the University of Chicago) received their doctorates under Mayer’s direction.

Joseph and Maria Mayer were known for their gracious life-style. They entertained frequently and lavishly, and were particularly famous for their New Year’s Eve parties. Mayer traveled extensively throughout her life. From 1930 until her mother’s death in 1937, she spent most of every summer in Germany. After World War II, and as a result of her connection with the Manhattan Project, she and her family traveled frequently in the American Southwest. On these trips Mayer pursued her strong interest in Native American pottery and archaeology. By the mid 1950’s she and Joseph were again traveling abroad: in 1953 they spent six months going around the world, giving lectures and attending conferences. These trips did not stop after Mayer’s stroke; in 1965 she was guest of honor at Women’s Week in Japan, and in 1966 and 1967 she was a visiting lecturer in India.

Unlike most of the scientific refugees arriving in the United States in the 1930’s, Mayer came voluntarily and not as a result of the Nazi racial laws. She was active in an organization formed to give aid to displaced German scientists in the 1930’s, but she still had family and close friends living in Germany during the war, and her feelings about celebrating V-E Day were ambivalent. In the same way, although she worked willingly on the Manhattan Project, she was also active in 1945 and 1946 in the campaign against military control of nuclear energy.

By the end of her life. Mayer was a highly respected member of the physics community. In addition to receiving the Nobel Prize, she was elected a member of the National Academy of Sciences and the American Philosophical Society and a fellow of the American Physical Society and the American Academy of Arts and Sciences. She was awarded five honorary D.Sc. degrees.

BIBLIOGRAPHY

I. OriginalWorks. The most complete bibliography of Mayer’s publications is in Robert G. Sachs, “Maria Goeppert Mayer,” in Biographical Memoirs National Academy of Sciences, 50 (1979), 311–328. Publications resulting from her doctoral dissertation are “Über die Wahrscheinlichkeit des Zusammenwirkens zweier Lichtquanten in einem Elementarakt,” in Die Naturwissenschaften, 17 (1929), 932; and “Über Elementarakte mit zwei Quantensprüngen,” in Annalen der Phvsik, 9 (1931), 273–294.

Mayer published five papers with Karl F. Herzfeld; among them are “On the Theory of Fusion,” in Physical Review, 2nd ser., 46 (1934), 995–1001; “On the States of Aggregation,” in Journal of Chemical Physics, 2 (1934), 38–45; and “On the Theory of Dispersion,” in Physical Review, 2nd ser., 49 (1936), 332–339. During the same period she wrote “The Entropy of Polyatomic Molecules and the Symmetry Number,” in Journal of the American Chemical Society, 55 (1933), 37–53, with Joseph E. Mayer and Stephen Brunauer; “The Polarizability of lons from Spectra,” in Physical Review, 2nd ser., 43 (1933), 605–611, written with Joseph E. Mayer; “Double Beta-Disintegration,” ibid., 2nd ser., 48 (1935), 512–516; and “Calculations of the Lower Excited Levels of Benzene,” in Journal of Chemical Physics, 6 (1938), 645–652, written with Alfred L. Sklar. Statistical Mechanics (New York, 1940; 2nd ed., 1977) was written with Joseph E. Mayer.

Between 1940 and 1945 Mayer wrote “Rare Earth and Transuranic Elements,” in Physical Review, 2nd ser., 60 (1941), 184–187; “Calculation of Equilibrium Constants for Isotopic Exchange Reactions,” in Journal of Chemical Physics, 15 (1947), 261–267, written with Jacob Bigeleisen; and “Vibrational Spectrum and Thermodynamic Properties of Uranium Hexafluoride Gas,” ibid., 16 (1948), 442–445, written with Jacob Bigeleisen, Peter C. Stevenson, and John Turkevich. See also Gerhard H. Dieke and A. B. F. Duncan, Spectroscopic Properties of Uranium Compounds (New York, 1949).

At the University of Chicago Mayer wrote two papers with Edward Teller: “On the Origin of the Elements,” in Physical Review, 2nd ser., 76 (1949), 1226–1231; and “On the Abundance and Origin of Elements,” in Les particules élémentaires: Institut International de Chimie Solvay: Huitieme Conseil de Physique, 1948 (Paris, 1950), 59–88.

Mayer’s development of the nuclear shell model is summarized in “On Closed Shells in Nuclei,” in Physical Review, 2nd ser., 74 (1948), 235–239; “On Closed Shells in Nuclei. II .” ibid., 2nd ser., 75 (1949), 1969–1970: “Nuclear Configurations in the Spin-Orbit Coupling Model. I . Empirical Evidence,” ibid., 2nd ser., 78 (1950), 16–21; “Nuclear Configurations in the Spin-Orbit Coupling Model. II . Theoretical Considerations,” ibid., 22–23; and Elementary Theory of Nuclear Shell Structure (New York, 1955), written with J. Hans D. Jensen. Mayer applied the shell model in a series of papers written between 1951 and 1965; “Nuclear Shell Structure and Beta Decay. I. Odd A Nuclei,” in Reviews of Modern Physics, 23 (1951), 315–321, written with Steven A. Moszkowski and Lothar Nordheim; “Electromagnetic Effects Due to Spin-Orbit Coupling,” in Physical Review, 2nd ser., 85 (1952), 1040–1041, written with J. Hans D. Jensen; “Classifications of β-Transitions,” in Kai Siegbahn, ed., Beta-and Gammaray Spectroscopy (New York, 1955), 433–452; “Statistical Theory of Asymmetric Fission,” in Ilya Prigogene, ed., Proceedings of the International Symposium on Transport Processes in Statistical Mechanics (New York, 1958), 187–191; and “The Shell Model: Shell Closure and jj Coupling,” in Kai Siegbahn, ed., Alpha-, Beta- and Gamma-Ray Spectroscopy, 1 (Amsterdam, 1965), 557–582, with J. Hans D. Jensen.

Mayer’s more general accounts of the nuclear shell model include “The Structure of the Nucleus,” in Scientific American, 184, no. 3 (1951), 22–26, 72; and “The Shell Model,” in Nobel Lectures: Physics, IV (Amsterdam, 1972), 20–37.

Mayer’s papers and correspondence, along with those of Joseph E. Mayer, are deposited in the Special Collections of Mandeville Library. University of California at San Diego.

II. Secondary Literature. For the most complete account of Mayer’s life and career, see Joan Dash. A Life of One’s Own: Three Gifted Women and the Men They Married (New York, 1973). See also Mary Harrington Hall, “The Nobel Genius,” in San Diego, 16 (1964), 64–69, 108–111; and Robert G. Sachs, “Maria Goeppert Mayer—Two-fold Pioneer,” in Physics Today, 35 , no. 2 (1982), 46–51.

For discussions of Mayer’s scientific contributions. See Karen E. Johnson,” Maria Goeppert Mayer and the Development of the Nuclear Shell Model” (Ph.D. diss., University of Minnesota, 1986), and “Maria Goeppert Mayer: Atoms, Molecules and Nuclear Shells,” in Physics Today, 39 no. 9 (1986), 44–49; Robert G. Sachs, in Biographical Memoirs. National Academy of Sciences (above); Harold C. Urey, “Maria Goeppert Mayer (1906–1972),” in American Philosophical society Year Book 1972 (1973), 234–236; and Eugene Wigner, “Maria Goeppert Mayer,” in Physics Today, 25 , no. 5 (1972), 77, 79. See also J. Hans D. Jensen, “Glimpses at the History of the Nuclear Structure Theory,” in Nobel Lectures: Physics, IV (Amsterdam, 1972), 40–50; and Peter Zacharias, “Zur Entstehung des Einteilchen-Schalenmodells,” in Annals of Science, 28 (1972), 401–411.

Karen E. Johnson

Maria Goeppert-Mayer

In 1963, Maria Goeppert-Mayer became the first woman to receive the Nobel Prize in physics. She earned the prize for her work on the structure of the atomic nucleus.

Maria Goeppert-Mayer was one of the inner circle of nuclear physicists who developed the atomic fission bomb at the secret laboratory at Los Alamos, New Mexico, during World War II. Through her theoretical research with nuclear physicists Enrico Fermi and Edward Teller, Goeppert-Mayer developed a model for the structure of atomic nuclei. In 1963, for her work on nuclear structure, she became the first woman awarded the Nobel Prize for theoretical physics, sharing the prize with J. Hans D. Jensen, a German physicist. The two scientists, who had reached the same conclusions independently, later collaborated on a book explaining their model.

An only child, Goeppert-Mayer was born Maria Göppert on July 28, 1906, in the German city of Kattowitz in Upper Silesia (now Katowice, Poland). When she was four, her father, Dr. Friedrich Göppert, was appointed professor of pediatrics at the University at Göttingen, Germany. Situated in an old medieval town, the university had historically been respected for its mathematics department, but was on its way to becoming the European center for yet another discipline—theoretical physics. Maria's mother, Maria Wolff Göppert, was a former teacher of piano and French who delighted in entertaining faculty members with lavish dinner parties and providing a home filled with flowers and music for her only daughter.

Dr. Göppert was a most progressive pediatrician for the times, as he started a well-baby clinic and believed that all children, male or female, should be adventuresome risk-takers. His philosophy on child rearing had a profound effect on his daughter, who idolized her father and treasured her long country walks with him, collecting fossils and learning the names of plants. Because the Göpperts came from several generations of university professors, it was unstated but expected that Maria would continue the family tradition.

When Maria was just eight, World War I interrupted the family's rather idyllic university life with harsh wartime deprivation. After the war, life was still hard because of postwar inflation and food shortages. Maria Göppert attended a small private school run by female suffragists to ready young girls for university studies. The school went bankrupt when Göppert had completed only two of the customary three years of preparatory school. Nonetheless, she took and passed her university entrance exam.

The University of Göttingen that Göppert entered in 1924 was in the process of becoming a center for the study of quantum mechanics—the mathematical study of the behavior of atomic particles. Many well-known physicists visited Göttingen, including Niels Bohr, a Danish physicist who developed a model of the atom. Noted physicist Max Born joined the Göttingen faculty and became a close friend of Göppert's family. Göppert, now enrolled as a student, began attending Max Born's physics seminars and decided to study physics instead of mathematics, with an eye toward teaching. Her prospects of being taken seriously were slim: there was only one female professor at Göttingen, and she taught for "love," receiving no salary.

In 1927 Göppert's father died. She continued her study, determined to finish her doctorate in physics. She spent a semester in Cambridge, England, where she learned English and met Ernest Rutherford, the discoverer of the electron. Upon her return to Göttingen, her mother began taking student boarders into their grand house. One was an American physical chemistry student from California, Joseph E. Mayer, studying in Göttingen on a grant. Over the next several years, Maria and Joe became close, going hiking, skiing, swimming and playing tennis. When they married, in 1930, Maria adopted the hyphenated form of their names. (When they later moved to the United States, the spelling of her family name was anglicized to "Goeppert.") Soon after her marriage she completed her doctorate with a thesis entitled "On Elemental Processes with Two Quantum Jumps."

After Joseph Mayer finished his studies, the young scientists moved to the United States, where he had been offered a job at Johns Hopkins University in Baltimore, Maryland. Goeppert-Mayer found it difficult to adjust. She was not considered eligible for an appointment at the same university as her husband, but rather was considered a volunteer associate, what her biographer Joan Dash calls a "fringe benefit" wife. She had a tiny office, little pay, and no significant official responsibilities. Nonetheless, her position did allow her to conduct research on energy transfer on solid surfaces with physicist Karl Herzfeld, and she collaborated with him and her husband on several papers. Later, she turned her attention to the quantum mechanical electronic levels of benzene and of some dyes. During summers she returned to Göttingen, where she wrote several papers with Max Born on beta ray decay—the emissions of high-speed electrons that are given off by radioactive nuclei.

These summers of physics research were cut off as Germany was again preparing for war. Max Born left Germany for the safety of England. Returning to the states, Goeppert-Mayer applied for her American citizenship and she and Joe started a family. They would have two children, Marianne and Peter. Soon she became friends with Edward Teller, a Hungarian refugee who would play a key role in the development of the hydrogen bomb.

When Joe unexpectedly lost his position at Johns Hopkins, he and Goeppert-Mayer left for Columbia University in New York. There they wrote a book together, Statistical Mechanics, which became a classic in the field. As Goeppert-Mayer had no teaching credentials to place on the title page, their friend Harold Urey, a Nobel Prize-winning chemist, arranged for her to give some lectures so that she could be listed as "lecturer in chemistry at Columbia."

In New York, Goeppert-Mayer made the acquaintance of Enrico Fermi, winner of the Nobel Prize for physics for his work on radioactivity. Fermi had recently emigrated from Italy and was at Columbia on a grant researching nuclear fission. Nuclear fission—splitting an atom in a way that released energy—had been discovered by German scientists Otto Hahn, Fritz Strassmann, and Lise Meitner. The German scientists had bombarded uranium nuclei with neutrons, resulting in the release of energy. Because Germany was building its arsenal for war, Fermi had joined other scientists in convincing the United States government that it must institute a nuclear program of its own so as not to be at Hitler's mercy should Germany develop a nuclear weapon. Goeppert-Mayer joined Fermi's team of researchers, although once again the arrangement was informal and without pay.

In 1941, the United States formally entered World War II. Goeppert-Mayer was offered her first real teaching job, a half-time position at Sarah Lawrence College in Bronxville, New York. A few months later she was invited by Harold Urey to join a research group he was assembling at Columbia University to separate uranium-235, which is capable of nuclear fission, from the more abundant isotope uranium-238, which is not. The group, which worked in secret, was given the code name SAM—Substitute Alloy Metals. The uranium was to be the fuel for a nuclear fission bomb.

Like many scientists, Goeppert-Mayer had mixed feelings about working on the development of an atomic bomb. (Her friend Max Born, for instance, had refused to work on the project.) She had to keep her work a secret from her husband, even though he himself was working on defense-related work, often in the Pacific. Moreover, while she loved her adopted country, she had many friends and relatives in Germany. To her relief, the war in Europe was over early in 1945, before the bomb was ready. However, at Los Alamos Laboratory in New Mexico the bomb was still being developed. At Edward Teller's request, Goeppert-Mayer made several visits to Los Alamos to meet with other physicists, including Niels Bohr and Enrico Fermi, who were working on uranium fission. In August of 1945 atomic bombs were dropped on the Japanese cities of Hiroshima and Nagasaki with a destructive ferocity never before seen. According to biographer Joan Dash, by this time Goeppert-Mayer's ambivalence about the nuclear weapons program had turned to distaste, and she was glad she had played a relatively small part in the development of such a deadly weapon.

After the war, Goeppert-Mayer returned to teach at Sarah Lawrence. Then, in 1946, her husband was offered a full professorship at the University of Chicago's newly established Institute of Nuclear Studies, where Fermi, Teller, and Urey were also working. Goeppert-Mayer was offered an unpaid position as voluntary associate professor; the university had a rule, common at the time, against hiring both a husband and wife as professors. However, soon afterwards, Goeppert-Mayer was asked to become a senior physicist at the Argonne National Laboratory, where a nuclear reactor was under construction. It was the first time she had been offered a position and salary that put her on an even footing with her colleagues.

Again her association with Edward Teller was valuable. He asked her to work on his theory about the origin of the elements. They found that some elements, such as tin and lead, were more abundant than could be predicted by current theories. The same elements were also unusually stable. When Goeppert-Mayer charted the number of protons and neutrons in the nuclei of these elements, she noticed that the same few numbers recurred over and over again. Eventually she began to call these her "magic numbers." When Teller began focusing his attention on nuclear weapons and lost interest in the project, Goeppert-Mayer began discussing her ideas with Enrico Fermi.

Goeppert-Mayer had identified seven "magic numbers": 2, 8, 20, 28, 50, 82, and 126. Any element that had one of these numbers of protons or neutrons was very stable, and she wondered why. She began to think of a shell model for the nucleus, similar to the orbital model of electrons spinning around the nucleus. Perhaps the nucleus of an atom was something like an onion, with layers of protons and neutrons revolving around each other. Her "magic numbers" would represent the points at which the various layers, or "shells," would be complete. Goeppert-Mayer's likening of the nucleus to an onion led fellow physicist Wolfgang Pauli to dub her the "Madonna of the Onion." Further calculations suggested the presence of "spin-orbit coupling": the particles in the nucleus, she hypothesized, were both spinning on their axes and orbiting a central point—like spinning dancers, in her analogy, some moving clockwise and others counter-clockwise.

Goeppert-Mayer published her hypothesis in Physical Review in 1949. A month before her work appeared, a similar paper was published by J. Hans D. Jensen of Heidelberg, Germany. Goeppert-Mayer and Jensen began corresponding and eventually decided to write a book together. During the four years that it took to complete the book, Jensen stayed with the Goeppert-Mayers in Chicago. Elementary Theory of Nuclear Shell Structure gained widespread acceptance on both sides of the Atlantic for the theory they had discovered independently.

In 1959, Goeppert-Mayer and her husband were both offered positions at the University of California's new San Diego campus. Unfortunately, soon after settling into a new home in La Jolla, California, Goeppert-Mayer suffered a stroke which left an arm paralyzed. Some years earlier she had also lost the hearing in one ear. Slowed but not defeated, Goeppert-Mayer continued her work.

In November of 1963 Goeppert-Mayer received word that she and Jensen were to share the Nobel Prize for physics with Eugene Paul Wigner, a colleague studying quantum mechanics who had once been skeptical of her magic numbers. Goeppert-Mayer had finally been accepted as a serious scientist. According to biographer Olga Opfell, she would later comment that the work itself had been more exciting than winning the prize.

Goeppert-Mayer continued to teach and do research in San Diego, as well as grow orchids and give parties at her house in La Jolla. She enjoyed visits with her granddaughter, whose parents were daughter Marianne, an astronomer, and son-in-law Donat Wentzel, an astrophysicist. Her son Peter was now an assistant professor of economics, keeping up Goeppert-Mayer's family tradition of university teaching.

Goeppert-Mayer was made a member of the National Academy of Sciences and received several honorary doctorates. Her health, however, began to fail. A lifelong smoker debilitated by her stroke, she began to have heart problems. She had a pacemaker inserted in 1968. Late in 1971, Goeppert-Mayer suffered a heart attack that left her in a coma. She died on February 20, 1972.

Further Reading

Dash, Joan, The Triumph of Discovery: Women Scientists Who Won the Nobel Prize, Messner, 1991.

Opfell, Olga S., The Lady Laureates: Women Who Have Won the Nobel Prize, Scarecrow, 1978, pp. 194-208.

Sach, Robert G., Maria Goeppert-Mayer, 1906-1972: A Biographical Memoir, National Academy of Science of the United States, 1979. □