Maria Mayer Shell Model

Maria Mayer And Her Shell Model Of Nuclear Physics

To date, 51 women have won the prestigious Nobel Prize in distinguished fields. Maria Mayer is one of these genius women, rather, the first woman ever to have earned this honor in the field of theoretical Nuclear Physics. However, many people believe that Marie Curie was the first woman to win it in this field.

No doubt, that Marie Curie was the first woman ever to have won this award in 1903, but, the lady won it for her work on Radioactivity (particularly radiation physics), not Nuclear Physics. The field of nuclear physics stemmed from the discovery of the atomic nucleus in the second decade of 1900. This article aims to learn about the lesser-known life of Maria Mayer and what lead her way to the Nobel Prize.

Maria Goeppert Mayer
Image courtesy: wikipedia
Maria Goeppert Mayer
Image courtesy: wikipedia

Early life and Education :

Maria Mayer was born on June 28, 1906, in Kattowitz, which was part of Germany at that time. In 1910, her family moved to Göttingen, where her father was a professor of pediatrics. Maria’s father always encouraged her to grow up to be more than a housewife. After attending public school and a college preparatory academy for girls, in 1924 she entered the University of Göttingen.

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At first, she intended to study mathematics. But after attending Max Born’s quantum mechanics seminar, she switched her focus to physics. Consequently, she completed her Ph.D. in 1930, with a brilliant thesis on double photon reactions.

Marriage and the struggle for recognition:

After completing her Ph.D., she married the American chemical physicist Joseph E. Mayer. Together they moved to Baltimore, United States. For years after moving to the United States, nepotism played its part. Despite being highly deserving, Maria Mayer was still only getting offered jobs with no pay or unofficial jobs in University laboratories. But the lady never gave up!

Joseph E Mayer and Maria Mayer
Image courtesy: Science photo library
Joseph E Mayer and Maria Mayer
Image courtesy: Science photo library

Over the next nine years, she got associated with Johns Hopkins as a volunteer associate. During that time she collaborated with Karl Herzfeld and her husband in the study of organic molecules. She became a U.S. citizen in 1933 and after six years, in1939, she and her husband both received appointments in chemistry at Columbia University, where Maria Mayer worked on the separation of uranium isotopes for the atomic bomb project. The Mayers published Statistical Mechanics in 1940 and remained at Columbia throughout World War II.

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The Groundbreaking discovery and the Nobel Prize :

However, after World War II, Maria shifted her focus to nuclear physics, unknowingly setting herself on a path to the most groundbreaking discovery of her life. During that time, studying the nuclear structure and magic numbers was one of the hottest topics of research. In 1937, Neils Bohr and F. Kalcar proposed the Liquid drop model of the nucleus, where the atomic nucleus was compared to a liquid drop.

Although this model is of utmost importance to understand some of the basics of binding energies, it could not explain why some nuclei having protons or neutrons or both as 2, 8, 20, 28, 50, 82, 126 (magic numbers) have higher binding energies, making them more stable than others. This led scientists to find a better model for enhanced explanations. This is where Maria Mayer’s shell model came into the picture.

No doubt, the shell model was first proposed by Dmitry Ivanenko in 1932. But, to understand the ambiguity about magic numbers, it was further developed independently by Maria Mayer along with some other physicists in 1949. The nuclear shell model is partly analogous to the atomic shell model which describes the arrangement of electrons in an atom, in that a filled shell resulting in greater stability.

Magic numbers as explained by the Shell Model
Image courtesy: wikipedia
Magic numbers as explained by the Shell Model
Image courtesy: wikipedia

This model proved instrumental in explaining the existence of magic numbers and the stability and high binding energy on the basis of closed shells. It also provided an explanation for the ground state spins and the magnetic dipole moment of nuclei. This enhancement of the shell model helped Maria Mayer to step up to the podium in Stockholm, Sweden to accept the Nobel Prize in Physics in 1963.

Other notable works :

Most of Maria’s other works, which are not as well known, demonstrate her 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 Mayer And Her Shell Model Of Nuclear Physics 2
Maria Mayer

During World War II, she contributed significantly as a member of the Manhattan Project team. She also worked as a lecturer in some distinguished institutes. This includes accepting an appointment at the University of California at San Diego in 1960.

Goeppert-Mayer died due to heart failure in San Diego, California, on February 20, 1972, aged 65. Maria’s life is nothing short of an inspiration. Though she faced some problems at the beginning of her career, her perseverance helped her pave her way through all the obstacles, consequently winning the highest honor in the field of Science. Happy Birthday, Maria!

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7 thoughts on “Maria Mayer And Her Shell Model Of Nuclear Physics”

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  2. Goeppert and Mayer’s book on shell structure was instrumental in leading to my discovery some years back that intruder levels inserted themselves nucleon countwise into the previous shell structures in a sequence that follows doubled triangular numbers. Pascal Triangle combinatorics mathematically motivate shell structures. This is because the quantum harmonic oscillator always delivers numbers of stable states whose sizes are terms in Pascal Triangle diagonals. The only variable is the dimensionality of the oscillator system. The more dimensions, the deeper into the Triangle the utilized diagonal is. For the spherical nucleus, each shell size is a doubled triangular number: 1s=2, 1p=6, 1d2s=12, 1f2p=20, 1g2d3s=30, 1h2f3p=42 and so on. Thus the harmonic oscillator magic numbers, reflecting summations of shells, are all sized as doubled tetrahedral numbers: 2, 8, 20, 40, 70, 112, 168 and so on. It turned out that for spherical shells in the more realistic spin-orbit model intruder 1g9/2 inserted 2 moves (nucleons) from its harmonic oscillator position. 1h11/2 6 moves; 1i13/2 12 moves, 1j15/2 20 moves. All this is due to the internal structure of the shells following the Pascal Triangle combinatorics- the intruders cannot break up a spin-split orbital partial. It also turns out that except for one possible anomaly in the proton shell structure, ALL intruder levels in spherical shells insert exactly after THREE spin-split orbital partials from the previous shell have filled, and even with this anomaly the depth of insertion (20 rather than the expected 12) is still a doubled triangular number.

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