# Magic Numbers in the Nuclear Shell Model

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The nuclear shell model is an analog of the Aufbau principle, which describes the electronic structure of atoms. It was developed independently in 1949 by Maria Goeppert-Mayer and by J. Hans D. Jensen and coworkers. Goeppert-Mayer and Jensen shared the 1963 Nobel Prize in physics. According to the shell model, nuclear energy levels, individually for neutrons and protons, are filled successively, in conformity with the Pauli exclusion principle. Just as in the atomic case, there are certain "magic numbers" in the occupancy of nucleon shells: 2, 8, 20, 28, 50, 82, and 126, which confer enhanced stability to nuclei. (This is analogous to the atomic magic numbers 2, 10, 18, 36, 54, 86.)

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Contributed by: S. M. Blinder (July 2009)

Open content licensed under CC BY-NC-SA

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"Magic Numbers in the Nuclear Shell Model"

http://demonstrations.wolfram.com/MagicNumbersInTheNuclearShellModel/

Wolfram Demonstrations Project

Published: July 31 2009