A model describing nucleon energy levels in a nucleus, predicting properties like lifetimes and transition probabilities.The nuclear shell model describes the structure of atomic nuclei by arranging protons and neutrons into discrete energy levels, or shells, analogous to the electron shells in atoms. It explains why certain numbers of nucleons (2, 8, 20, 28, 50, 82, 126) are particularly stable — these are the 'magic numbers' where shells are completely filled. The model predicts nuclear properties such as spin, parity, and the lifetimes of excited states, and it is essential for understanding nuclear stability and radioactive decay.
The model was developed independently by Maria Goeppert Mayer and Hans Jensen in 1949, who introduced the concept of spin-orbit coupling to correctly reproduce the magic numbers. They shared the Nobel Prize in Physics in 1963 for this work.
Nucleons move in a mean potential created by all the other nucleons. Quantum mechanics dictates that they occupy discrete energy levels, and the Pauli exclusion principle prevents two identical nucleons from occupying the same state. When a shell is filled, the nucleus is especially tightly bound. Excited states occur when a nucleon jumps to a higher shell, and the model calculates the probabilities of transitions between these states, which correspond to gamma-ray emissions or particle decays.
It is used to predict the properties of isotopes for nuclear energy, medical isotopes, and to understand the synthesis of heavy elements in stars and supernovae.
The magic number 126 is the highest that has been observed in stable nuclei, but scientists are searching for an 'island of stability' around element 114, where the shell model predicts unusually long-lived superheavy nuclei.





