Nuclear Shell Model
The nuclear shell model treats nucleons as moving independently in an average potential, with filled shells explaining the special stability of nuclei at the magic numbers.
Definition
The nuclear shell model is a description of the nucleus in which each nucleon moves nearly independently in an average potential created by all the others, occupying quantized energy levels grouped into shells whose closure at magic numbers confers extra stability.
Scope
This topic covers the independent-particle description of the nucleus, in which protons and neutrons fill quantized single-particle levels in a mean-field potential. It treats the crucial role of the strong spin-orbit interaction in reproducing the observed magic numbers 2, 8, 20, 28, 50, 82, and 126, and the model's success in predicting nuclear spins, parities, and magnetic moments for nuclei near closed shells.
Core questions
- How can nucleons be treated as independent particles despite the strong forces between them?
- What is the origin of the magic numbers of enhanced nuclear stability?
- Why is a spin-orbit interaction essential to reproduce the observed shell structure?
- How does the model predict ground-state spins and parities of nuclei?
Key concepts
- Mean-field potential
- Single-particle energy levels
- Spin-orbit coupling
- Magic numbers
- Closed shells
- Ground-state spin and parity
Key theories
- Spin-orbit shell model
- Goeppert Mayer and Jensen showed that adding a strong spin-orbit coupling to the mean-field potential splits the single-particle levels in just the way needed to reproduce all the observed magic numbers.
- Single-particle predictions
- For nuclei with one nucleon outside a closed shell, the model predicts the ground-state spin and parity from the orbital of the unpaired nucleon, in good agreement with measurement.
Clinical relevance
The shell model accounts for the enhanced stability and abundance of magic nuclei, guides the prediction of nuclear properties used in astrophysical nucleosynthesis and reactor physics, and motivates searches for new regions of stability such as the predicted island of superheavy elements.
History
Persistent regularities in nuclear stability at particular nucleon numbers resisted explanation until 1949, when Maria Goeppert Mayer and, independently, the group of Haxel, Jensen, and Suess recognized that a strong spin-orbit interaction reorders the nuclear levels to yield the magic numbers. The achievement earned Goeppert Mayer and Jensen a share of the 1963 Nobel Prize in Physics and made the shell model a cornerstone of nuclear theory.
Key figures
- Maria Goeppert Mayer
- Hans Jensen
- Eugene Wigner
Related topics
Seminal works
- mayer1949
- haxel1949
Frequently asked questions
- What are the nuclear magic numbers?
- They are the proton or neutron numbers 2, 8, 20, 28, 50, 82, and 126, at which a nuclear shell is filled. Nuclei with these numbers are more tightly bound and more stable than their neighbors.
- Why is spin-orbit coupling so important in the shell model?
- Without a strong spin-orbit interaction, a simple potential predicts the wrong magic numbers. The spin-orbit term splits the levels in just the right way to reproduce the experimentally observed shell closures.