From Nucleons to Nucleus pp 3-21 | Cite as

# Angular Momentum Coupling

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## Abstract

In nuclear physics, as also in atomic and molecular physics, the entities to be described consist of sub-entities with some orbital angular momentum and spin. The angular momentum of the entity is built, then, of the angular momenta of the sub-entities. This building process leads to quantum-mechanical angular momentum coupling. This chapter presents the basic machinery for treating angular momentum and its coupling. Clebsch-Gordan coefficients and 3*j* symbols are introduced. It is shown that Clebsch-Gordan coefficients and 3*j* symbols relate to the coupling of two angular momenta. Increasing the number of angular momenta to be coupled leads to more complicated coupling patterns. Transformations between different coupling schemes are mediated by 6*j* symbols and 9*j* symbols, relating to the coupling of three and four angular momenta respectively. A host of special relations and special cases are listed to make the manipulations of angular momentum algebra easier and more straightforward in the physical applications of the chapters to come.

## Keywords

Angular Momentum Quantum Number Orbital Angular Momentum Total Angular Momentum Coupling Scheme## Preview

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