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Australian Journal of Physics

Symmetrical Coupling Of Angular Momenta

Published Jan 1, 1966• 9 citations
Publisher

Abstract

An expression is given for the integral over the domain of Euler angles of a product of any number of rotation matrices. As a result a scheme has been set up in which any number of angular momenta may be coupled on an equal footing. Explicit algebraic exp
DOI
10.1071/ph660719

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We give manifest rotation symmetric expressions for eigenfunctions for spin s , orbital angular momentum l and total angular momentum j = l + s ,...,| l - s | in terms of (2 j + 1) × (2 s + 1) multipole transition matrices (MTM). These matrices, which are irreducible tensor matrices, have an algebra together with ordinary spin matrices for spin s and spin j . Explicit expressions for MTM's and their algebra are given for angular momenta ⩽ 3. By means of some examples we show that within this formalism angular integrations in central field problems will be simplified considerably. Thus the formalism turns out to be very useful for instance for calculations within the MIT-bag and also within spin-spin interactions in atomic physics.