Graphical evaluation of relativistic matrix elements

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Abstract
A graphical representation of angular momentum is used to evaluate relativistic matrix elements between antisymmetrized states of many- particle configurations having any number of open shells. The antisymmetrized matrix element is expanded as a sum of semisymmetrized matrix elements, which can be evaluated expediently in terms of radial integrals from easily constructed diagrams. The diagram representing a semisymmetrized matrix element is composed of four diagram blocks, namely, the bra block, the ket block, the spectator block, and the interaction block. The first three blocks indicate the couplings of the two interacting configurations while the last depends on the interaction and is the replaceable component. Interaction blocks for relativistic operators and commonly used potentials are summarized in ready-to-use forms. A simple step-by-step procedure is prescribed generally for calculating antisymmetrized matrix elements of one- and two-particle operators. A modified covarient 3-jm coeffecient is also introduced along with certain new graphical notations. Although we focus on the case of jj-coupled states, which comes naturally in relativistic formulation, the general procedure holds in any coupling scheme.

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