Maple procedures for the coupling of angular momenta I. Data structures and numerical computations

The theory of angular momentum and of spherieal tensor operators leads to algebrair expressions which arc usually written in terms of generalized Clebsch-Gordan coefficients and/or Wigner n - j symbols. In principle, the evaluation and simplification of such expressions is a straigthforward task but it can also become extremely cumbersome in more complex applications, for instance, in atomic and nuclear structure theory or in the study of angular dependent properties. In these fields, simplification techniques arc cither based on graphical methods or on the explicit knowledge of special values and sum rules which can be found in some standard form in the literature. The direct application of these rules, however, is often laborious due to a large number of symmetric forms of the Wigner and related symbols and due to the complexity of the expressions in Racah algebra.In order to facilitate the evaluation of Racah algebra expressions a set of Maple procedures is presented for interactive work. In this paper, I first define proper data structures to deal with Racah algebra. These structures are the basis to provide procedures for various numerical computations. The use of recursion formulas and simplifications of typical expressions due to special values is also supported here. The impact of this interactive tool on atomic many-body perturbation theory is briefly discussed.