In order to obtain accurate values of atomic quantities it is necessary to account for relativistic and correlation effects (see for example Froese Fischer et al [1]). Relativistic effects may be taken into account as Breit-Pauli corrections or in a fully relativistic approach. In both cases for complex atoms and ions, a considerable part of the effort must be devoted to integrations over spin-angular variables, occurring in the matrix elements of the operators under consideration.
Many existing codes for integrating are based on a scheme first proposed by Fano [2]. In this approach, the integrations over spin-angular variables constitute a considerable part of the computation, especially when atoms with many open shells are treated, and the operators are non-trivial. Over the last decade, an efficient approach for finding matrix elements of any one- and two-particle atomic operator between complex configurations has been developed (see papers Gaigalas and Rudzikas [3] (later on referred to as P1), Gaigalas et al [4] (later on referred to as P2), Gaigalas et al [5] (later on referred to as P3), and Gaigalas et al [6] (later on referred to as P4)). It is free of the shortcomings of previous approaches (see Gaigalas [7]). This method is introduced in the library SAI prsented in this paper. It extends other program's in atomic physic capabilities and has resulted in faster execution of angular integrations.