Calculation of unit tensor operators using a restricted set of Slater determinants

•We demonstrate a new, simple, and robust method to calculate atomic data.•We show that the Wigner-Eckart theorem can be used to obtain reduced matrix elements from a small set of magnetic sublevels.•We describe the implementation of this method in the code ALICE II.

In this paper we present a new result involving the properties of the Clebsch-Gordan coefficients well-used in atomic physics. We also demonstrate a practical use of this result: a new and simple method of calculation of unit tensor operators of multi-electron atoms while working within the Slater-Condon scheme. This results in a significant increase in the ease of implementation of multi-electron atomic physics models, and we discuss the computational complexity of the resulting algorithm.