Direct Matrix Elements of Spin– Other-Orbit Interaction in Configurations with p and h Electrons in Outer Shells

Abstract

The direct matrix elements of the energy operator for the npn′h and np5n′h configurations are determined taking into account the spin–other-orbit interaction. Direct matrix elements, together with exchange ones, are intended for further numerical calculation of fine structure parameters and other characteristics of atoms, such as gyromagnetic ratios. The coefficients for radial integrals are calculated in the singleconfiguration approximation, in the formalism of irreducible tensor operators, and in two representations: LSJM and the representation of unrelated moments. A formula has been derived for calculating the direct matrix elements of the considered configurations in the representation of unrelated moments. It has been carefully tested on small rank matrices with M = ±7 (1 rank) and M = ±6 (4 rank). The calculation of all other direct matrix elements has been performed for a matrix with M = 0 (12 rank). The values obtained have been transformed into the LSJM-representation using the matrix of Clebsch-Gordan coefficients and compared with an independent calculation in the LSJM-representation. The complete agreement of direct matrix elements of the interaction considered in two different calculation schemes indicates the reliability of the results obtained.