Account for the spin-spin interaction in the energy matrices of two-electron configurations with p and f electrons

Expressions are presented for calculation of the matrix elements of the energy operator for the spin-spin interaction (direct and exchange terms in the single-configuration approximation) in the LSJM representation (the LS-coupling scheme) and in the representation of uncoupled angular momenta. The formulas for the case of permutation of electrons (the fp configuration) are discussed in detail. The matrix elements for the electron pf configuration are derived in both representations, while the matrix elements for the hole p(5)f configuration are obtained in the uncoupled angular momentum representation only. All the calculations are performed in the formalism of irreducible tensor operators. The spin-spin interaction is represented in the two-electron energy matrix by four radial integrals of the Marvin spin interactions: by three direct integrals S-1, S-2, and S'(2) and one exchange integral S-3.