Matrix elements of the electric multiple transition and relativistic correction operators in the case of complex configurations

Operators and their submatrix elements are studied in the framework of the electric multipole transitions of complex atoms with account of relativistic corrections of the order of the square of the fine structure constant. The analysis is performed by means of irreducible tensor operators and genealogical coefficients. It has been assumed that angular momenta of individual shells are coupled with each other according to ls, lk, jk and jj coupling. Formulas are given for the operator which causes the relativistic corrections for the single-electron multipole transition and for its submatrix element in the case of configurations with two unfilled shells. A possibility is discussed of using the formulas suggested for calculation. As follows from analysis, the relativistic correction operators even with the pure ls coupling allow intercombination transitions with ΔS equals +-1. The expressions obtained may turn out to be useful for performing calculations in the case of the intermediate type of coupling