Standard atomic operators and Coulomb interaction operator in the quasispin space

Atomic operators can be expressed in the terms of standard operators acting in the spin, orbital and quasispin spaces. Expressions for the tensorial p roducts of such standard operators for d(N), f(N) and g(N) shells are obtai ned in terms of some simple operators and a minimal number of operators hav ing nondiagonal matrix elements. These formulas are used to derive the expa nsion for the Coulomb interaction operator and to investigate some of its p roperties. The sum rule for the coefficients f(k) as well as some algebraic relations for the main part of the Coulomb interaction energy are given. T he symmetry of these coefficients and of their linear combinations for the ground state of atoms are considered.