Coupled tensorial forms of the second-order effective Hamiltonian for open-subshell atoms in jj-coupling

General expressions for the second-order effective atomic Hamiltonian are derived for open-subshell atoms in jj-coupling. The expansion terms are presented as N  -body (N=0,1,2,3)(N=0,1,2,3) effective operators given in the second quantization representation in coupled tensorial form. Two alternative coupled tensorial forms for each expansion term have been developed. To reduce the number of expressions of the effective Hamiltonian, the reduced matrix elements of antisymmetric two-particle wavefunctions are involved in the consideration. The general expressions presented allow the determination of the spin-angular part of expansion terms when studying correlation effects dealing with a number of problems in atomic structure calculations.