Hartree-Fock perturbation theory for systems with one-particle perturbation

The Hartree-Fock perturbation theory for theN-electron system with a one-particle perturbation is rederived using the resolvent operator formalism. It is shown that the second-order contribution to the total energy can be expressed in a compact form using a properly defined effective one-particle operator. Relations of the Hartree-Fock perturbation theory with both the many-body theory and the regular Hartree-Fock formalism are discussed.