New formulation of the random-phase approximation of atomic physics

The equations of the random-phase approximation (RPA), completely describing excitation energies and transition matrix elements for N-electron atomic systems, are reformulated in the language of Hartree-Fock theory, for single-particle orbitals. RPA is shown to be fully equivalent to the solution of a coupled Hartree-Fock-like problem, in the field of a (N-1)-electron system. By neglecting coupling effects, a convenient computational model of the literature is recovered.