Self-consistent polarization propagator approximation as a modified random phase method

A formal scheme is developed for finding the particle-hole propagator by means of a self-consistent decoupling procedure analogous to the Hartree-Fock decoupling for the electron propagator. The self-consistency comes from a contour integration of the Fourier transform of the propagator, utilizing a method introduced by Coulson. The method yields oscillator strengths and excitation energies, as well as the two-particle density matrix, which allows any one- or two-particle operator expectation value to be evaluated. The stability of the scheme is discussed, and comparisons with other, related, approximations are made.