Quasiparticles in Neon using the Faddeev Random Phase Approximation

The spectral function of the closed-shell Neon atom is computed by expanding the electron self-energy through a set of Faddeev equations. This method describes the coupling of single-particle degrees of freedom with correlated two-electron, two-hole, and electron-hole pairs. The excitation spectra are obtained using the Random Phase Approximation, rather than the Tamm-Dancoff framework employed in the third-order algebraic diagrammatic contruction [ADC(3)] method. The difference between these two approaches is studied, as well as the interplay between ladder and ring diagrams in the self-energy. Satisfactory results are obtained for the ionization energies as well as the energy of the ground state with the Faddeev-RPA scheme that is also appropriate for the high-density electron gas.