The accuracy of the Faddeev random phase approximation (FRPA) method is tested by evaluating total and ionization energies in the basis-set limit. A set of light atoms up to Ar is considered. Comparisons are made with the results of coupled-cluster singles and doubles (CCSD), with third-order algebraic diagrammatic construction [ADC(3)], and with the experiment. It is seen that even for two-electron systems, He and Be ${}^{2+}$ , the inclusion of RPA effects leads to satisfactory results, and therefore it does not overcorrelate the ground state. The FRPA becomes progressively better for larger atomic numbers, where it gives $\ensuremath{\approx}$5 mH more correlation energy, and it shifts ionization potentials by 2--10 mH with respect to the similar ADC(3) method. The ionization potentials from FRPA tend to reduce the discrepancies with the experiment.The accuracy of the Faddeev random phase approximation (FRPA) method is tested by evaluating total and ionization energies in the basis-set limit. A set of light atoms up to Ar is considered. Comparisons are made with the results of coupled-cluster singles and doubles (CCSD), with third-order algebraic diagrammatic construction [ADC(3)], and with the experiment. It is seen that even for two-electron systems, He and Be${}^{2+}$, the inclusion of RPA effects leads to satisfactory results, and therefore it does not overcorrelate the ground state. The FRPA becomes progressively better for larger atomic numbers, where it gives $\ensuremath{\approx}$5 mH more correlation energy, and it shifts ionization potentials by 2--10 mH with respect to the similar ADC(3) method. The ionization potentials from FRPA tend to reduce the discrepancies with the experiment.

arXiv:1004.2607Physical Review AJan 3, 20128 citations

Quasiparticles in neon using the Faddeev random-phase approximation

C. Barbieri, Dimitri Van Neck, Willem H Dickhoff

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 (RPA), rather than the Tamm-Dancoff framework employed in the third-order algebraic diagrammatic construction 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, which is also appropriate for the high-density electron gas.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 (RPA), rather than the Tamm-Dancoff framework employed in the third-order algebraic diagrammatic construction 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, which is also appropriate for the high-density electron gas.

arXiv:0704.1542Physical Review ANov 6, 200747 citations

Self-Consistent Random Phase Approximation

Daniel R. Rohr, Maria Hellgren, Eberhard K. U. Gross

Bulletin of the American Physical SocietyFeb 29, 20120 citations

An extension of the random phase approximation

João da Providência

Nuclear Physics AFeb 1, 196843 citations

{}^{2+}

, the inclusion of RPA effects leads to satisfactory results, and therefore it does not overcorrelate the ground state. The FRPA becomes progressively better for larger atomic numbers, where it gives $\ensuremath{\approx}$5 mH more correlation energy, and it shifts ionization potentials by 2--10 mH with respect to the similar ADC(3) method. The ionization potentials from FRPA tend to reduce the discrepancies with the experiment.