Self-consistent solution of Dyson's equation up to second order for atomic systems

摘要

In this paper, the single-particle Green's function approach is applied to the atomic many-body problem. We present the self-consistent solution of the Dyson equation up to second order in the self-energy for nonrelativistic spin-compensated atoms. This Dyson second-order scheme requires the solution of the Hartree-Pock integro-differential equations as a preliminary step, which is performed in coordinate space (i.e., without an expansion in a basis set). To cope with the huge amount of poles generated in the iterative approach to tackle Dyson' s equation in second order, the BAGEL (BAsis GEnerated by Lanczos) algorithm is employed. The self-consistent scheme is tested on the atomic systems He, Be, Ne,Mg, and Arwith spin-saturated ground state 1 S 0. Predictions of the total binding energy, ionization energy, and single-particle levels are compared with those of other computational' schemes [density functional theory, Hartree-Pock (HP), post-HP, and configuration interaction} and with experiment. The correlations included in the Dyson second-order algorithm produce a shift of the Hartree- Pock single-particle energies that allow for a close agreement with experiment.