Ab initioself-consistent Gorkov-Green's function calculations of semi-magic nuclei: Numerical implementation at second order with a two-nucleon interaction

Abstract

The newly developed Gorkov-Green's function approach represents a promising\npath to the ab initio description of medium-mass open-shell nuclei. We discuss\nthe implementation of the method at second order with a two-body interaction,\nwith particular attention to the numerical solution of Gorkov's equation.\nDifferent sources of theoretical error and degrees of self-consistency are\ninvestigated. We show that Krylov projection techniques with a multi-pivot\nLanczos algorithm efficiently handle the growth of poles in the one-body\nGreen's function when Gorkov's equation is solved self-consistently. The end\nresult is a tractable, accurate and gently scaling ab initio scheme applicable\nto full isotopic chains in the medium-mass region.\n