A Hermitian open-shell many-body perturbation theory for treating intruder states

Abstract

In this paper we have formulated an open-shell many-body perturbation theory (mbpt) that applies to an incomplete model space. The effective Hamiltonian H^eff generated in our theory is hermitian. We follow the resolvent-operator based time-dependent formulation ofmbpt of Banerjeeet al, and show quite generally that, by classifying the various determinants spanning the Hilbert space as model valence space P, virtual valence space R and virtual space Q, a diagrammatic MBPT satisfying size consistency can be developed. The chief new features of the theory are (i) manifest hermiticity of H^eff; (ii) presence of disconnected diagrams no part of which is a legitimate diagram (irreducible disconnected diagrams); (iii) presence of folded diagrams with components that may be irreducible disconnected diagrams; (iv) a consistent treatment of the variousn-valence sectors of the Hilbert space that may be interacting through H ^eft if valence-holes are present-in particular a modified treatment of the core-valence separation. The generalisation afforded by the theory offers useful conceptual as well as computational advantages because the convergence difficulty encountered in a complete valence space formulation may be bypassed here by keeping the offending valence space determinants out of the model space. A brief critique of the developmentvis-a-vis the only other general model space development leading to a nonhermitian H^eff is also given.