Ab initio-driven nuclear energy density functional method

Abstract

Abstract. This programmatic paper lays down the possibility to reconcile the necessity to resum many-body correlations into the energy kernel with the fact that safe multi-reference energy density functional (EDF) calculations cannot be achieved whenever the Pauli principle is not strictly enforced, as is for example the case when many-body correlations are parametrized under the form of empirical density dependencies. Our proposal is to exploit a newly developed ab initio many-body formalism to guide the construction of safe, explicitly correlated and systematically improvable parametrizations of the off-diagonal energy and norm kernels that lie at the heart of the nuclear EDF method. The manybody formalism of interest relies on the concepts of symmetry breaking and restoration that have made the fortune of the nuclear EDF method and is, as such, amenable to this guidance. After elaborating on our proposal, we briefly outline the project we plan to execute in the years to come. PACS

Properties of nuclei in the nobelium region studied within the covariant, Skyrme, and Gogny energy density functionals

“…Only very recently this route was started to be explored in non-relativistic EDFs, see, Refs. [83][84][85][86][87][88][89][90][91], so its eventual impact on the physics discussed here is not yet known. …”

From the liquid drop model to lattice QCD

“…The former showed typically an underbinding that was increasing with A. In the latter, the saturation point 20 was predicted at too high density and energy, see Fig. 14.…”

“…These pathologies are not present if one follows the original route that requires starting with a Hamiltonian operator. In order to tackle these shortcomings, novel formal developments are being proposed on several aspects including possible connections with ab initio approaches [20,21].…”

Nuclear density functional theory

“…The systematic construction of exchange-correlation functionals based on the state-of-the-art calculations of the electron gas does not have a real counterpart in nuclear physics, despite some attempts to start from Brueckner-Hartree-Fock calculations and build the volume part of an EDF [106], or a Skyrme interaction [107,108]. The strategy proposed in Ref [59] has still to be developed, and also in the case of EDFs built around the idea of symmetry breaking and restoration [109] there are still steps to be undertaken in order to include all correlations from many-body perturbation theory, overcoming the technical difficulties. The most general program for an ab initio-based DFT, that has been outlined in Ref [110], based on the idea of the Legendre transformation of the effective action, is even more in its infancy.…”