Model nuclear energy density functionals derived from ab initio calculations

Abstract

This monograph focused on a method to link nuclear energy density functionals to the ab initio solution of the nuclear many-body problem. This method, proposed in Ref. [1], was here discussed in many aspects as well as applied to a state-of-art ab initio approach. We introduced the basis of the density functional theory, paying attention to the concept of generators of the functional. In parallel, we explored the Self-Consistent Green's Function approach as ab initio framework to calculate ground-state energies. We derived the model functional based on the Levy-Lieb constrained variation, which exploited the response of the nucleus to an external perturbation. Using the Green's function technique and the NNLOsat chiral interaction in the ab initio Hamiltonian, seven semi-magic nuclei were probed with perturbations induced by generators of two- and three-body contact interaction (Skyrme-like). We employed the same generators to built model functionals, whereupon the coupling constants were fitted to reproduce the perturbed ground-state energies. Several parametrizations of the functionals were obtained for given choices of generators, selection of data points, and assumed uncertainties. We analysed the derived parametrizations according to their statistical performances, magnitude of the propagated errors, and corresponding nuclear matter description. Two parametrizations emerged as the most promising, but the model functionals built from them did not produce meaningful results. As it turned out, zero-range generators provided a poor description of the chiral interaction. Moreover, the performed error analysis suggested that the actual precision of the ab initio approach may not be sufficient to improve the quality of the novel energy density functionals.