Higher-order energy density functionals in nuclear self-consistent theory

Abstract

In this thesis consisting of two publications and an overview part, a study of two aspects of energy density functionals has been performed. Firstly, we have linked the next-to-next-to-next-to-leading order nuclear energy density functional to a zero-range pseudopotential that includes all possible terms up to sixth order in derivatives. Within the Hartree-Fock approximation, the quasi-local nuclear Energy Density Functional (EDF) has been calculated as the average energy obtained from the pseudopotential. The direct reference of the EDF to the pseudopotential acts as a constraint that allows for expressing the isovector coupling constants functional in terms of the isoscalar ones, or vice versa. The constraints implemented in this way imply a reduction by a factor of two of the number of the free coupling constants in the functional. Three main applications have been studied: we have considered the functional restricted by the Galilean symmetry, gauge symmetry, and again Galilean symmetry along with the spherical symmetry. As second aspect concerning the next-to-next-to-next-to-leading order nuclear energy density functional, we analyzed conditions under which the continuity equation is valid for functionals or pseudopotentials built of higher-order derivatives. We derived constraints on the coupling constant of the energy density functional that guarantee the validity of the continuity equation in all spinisospin channels. We also linked these constraints to local gauge symmetries for abelian and non-abelian groups.