Symmetry Energy I: Semi-Infinite Matter

TL;DR

This paper investigates the role of neutron-proton asymmetry and symmetry energy in nuclear matter using macroscopic models, density functional theory, and Skyrme-Hartree-Fock calculations, revealing universal relations and parameter dependencies.

Contribution

It extends symmetry energy considerations from energy formulas to the Hohenberg-Kohn functional and tests these relations with Skyrme-Hartree-Fock calculations for semi-infinite nuclear matter.

Findings

Isoscalar and isovector densities exhibit universal relations.

Surface symmetry coefficients vary with symmetry energy slope.

Surface-to-volume symmetry coefficient ratio increases with symmetry energy slope.

Abstract

Energy for a nucleus is considered in macroscopic limit, in terms of nucleon numbers. Further considered for a nuclear system is the Hohenberg-Kohn energy functional, in terms of proton and neutron densities. Finally, Skyrme-Hartree-Fock calculations are carried out for a half-infinite particle-stable nuclear-matter. In each case, the attention is focused on the role of neutron-proton asymmetry and on the nuclear symmetry energy. We extend the considerations on the symmetry term from an energy formula to the respective term in the Hohenberg-Kohn functional. We show, in particular, that in the limit of an analytic functional, and subject to possible Coulomb corrections, it is possible to construct isoscalar and isovector densities out of the proton and neutron densities, that retain a universal relation to each other, approximately independent of asymmetry. In the so-called local approximation, the isovector density is inversely proportional to the symmetry energy in uniform matter at the local isoscalar density. Generalized symmetry coefficient of a nuclear system is related, in the analytic limit of a functional, to an integral of the isovector density. We test the relations, inferred from the Hohenberg-Kohn functional, in the Skyrme-Hartree-Fock calculations of half-infinite matter. Within the calculations, we obtain surface symmetry coefficients and parameters characterizing the densities, for the majority of Skyrme parameterizations proposed in the literature. The volume-to-surface symmetry-coefficient ratio and the displacement of nuclear isovector relative to isoscalar surfaces both strongly increase as the slope of symmetry energy in the vicinity of normal density increases.