Hartree-Fock calculations in the density matrix expansion approach

Abstract

The density matrix expansion is used to derive a local energy density functional for finite range interactions with a realistic meson exchange structure. Exchange contributions are treated in a local momentum approximation. A generalized Slater approximation is used for the density matrix where an effective local Fermi momentum is chosen such that the next to leading order off-diagonal term is canceled. Hartree-Fock equations are derived incorporating the momentum structure of the underlying finite range interaction. For applications a density dependent effective interaction is determined from a G-matrix which is renormalized such that the saturation properties of symmetric nuclear matter are reproduced. Intending applications to systems far off stability special attention is paid to the low density regime and asymmetric nuclear matter. Results are compared to predictions obtained from Skyrme interactions. The ground state properties of stable nuclei are well reproduced without further adjustments of parameters. The potential of the approach is further exemplified in calculations for A=100. . .140 tin isotopes. Rather extended neutron skins are found beyond 130 Sn corresponding to solid layers of neutron matter surrounding a core of normal composition.21.60-n,21.60Jz,21.10.Dr

Pygmy dipole strength inZr90

“…H sp describes the motion of protons and neutrons in a static, spherically-symmetric mean field and H pair accounts for the monopole pairing between isospin-identical particles with phenomenologically adjusted coupling constants, fitted to data [34]. The mean-field hamiltonian compromises microscopic HFB effects [32,35] and phenomenological aspects like experimental separation energies and, when available, also charge and mass radii. For numerical convenience the mean-field potential is parametrized in terms of a superpositions of Wood-Saxon (WS) potentials with adjustable parameters [32].…”

Nuclear skin emergence in Skyrme deformed Hartree-Fock calculations

“…[17,18]) or the Hartree-Fock-Bogoliubov (HFB) method including pairing correlations [19][20][21][22][23][24]. The latter predicts well the monotonic increase of the neutron skin thickness for different chains of isotopes up to the drip line [19].…”

Probing nuclear skins and halos with elastic electron scattering

“…On the theoretical side the difference between the proton and neutron distributions can be obtained in the framework of Hartree-Fock (HF) method (see for example [8]) or HartreeFock-Bogoliubov (HFB) method (see for example [9,10]). As a rule of thumb, a theoretical calculation of the nuclear density is considered good when it reproduces the data on elastic electron scattering.…”