Kohn–Sham density functional inspired approach to nuclear binding

Abstract

A non-relativistic nuclear density functional theory is constructed, not as done most of the time, from an effective density dependent nucleon–nucleon force but directly introducing in the functional results from microscopic nuclear and neutron matter Bruckner G-matrix calculations at various densities. A purely phenomenological finite range part to account for surface properties is added. The striking result is that only four to five adjustable parameters, spin–orbit included, suffice to reproduce nuclear binding energies and radii with the same quality as obtained with the most performant effective forces. In this pilot work, for the pairing correlations, simply a density dependent zero range force is adopted from the literature. Possible future extensions of this approach are pointed out

Density dependence of the symmetry energy from neutron skin thickness in finite nuclei

“…7 we have included RMF models with non-linear meson couplings (these are the models with names starting by NL or PK, plus the models FSUGold, G1, G2, and TM1), meson-exchange models with density-dependent couplings (DD-ME and RHF-PK models), and finally, zero-range point-coupling models (DD-PC1, PC-PK1, and PC-PF1 models). The original references to these nuclear models can be found in the papers [20,30,33,81,82].…”

Density dependence of the nuclear symmetry energy from measurements of neutron radii in nuclei

“…The scattering problem has been solved in exact DWBA calculations for electrons that scatter from lead at an energy of 1.06 GeV and an angle of 5 • , which is close to the operating conditions of PREX. The sample of 47 nuclear models [34,37,19,71,72] used in Fig. 3 is representative of models of very different kind.…”

Remarks on the use of projected densities in the density-dependent part of Skyrme or Gogny functionals

“…Apart from some scarce versions of Skyrme, there is a recently proposed functional with this property, the Barcelona-Catania-Paris (BCP) functional [16,17] (see also an article in this issue by Baldo et al concerning this functional [27]) which is based on a fit to a realistic nuclear matter equation of state followed by a Local Density Approximation map to produce a functional for finite nuclei. Additional finite range surface terms, spin-orbit, Coulomb and density dependent pairing are ingredients of this functional.…”