Towards a universal nuclear density functional

A new form of the nuclear energy-density functional for describing the ground-state properties of finite nuclei up to the drip lines and beyond is proposed. The volume part in this functional is fit to the Friedman-Pandharipande and Wiringa-Fiks-Fabrocini equation of state for the UV14 plus TNI model up to densities ρ≈1 fm−3 by a fractional expression in ρ which can be extended to higher densities while preserving causality. For inhomogeneous systems, a surface energy-density term is added, with two free parameters, which also has a fractional form like the Padé approximant containing (∇ρ)2 in both the numerator and denominator. In addition to the Coulomb direct and exchange interaction energy, an effective ρ-dependent Coulomb-nuclear correlation term is included with one more free parameter. A three-parameter fit to the masses and radii of real nuclei shows that the latter term gives a contribution to the Coulomb displacement energy of the same order of magnitude as the Nolen-Schiffer anomaly. The first self-consistent run with the proposed functional, performed for about 100 spherical nuclei, gives rms deviations from experiment of ≈1.2 MeV in the masses and ≈0.01 fm in the radii, which are about a factor of two better than those obtained with the Skyrme functionals or with the Gogny force. The extrapolation to the drip lines lies in between the ETFSI and the macroscopic-microscopic model predictions.

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